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A survey of low-noise nucleonic amplifiers Heywood, Donald Robert 1963

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A SURVEY OP LOW-NOISE NUCLEONIC AMPLIFIERS  \  /  by  DONALD ROBERT HEYWOOD B.A.Sc., U n i v e r s i t y o f B r i t i s h  C o l u m b i a , 1961  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  I n t h e Department Electrical  We  accept  standards degree  this  thesis  of  Engineering  as c o n f o r m i n g t o t h e  r e q u i r e d from candidates  of Master of A p p l i e d  f o r the  Science  Members o f t h e Department of E l e c t r i c a l E n g i n e e r i n g The  U n i v e r s i t y of B r i t i s h AUGUST 1963  Columbia  lh presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study.  I further agree that permission  for extensive copying of this thesis for scholarly purposes may  be  granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of E l e c t r i c a l E n g i n e e r i n g The University of B r i t i s h Columbia, Vancouver 8, Canada. Date_  September 25,  1963  ABSTRACT  In n u c l e o n i c sources  must be  noise.  The  amplified with  and  theory  modern s o l i d - s t a t e  are  relating  characteristics  noise It  from c a p a c i t i v e  a d d i t i o n o f a minimum amount  i n t h i s were c o n s i d e r e d  of G i l l e s p i e  the  detectors  c h a r g e and  A relationship the  and  charge"  to  p r e a m p l i f i e r , and  noise  figure  of an  The Nuvistors, for  this  metric  theoretical and  field  a m p l i f i e r s and  tubes,  Nuvistors^  equiv-  amplifier.  study  shows t h a t c o n v e n t i o n a l transistors  are  Junction transistors, Masers are  shown t o be  the  best  tunnel  tubes,  active  devices  diodes,  measurements made on p r e a m p l i f i e r s b u i l t  and  field  effect  transistors  i s 20pf* t h e p r e a m p l i f i e r s e x h i b i t e d n o i s e 670  electronic  s u p e r i o r to other  transistor  good a c c u r a c y .  confirm  capacitance and  para-  unsuitable.  predictions with  360  noise  vacuum  theoretical  310,  pulse-  db.  effect  application.  Experimental  1  the  the  shows t h a t a m p l i f i e r s s u i t a b l e f o r n u c l e o n i c work have  f i g u r e s much l o w e r t h a n  is  Expressions  i s d e r i v e d between the  conventional  When t h e  charges r e s p e c t i v e l y .  tubes c u r r e n t l y used, w h i l e  i s , at present^  ion  systems  amplifiers.  "equivalent input noise  o f t h e d e t e c t o r , the  network.  of  both  f o r systems u s i n g  tube a m p l i f i e r s i s g e n e r a l i z e d to i n c l u d e  u s i n g the  shaping  pulses  experimentally.  "classical"  chambers and  found  the  problems encountered  theoretically The  energy d e t e r m i n a t i o n s ,  the  best  solid-state  the detector  The  the  with  charges  E810F t u b e  field  device*  of  effect  ACKNOWLEDGEMENT  The grant  p r o j e c t was c a r r i e d  to the E l e c t r i c a l  of Canada L i m i t e d g r a n t these  general  studentship  out under a N a t i o n a l R e s e a r c h  Engineering  D e p a r t m e n t , and an A t o m i c  t o the P h y s i c s Department.  g r a n t s , the author  was a r e c i p i e n t  f o r t h e 1962—63 u n i v e r s i t y  gratefully The  staff  In addition to  o f an NRC  This f i n a n c i a l  assistance  acknowledged.  author  and g r a d u a t e  Engineering  Energy  t e r m and a UBC G r a d u a t e  S t u d e n t S c h o l a r s h i p f o r t h e 1961-62 t e r m . is  Council  i s also indepted student  departments*  t o many member o f t h e f a c u l t y ,  body o f b o t h  the P h y s i c s  P a r t i c u l a r l y h e l p f u l were  F . K. Bowers o f t h e E l e c t r i c a l  Engineering  Dr.  B. L . White  the  p r o j e c t through to completion  and E l e c t r i c a l Professor  D e p a r t m e n t and  o f t h e P h y s i c s D e p a r t m e n t whose p a t i e n c e  xii  was a p p a r e n t l y  i n seeing  unbounded.  TABLE OF CONTENTS Page ABSTRACT  i i  L I S T OF ILLUSTRATIONS  v i i  L I S T OF TABLES  xi  ACKNOWLEDGEMENT ......**•>................. 1.  x i i  INTRODUCTION  .....  1.1  Thesis Outline  1*2  " T y p i c a l " Nucleonic 1.2.1 1.2.2  1*3  The S i g n a l Detectors  3 C o u n t i n g System  ...........  5  The O u t p u t S p e c t r u m  Methods o f C o u p l i n g  ....................  2.  8  the D e t e c t o r to the •••  1.3.1  The P a s s i v e  1.3.2 1.3.3  The " B e s t " P a s s i v e C o u p l i n g Network .... C o u p l i n g w i t h ant I d e a l T r a n s f o r m e r •  C o u p l i n g Network . . . . . . . . . . .  C o m p a r i s o n o f Charge Sensitive  4  P r o d u c e d by P a r t i c l e  Amplifier  1.4  1  Sensitive  10 11 12 13  and V o l t a g e  Configurations  14  1.4.1  C l o s e d Loop G a i n  15  1.4.2  System C a l i b r a t i o n  1.4.3  Stability  1.4.4  Input D r i f t  1.4.5  Noise i n Feedback A m p l i f i e r s  .....................  16 17  a t H i g h Count R a t e s . . . . . . . .  19  ...........  20  SIGNAL, NOISE AND THE FREQUENCY RESPONSE ........... 2.1 The E f f e c t o f t h e F r e q u e n c y Response on N u c l e o n i c S i g n a l s .............................  23  2.2  27  Noise i n the Nucleonic 2.2.1  System  G e n e r a l N o i s e Model System iii  23  f o r the Nucleonic 27  Page 2.2.2 2*3  The  Effect  o f F r e q u e n c y Response  "Equivalent  2.3.1  on N o i s e •*  Input Noise Charge"  Definition  33  of the E q u i v a l e n t Input  N o i s e Charge 2.3.2  Equations  2.3.3  Calculation  33  f o r t h e N o i s e Charge o f N o i s e Charge  .........  3.  39  The N o i s e F i g u r e  42  2.4.1  The N o i s e F i g u r e  of a N u c l e o n i c  2.4.2  The R e l a t i o n s h i p Between N and F  System  3.2  N o i s e i n Tubes  .  .... .  and N u v i s t o r s  42 44  NOISE SOURCES IN ACTIVE DEVICES 3.1  36  of a  Feedback A m p l i f i e r 2.4  31  ...  48 48  3.1.1  S h o t N o i s e i n Tubes  3.1.2  G r i d Leakage N o i s e  50  3.1.3  Flicker  51  3.1.4  P a r t i t i o n Noise i n M u l t i g r i d  Equivalent Field  ..... •  Noise  Circuit  Effect  and N u v i s t o r s  and N o i s e Model  Transistor  Tubes  .....  49  52  f o r the ..  52  3.2.1  Theory of F . e . t . O p e r a t i o n  54  3.2.2  F.e.t. Equivalent  57  3.2.3  N o i s e Model  3.2.4  Channel Noise i n F . e . t .  3.2.5  Gate N o i s e i n F . e . t .  Circuit  of F.e.t.  3.3  N o i s e Model  3.4  Modern " E x o t i c " Low-Noise  ..............*•..  59  ................  60  ...................  62  for Junction Transistors  ..........  64  ..........  68  .......................  68  Amplifiers  3.4.1  The T u n n e l D i o d e  3.4.2  Parametric Amplifiers iv  and M a s e r s  .».*.*•  69  Page  3.5  Summary o f T h e o r e t i c a l 3.5.1  Choice  Results  ..............  o f Tube, N u v i s t o r  and F . e . t .  Type s 3.5.2 4.  «  Comparison of Noise Performance  71 73  MEASUREMENTS OF NOISE PARAMETERS  75  4.1  75  4.2  4.3  5.  71  Tube and N u v i s t o r P a r a m e t e r s 4.1.1  Grid  C u r r e n t Measurement  Techniques  4.1.2  Grid  C u r r e n t Measurement  Results  4.1.3  R  4.1.4  R  and K Measurement  Technique  75  .....  76  .......  and K Measurement R e s u l t s  Measurement  of F . e . t . Parameters  ............  F.e.t. Static  4.2.2  F . e . t . Gate Leakage Measurements  4.2.3  F . e . t . N o i s e R e s i s t o r Measurements  Characteristics  ........  Choice  of Bias Points  4.3.2  Calculated Charge  88  ....  94  ................  94  C u r v e s f o r Minimum N o i s e 98  DESIGN AND PERFORMANCE  E810F Charge S e n s i t i v e  ...... ....  Preamplifier  ..  E810F V o l t a g e  5.1.3  Nuvistor  5.1.4  F.e.t. Preamplifier  5.1.5  C o n s t r u c t i o n T e c h n i q u e s f o r Low-Noise Preamplifiers  Measurement  5.3  Results  Sensitive  102  5.1.2  5.2  86  90  D e s i g n and C o n s t r u c t i o n o f P r e a m p l i f i e r s .5.1.1  86  ...  Summary o f E x p e r i m e n t a l N o i s e P a r a m e t e r s 4.3.1  77 81  4.2.1  PREAMPLIFIER 5.1  n  ..  Preamplifier..  Test A m p l i f i e r  of P r e a m p l i f i e r  104 106 107 109  Noise Performance  o f N o i s e Charge Measurements v  104  I l l 113 115  Page 6.  CONCLUSIONS  .......  124  APPENDIX I  EVALUATION OP INTEGRALS USED IN THEORY .  128  APPENDIX I I  F.E.T. ADMITTANCE  131  APPENDIX I I I  DERIVATION OF PREAMPLIFIER GAIN  PARAMETERS  EXPRESSIONS APPENDIX IV  140  SUBSIDIARY ELECTRONIC EQUIPMENT  REFERENCES  ..... ...  144 148  vi  LIST  OP  ILLUSTRATIONS  Figure Chapter  Page 1  1.1  Typical  1.2  The  Nucleonic Counting  P a r t i c l e Detector  (b)  (a)  as a Charge S o u r c e  1.3  Nucleonic Voltage Signal  1.4  Pulse Amplitude (b)  Noisy  System  as a C u r r e n t  5  Source  ......................  7 8  S p e c t r a (a)  Noise  Free  . . . . . . . . . . . o . . . . . . ...«««««......... . . .  1.5  Matching  1.6 1.7  Improvement i n S i g n a l L e v e l (a) V o l t a g e S e n s i t i v e A m p l i f i e r Sensitive Amplifier  Chapter  ............  Detector to A m p l i f i e r  ...............  9 11 13  (b)  Charge 15  2  2.1  S t e p Response o f P u l s e S h a p i n g  Network .......  26  2.2  Peak Response o f P u l s e S h a p i n g  Network  26  2.3  General Noise Models Model  (b)  Two  (a)  Generator  Single  .......  Generator  N o i s e Model  .........  2.4  D e t a i l e d N o i s e Model o f N u c l e o n i c System  2.5  Effect  2.6  C o r r e c t i o n F a c t o r f o r High Frequency  o f T^  .....  on N o i s e V o l t a g e Components  28 32  Effects  on N  37  2.7  F e e d b a c k Loops o f T y p i c a l  2.8  N o i s e Model f o r R e s i s t i v e l y  Preamplifier  39  Terminated  A m p l i f i er . . . .<>*•** . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter  27  44  3  3.1  T r i o d e Noise Model'...  3.2  Typical  3.3  F . e . t . Schematic  49  G r i d C u r r e n t v s G r i d V o l t a g e Curve (a) (b)  ...  51  Nonpinch-off Operation . Pinch-off Operation *  54 55  vii  Page 3.4  Typical  3.5  F . e . t . E q u i v a l e n t C i r c u i t s (a) B a s i c E q u i v a l e n t C i r c u i t (b) S i m p l i f i e d E q u i v a l e n t C i r c u i t . . • » . . « • . •  58  T r a n s i s t o r N o i s e M o d e l s (a) B a s i c N o i s e Model (b) Common E m i t t e r N o i s e Model f o r Loop A n a l y s i s ...  64 65  3.6  Static  Characteristics  of F.e.t.  56  Chapter 4 4.1  G r i d Current  4.2  Typical  4.3  G r i d Leakage  4.4  G r i d Leakage  4.5  Resistive  4.6  E q u i v a l e n t N o i s e R e s i s t o r f o r t h e E810F  4.7  E q u i v a l e n t N o i s e R e s i s t o r f o r t h e 7586 N u v i s t o r  4.8  (a) S t a t i c C h a r a c t e r i s t i c s f o r F . e . t . #1 C h a r a c t e r i s t i c s o f F . e . t . #2  4.9  Test C i r c u i t  Grid Current  76  C u r v e s f o r E810F  77  Current  f o r ,E810F Tube  78  Current  f o r 758.6 N u v i s t o r  ................. ..............  S u b s t i t u t i o n T e s t System  Gate Leakage  Test C i r c u i t  78 79  Tube  ........  (b)  .....  85 85  Static 87 88  . . . . a . . . . . . . . . . . . . . . . . . . . ? .  4.10 (a) Gate Leakage C u r r e n t f o r F . e . t . #1 (b) Gate Leakage C u r r e n t f o r F . e . t . #2 •.............*....«•*•••..*••«  89  4.11 F . e . t . R e s i s t i v e  ,......«««  92  (a) '. E q u i v a l e n t N o i s e R e s i s t o r f o r F . e . t . #1 (b) E q u i v a l e n t N o i s e R e s i s t o r f o r F . e . t . #2 . . . . . . . . . . . . .  93  4.12  S u b s t i t u t i o n Test C i r c u i t  4.13 B i a s P o i n t f o r Minimum N o i s e  95  4.14 N  . v s t (a) l n a D e t e c t o r Leakage C u r r e n t (b) l O n a mm D e t e c t o r Leakage C u r r e n t . . ........ . . . . . . . . . . . » <>> .*> . &  4.15 N . T S C, ( a ) l n a D e t e c t o r Leakage mm d D e t e c t o r Leakage C u r r e n t  C u r r e n t (b) l O n a . ...... ..••..«•«  &  Chapter  5  w  5.1  E810F  Charge  5.2  E810F V o l t a g e  5.3  Nuvistor Test P r e a m p l i f i e r  5.4  F.e.t. Preamplifier  99  100  „ ..•  Sensitive Preamplifier  103  S e n s i t i v e P r e a m p l i f i e r .*.«.«.*•*...**•• •  107 108 110  viii  Ijage 5.5  I n p u t Tube Shield  Shields  (a)  S h i e l d Used  N o i s e Charge M e a s u r i n g System  5.7  (a) (b) (a) (b)  5.8 5.9  vs vs vs vs  X C X C  d  d  f o r E810P f o r E810F f o r E810F f o r E810P  N vs X  ..............*.......••  Charge S e n s i t i v e P r e a m p l i f i e r Charge S e n s i t i v e P r e a m p l i f i e r * Voltage Sensitive Preamplifier Voltage Sensitive Preamplifier  (a) N v s X f o r Nuvistor for F.e.t* Preamplifier  5.10 ( a )  Recommended  .a***..****.*..................*......*...••o »•  5.6  N N N N  (b)  P r e a m p l i f i e r (b) N v s C^ ................••»....*.  f o r F.e.t. Preamplifier  (b)  N vs C  for F.e.t* Preamplifier  112 113  116 117 118  fl  ...*....  119  APPENDIX I I 11.1  J i g t o Measure T  f  of F.e.t.  11.2  J i g t o Measure T  r  of F.e.t.  11*3 11.4  132 ........  133  (a) (b)  J i g t o Measure Y^ o f F . e . t . D i r e c t l y •••*•••••• J i g t o Measure Y.^ o f F . e . t . I n d i r e c t l y * * * • * « « *  133 134  (a)  J i g t o Measure Y  Q  of F.e.t.  (b)  J i g t o Measure Y  q  of F.e.t. I n d i r e c t l y  11.5  (a)  Y  (b)  11.6  (a)  C  11.7  (a)  C  for 11.8  F  d g  ±  o f F . e . t * #1 o f F . e * t . #1 = C  g g  + C  g d  Y  (b)  F  C  Directly  o f F . e . t . #2 d g  *•****-**.  .....**... ' 136  o f F . e . t . #2  f o r F . e . t . #1  (b)  C  i  = C  137 g g  +  C  g d  F . e * t . #2 *  (a)  Y  q  o f F * e * t * #1  135  138 (b)  Y  q  o f F . e . t . #2  .....*.*...  139  APPENDIX I I I III.l  (a)  B o o t s t r a p p e d Cascode  (b)  111*2 III.3  Simplified Equivalent C i r c u i t (a) F . e * t * — j u n c t i o n T r a n s i s t o r f i e d C i r c u i t •••*... •  Equivalent  Circuit  **.'. 140 140  C i r c u i t (b) S i m p l i ......•.••.•••*••  142  APPENDIX IV IV*1  Tube P o s t - a m p l i f i e r  146  ix  Page IV»2  T r a n s i s t o r P o s t — a m p l i f i e r ««<.«»««.•«.*..<>.<*•••»••  146  IV»3  D—c  147  IV*4  R i p p l e and O u t p u t V o l t a g e  Filament  Supply  «.**••««•«•«•••*••«<>«•**••««•« o f D-c  x  Filament  Supply  *  •  147  L I S T OP  TABLES Page  3.1  Theoretical  Noise Parameters  3.2  Theoretical  Comparison  4.1  D a t a f o r E810P R  4.2  72  of Noise Parameters  ......  Calculation n C a l c u l a t i o n o f R" f o r E810P  73 82 84  n 4.3  P.e.t. Noise Resistors  4.4  C o l l e c t e d N o i s e D a t a f o r t h e Optimum B i a s f o r t h e E810P Tube C o l l e c t e d N o i s e D a t a f o r t h e Optimum B i a s  4.5  ..........................  92  Points 96 Points  f o r t h e 7586 N u v i s t o r  97  5.1  Meter H i g h F r e q u e n c y C o r r e c t i o n s  5.2 5.3  C a l c u l a t i o n o f N f o r E810F P r e a m p l i f i e r ( C Data f o r C a l c u l a t i o n of N f o r P r e a m p l i f i e r s  xi  ................ d  = lOpf) .....  115 120 121  1.  Nuclear the  or  r e a c t i o n s a r e g e n e r a l l y s t u d i e d by m e a s u r i n g  energy d i s t r i b u t i o n  particles,  INTRODUCTION  of t h e i r  produc t s . ^ * ^  t h e most common t e c h n i q u e  solid-state  detectors to convert  When the. c o n v e r s i o n  i s linear,  utilizes  F o r charged  ionization  the energy i n t o  chambers  charge.  t h e e n e r g y s p e c t r u m becomes a  pulse  height  s p e c t r u m and c a n be measured e l e c t r o n i c a l l y w i t h a  pulse  height  analyzer  or " k i c k s o r t e r " .  Many e x p e r i m e n t s have e n e r g y s p e c t r a w i t h peaks.  Often  because  they  and  spaced  t h e peaks a r e n o t r e s o l v e d by t h e k i c k s o r t e r a r e b r o a d e n e d by f l u c t u a t i o n s i n t h e d e t e c t o r  by n o i s e  these  closely  i n the e l e c t r o n i c  equipment.  f a c t o r s may be t h e dominant  At present,  cause o f b r o a d e n i n g  yield  e i t h e r of ina  (12) given  experiment.  * '  reduction i n either Therefore  constant  However, t h e y  one r e s u l t s efforts  a r e a d d i t i v e , and a  i n an improvement .in r e s o l u t i o n . s  are being  made t o improve  both  d e t e c t o r s and a m p l i f i e r s . The  nucieonic a m p l i f i c a t i o n (13) w i t h t u b e s was p r e s e n t e d i n 1953 by G i l l e s p i e . " ' Since then, many new e l e c t r o n i c d e v i c e s have been d e v e l o p e d t h a t a p p e a r (1 4-Y promising  general  theory  of low-noise  f o r n u c l e o n i c work.  Studies  of N u v i s t o r s V  *  , and  j u n c t i o n t r a n s i s t o r s ^ * ^ \ have b e e n made, b u t as y e t no comprehensive of G i l l e s p i e was c a r r i e d project  survey  has b e e n r e p o r t e d  to include a l l devices. out by the author  i n cooperation with  t h a t g e n e r a l i z e d t h e work For this  as an e l e c t r i c a l  the n u c l e a r  physics  reason,  a  study  engineering g r o u p o f t h e UBC  Physics  department.  amplifiers,  the  t h e r e s o l u t i o n now  r e s o l u t i o n was  reported  i n manufacturers'  represented  by a n o i s e model s i m i l a r  and  provides  c a n t h e n be a p p l i e d w i t h  results  conventional  tubes or t h e i r  will  figure Secondly,  f i g u r e s was  slight  modification  as good r e s o l u t i o n as a  However, i n s i t u a t i o n s where t h e s i z e o f  showed t h a t N u v i s t o r s the b e s t d e v i c e s  and f i e l d  make them u n s u i t a b l e , effect  transistors  theory  (f.e.t. s) 1  available.  were b u i l t  and f . e . t .  with  the "best" a v a i l a b l e tube,  respectively.  p r e d i c t e d by t h e t h e o r y .  Their noise  The 7586 N u v i s t o r s  u s e d f o r some t i m e i n n u c l e o n i c . a m p l i f i e r s , t u b e s and 2N2386 f . e . t . ' s were  l e v e l s were as  s t u d i e d have b e e n b u t t h e E810F (7788)  studied i n detail  f o r the f i r s t  time.  " I t was  of any d e v i c e was  prepared  found  t h a t t h e E810F g i v e s t h e l o w e s t  currently available. by t h e a u t h o r  Instruments.  '  noise  levels  A note r e p o r t i n g t h i s  result  and D r . B.L. White o f t h e P h y s i c s  Department and has b e e n a c c e p t e d Scientific  The  comparison.  give  power r e q u i r e m e n t s  Amplifiers  Firstly  i t was p o s s i b l e t o p r e d i c t t h a t none  surveyed  tube.  suggest  to t h a t used f o r tubes.  a s e c o n d , more a c c u r a t e  of t h e new d e v i c e s  Nuvistor,  t o the' n o i s e  s u i t a b l e from r e p o r t e d n o i s e  of G i l l e s p i e  From t h e s e  are  r e s o l u t i o n , and t o  specifications.  deemed  a l l possible  obtainable.  related  each d e v i c e  theory  to survey  methods were d e r i v e d t o compare d e v i c e s .  nucleonic  commonly  intended  t o compare t h e i r n u c l e o n i c  ways o f i m p r o v i n g Two  The s t u d y was  f o r p u b l i c a t i o n i n t h e Review o f  '  The  theory,  i n more d e t a i l  than  a modern t e x t on that  the  experimental i s usual  low-noise  thesis will  methods and  results  are  i n a t h e s i s b e c a u s e o f the  nucleonic  help to f i l l  techniques.  reported l a c k of  I t i s hoped  this void for nuclear  physics  students.  1.1  Thesis  The reported  i n v e s t i g a t i o n of n o i s e  i n the  C h a p t e r 1, is  Outline  f o l l o w i n g sequence.  a "typical"  intended  counting  p r i m a r i l y as an  proportional  counting*  but  instance,  i t i s shown t h a t t h e  can be  carried  type  out w i t h  the r e m a i n d e r  system i s d i s c u s s e d .  i t also serves  preliminary results  for this  For  needed i n the use  "general" nucleonic  system i s i n t r o d u c e d on b o t h  signal  judging  nucleonic  is  then  d e f i n e d and  of  the  signal  and  and  and  noise  The  effect  expressions  The  r e l a t i o n s h i p to the  noise  For  noise  analysis  removed. c o n s i d e r a t i o n s of  frequency  figure  To  from the  provide  the  response  basic c r i t e r i a  f o r i t found  for  charge", results  a link  with  i s d i s c u s s e d and i t s  eharge f o u n d .  i t i s p o s s i b l e t o narrow the  some  analysis*  "equivalent noise  noise .derivations. noise  noise  of  g e n e r a l n o i s e model of of the  i s found.  a m p l i f i e r s , the  c o m m u n i c a t i o n s work* t h e  found  the  techniques  t h a t the  feedback loops  system.  This section  of m a t c h i n g n e t w o r k s i s  of s y s t e m , and  any  of  to i n t r o d u c e  Chapter 2 i s devoted to t h e o r e t i c a l the  systems i s  i n t r o d u c t i o n to the  important  impractical  i n nucleonic  field  From t h e  relationship  of p o s s i b l e a m p l i f i e r s  before  detailed  d i s c u s s i o n s of i n d i v i d u a l  I n C h a p t e r 3, transistor found than  theoretically* the  also given  application.  of the  The  others because  theoretical  i n tunnel  by  the  5 gives  f r o m the  noise  i n section  theoretical  be  the  are  detail A  brief  amplifiers  suitable for results  this of  the r e l a t i v e  the  the merit  noise  devices  and  With the  a i d of  and  these a more  given. four preamplifiers  measurements o f the  charge of the  models  i n Chapter 4  described  a d e s c r i p t i o n of t h e  preceding  p r e a m p l i f i e r s was  i n s e c t i o n 5.2,  with  the  determined  results  5*3. the  final  and  experimental  " T y p i c a l " Nucleonic  The  i n more  o f b i a s p o i n t i s d i s c u s s e d and  theory  I n C h a p t e r 6,  1.2  2N2386 a r e  methods d e s c r i b e d  reported  g e n e r a l model,  methods f o r f i n d i n g  parameters g i v e n .  choice  t o c h e c k the The  junction  parametric  summarized and  comparison of the  chapters.  given.  predicted.  experimental  p a r a m e t e r s , the  built  of the  not  are  unfamiliar.  and  chapter,  end  d i s c u s s i o n are  Chapter  diodes  At  the  and  i s considered  are  measured n o i s e  detailed  f.e.t.  i t is relatively  o f the E810P, 7586, and the  f.e.t.  showing t h a t t h e y  devices The  Nuvistor,  n o i s e m o d e l s , c o n f o r m i n g t o the  d i s c u s s i o n of n o i s e is  tube,  devices  chapter,  Counting  problems encountered  e x p l a i n e d most e a s i l y by  the  conclusions  work are  drawn  summarized  briefly.  System  i n measuring energy s p e c t r a  c o n s i d e r i n g the  "typical"  can  counting  5 s y s t e m shown i n F i g .  1.1,  cxr, ^ , ions |—.  Detector  \  Preamplifier  Fig.  The  1.1  T  T  Amplifier \ Kicksorter Pulse Shaping • X-X Plotter Network  Post  T y p i c a l Nucleonic  d e t e c t o r produces a s i g n a l ,  Counting  System  p r o p o r t i o n a l to  the  e n e r g y o f e a c h i n c i d e n t p a r t i c l e , w h i c h i s a m p l i f i e d by w i d e - b a n d p r e a m p l i f i e r and frequency Fig.  1.1  response by  the  "pulse  the  output  the  shaped p u l s e s  are  sorted into  according  of t h e  enter  finished.  The  "read  out" with  other  output  1.2.1  The  shaping  the p u l s e  amplitude*  an  and  the  height  a n a l y z e r where  (typically  In each channel total  100 the  stored u n t i l  they  or  256)  pulses the  i n t h i s way  t y p e w r i t e r , an X-T  is  are  experiment then  recorder,  or some  device.  S i g n a l P r o d u c e d by P a r t i c l e  Until  in  From t h e p o s t - a m p l i f i e r ,  energy spectrum found electric  The  n e t V p r k " ) i s c h o s e n t o maximize  a number of c h a n n e l s  to t h e i r  post-amplifier.  post-amplifier (represented  signal-to-noise ratio.  counted e l e c t r o n i c a l l y is  f e d t o the  the  Detectors  r e c e n t l y * t h e most commonly u s e d p a r t i c l e  detector  was  the  ionization  energy c r e a t i n g electron-volt  (1.6)  ion pairs  per  been l a r g e l y  chamber  i n gas  ion pair.  r e p l a c e d by  i n w h i c h the at  Now,  the  the  particle  average  however, the  rate ion  v a r i o u s t y p e s of  loses  of  30  chamber  has  solid-state,  (17) detectors, by  the  • In  creation  average larger  *  of  e n e r g y of  solid-state  hole—electron pairs. o n l y 3*5  c h a r g e and  of  traverse  the  the  During t h i s that as  on  detector  be  time  collected  t i m e s on  charge  chambers of  t h a n 10  i n the  carried  account f o r  risY  the  o r d e r of  In  the  arrive out  the  * '  solid-state  instantaneously. c h a r g e does n o t  the  " c o l l e c t i o n time"  i n the  external  i ( t ) f l o w s f r o m the the  detector  to  circuit*  detector,  so  i s a current  source  large  dimensions, T  may  as  Since  the  c a s e of  the  can  i f i t d o e s , and rise  output p u l s e s  time,  be  assumed t o  ionization  i n s t a n t a n e o u s l y , but  finite  i t is  m i c r o s e c o n d s f o r minimum  detector  chamber,  noise  a correction  (see  be  usually noise, arrive the  calculations made l a t e r  G i l l e s p i e ^ f o r  a  v  calculation detectors internal resistance  of  can  correction be  the  factors).  r e p r e s e n t e d as  capacitance of  a  resolution.  a finite  scale  an  detectors give  microseconds, while f o r semiconductor d e t e c t o r s ( l 8)  have r i s e  be  Since t h i s r e q u i r e s  d e t e c t o r s , the .charges c r e a t e d by  and  ionization  less  can  i s produced  1.2(a).  generally  the  signal  soli,drstate  superior  time, a current  shown i n F i g .  several  the  p a r t i c l e require  a microscopic  For  ev,  therefore  With both types of passage  d e t e c t o r s , the  C^  source  as  For  a source  shown i n F i g .  can  be  this of  thesis  then,  charge Q w i t h  1.2(b).  n e g l e c t e d because  The  the an  internal  i t will  be  to  7 much l a r g e r t h a n  the  impedance  of  at a l l frequencies  interest.  of  • .  i(t)  (a)  as  a current  source  Pig*  The amplitude  voltage Q/(C^  preamplifier. of t h e  1.2  generated  + C\) It will  by  where C\ be  (b)  The  the  shown l a t e r  2.2.1) so t h a t t h e v o l t a g e  several  particles  as  p u l s e s by This  the  output  of the  then g  The  Detector  charge  i s a step  input capacitance t h a t the  step decays  are  of  resistive  the  portion  When  input  differentiated  of  (see  slowly.  i n s u c c e s s i o n , the steps  source  voltage into  l i m i t e d - f r e q u e n c y p a s s band of t h e p o s t - a m p l i f i e r .  reduces t h e i r  response  •7JQ—+  are d e t e c t e d  shown i n P i g . 1.3.  Particle  l a r g e f o r minimum n o i s e  section  is  a charge  signal  i s the  i n p u t impedance must be  as  amplitude  pulse  shaping  each p a r t i c l e  ) x A-jA2S.  by  (A-^,, A  a factor  network to a u n i t  i s represented  2  S, where S i s t h e  are  the  by  step.  a pulse  of  amplifier voltage  At  peak the  amplitude gains).  8 Input Volts (Arbitrary scale)  Time (Arbitrary units) P i g . 1.3  1.2.-2  The  If with two  the  "typical"  system r e s u l t s  output  1.4(a) i n t h e  i n an  conducted  energy spectrum  f r o m t h e k i c k s o r t e r would l o o k The  peaks a r e  a r e b r o a d e n e d o n l y by  incident  p o i n t i n the  experiment being  absence of n o i s e .  since they  e n e r g y of the any  Signal  1  i t i s assumed t h a t the  separated  Voltage  Output S p e c t r u m  peaks, the  Pig.  Nucleonic  particles.  like well  "straggling"  When n o i s e  system, i t modulates the p u l s e  amplitude  Therefore  p u l s e s from monoenergetic p a r t i c l e s  a Gaussian  amplitude  d i s t r i b u t i o n with  to the  rms  n o i s e n*^*"''^  The  curves  slightly t o the  the  must be  shape o f t h e  w i t h which t h i s and  and  effect  c a n be  peaks b r o a d e n *  separated  total  by  spectrum.  done d i m i n i s h e s  acquire  a standard d e v i a t i o n of n o i s e  " / t y p i c a l " e x p e r i m e n t i s shown i n F i g . 1 . 4 ( b ) . overlap  i n the  i s introduced at  randomly.  equal  with  The  fitting  on  peaks two  W i t h the b e s t d e t e c t o r s and  now  Gaussian  C l e a r l y the  as the n o i s e  the  accuracy  increases amplifiers  9  No. of Counts  No. of Counts  (a)  Noise  — ^ _  Kicksorter Channel  Free  (b)  Fig.  it  :  — ^  Kicksorter Channel  i s currently possible  1.4  Pulse  to obtain  Amplitude  spectral line  Noisy  Spectra  widths  (1.2) equivalent  t o about  5 kev of p a r t i c l e  Compared t o t h e t y p i c a l of k e v , t h i s  From t h i s work, n o i s e are  particle  i s small, but i t s t i l l  of many e x p e r i m e n t s  obtained  i t i s evident  The than simply  This  contrasts  enables pulses  pulses  ratios  of nearly  communications  signal-to-noise  t o be d i s t i n g u i s h e d f r o m of the pulses  p r e s e n c e a l s o means t h a t  have e x t e m e l y good g a i n  i n nucleonic  signal-to-noise  with binary  dependence upon t h e h e i g h t their  that  o f t h e need t o r e s o l v e  systems s u c h as PCM where an a d e q u a t e one t h a t  o f hundreds  severely.  discussion*  because  energies  r e s t r i c t s the accuracy  i s a p r o b l e m even when l a r g e  equal amplitude.  is  energy.  ratio  spaces. rather  t h e a m p l i f i e r s must  s t a b i l i t y because a s h i f t i n g a i n  during  a long  experiment broadens  does.  Stability  f e e d b a c k around  spectral  i s generally  a l l amplifiers.  spectrum  spectrum  of P i g *  found.  This  and  To f i n d  generally  spectral simpler  line  the  location  peak.  calibration  the  An  be  particles  at the i n p u t  of  and  alternative,  i s performed w i t h p u l s e s of I f the d e t e c t o r  yield  peak f r o m t h e p u l s e g e n e r a t o r r e p r e s e n t s  o f a known e n e r g y  Besides giving  Mev)  i n the o u t p u t .  calibration  known, the s p e c t r a l  types  energy  introducing  a l p h a s of 5.3  known c h a r g e f r o m a p u l s e g e n e r a t o r . is  the two  c a l i b r a t i o n f o r t h e s y s t e m must  (e.g. Polonium  their  1.4,  the a b s o l u t e energy  i s done most a c c u r a t e l y by  known e n e r g y locating  In s e c t i o n  1.4(b) i s t h e r e l a t i v e  energy  noise  compared.  f o r the experiment.  output v o l t a g e / i n p u t  i n much t h e way  a c h i e v e d by a p p l y i n g n e g a t i v e  of f e e d b a c k commonly u s e d a r e The  lines  and  t h u s s e r v e s as a  the a b s o l u t e energy  c a n be u s e d  as a c h e c k  calibration  o f the p e a k s ,  on the l o n g - t e r m  the  stability  of the system w i t h r e s p e c t t o changes i n the d e t e c t o r  or  amplifiers. With t h i s experiment,  the b a s i c  To  summarize:  is  t o be  noise. its  description  a m p l i f i e d w i t h the a d d i t i o n The  of a  n a t u r e of the problem  an i n s t a n t a n e o u s c h a r g e  "typical"  has b e e n  defined.  from a c a p a c i t i v e  source  o f a minimum amount o f  shape o f t h e o u t p u t , p u l s e i s n o t i m p o r t a n t , o n l y  signal-to-noise  highly  1.3  rather brief  ratio  stable with respect  i s . F u r t h e r , the a m p l i f i e r s to g a i n  must be  drifts.  Methods o f C o u p l i n g t h e D e t e c t o r t o the  C o u p l i n g the d e t e c t o r d i r e c t l y  Amplifier  t o the a m p l i f i e r  resulted  in  i(t),  this voltage  where B i s the by  Q/CC^  a signal V = i ( t ) * Z ^  "tuning  larger  decrease Can  the  the  a similar  combination  source  s i g n a l would not  r e s p e c t t o the  detector  effect  and  o f B^  the  of n o i s e  and  arising  obtained  an a p p r o p r i a t e  n o i s e , but  later  1*5),  (see P i g . The  signal-to-noise ratio  or i n p u t c i r c u i t  signal,  increased toV=i(t)*B,  amplifier capacitances.  affect  i n c r e a s e be  s i g n a l s by u s i n g  ¥ i t h a narrow-band  c o u l d , i n p r i n c i p l e , be  parallel  out"  + C^).  i n the  with  i t would  system.  for impulsive,  hucleonic  coupling technique?  It will  be  shown t h a t some improvement i s t h e o r e t i c a l l y p o s s i b l e , b u t energy c o n s e r v a t i o n prevents  the  signal  from b e i n g  as  large  as  i(t)R.  1  I  1  Detector Fig.  1.3.1  The. P a s s i v e  Consider the to  a m p l i f i e r by "tune" C  d  and  detector results  the  1.5*  O-  o  O- — — U — — — — 1  Coupling Network Matching Detector  Coupling  Fig*  C^  1*5  O  Amplifier to A m p l i f i e r  Network  w h i c h shows the  p a s s i v e n e t w o r k N. I f N does t h i s ,  i n a voltage  detector coupled The  f u n c t i o n of N i s  a signal  l a r g e r than  Q/C,  to  i ( t ) from across  C,  the  indicating detector  that  charge  detector y i e l d , passive pulse  now s t o r e s a c h a r g e l a r g e r than^g. is strictly  l i m i t e d by t h e p a r t i c l e  t h e e x t r a c h a r g e must have been  network.  The s i g n a l i s o f one p o l a r i t y  can supply  charge t o the e x t e r n a l  e n e r g y and  s u p p l i e d by t h e only  r e q u i r e s a d d i t i o n a l charge from the network.  network  Since the  circuit  so e a c h But a passive  only  on a  r e c i p r o c a t i n g b a s i s : o t h e r w i s e i t i s a c t i n g as an e n e r g y Therefore  t h e network  c a n n o t be  An a c t i v e n e t w o r k shown t h a t i t w o u l d increased  built.  coulu*"tune"  increase  source*  the noise  C, and C. , b u t i t c a n be a xn at least  as much as i t  t h e s i g n a l so t h a t no n e t improvement would be  achieved*  1.3.2  The " B e s t "  Passive  Even though drastic  improvement  Coupling  a passive  Network  c o u p l i n g network  i n signal level  i t c a n cause  ment b y t r a n s f e r r i n g a l l t h e e n e r g y i n i t i a l l y t o C^ a t some l a t e r is  time*  If this  cannot give a some  improve—  s t o r e d on C^  i s done, t h e e n e r g y on C^  g i v e n by E . .  ...(1.1)  S o l v i n g f o r Q. and t h e i n p u t v o l t a g e V. u n d e r  this  condition gives  *..(1.2)  13 The  improvement  Q/(C^ + C^) coupling  i s p l o t t e d i n P i g . 1.6  gives  a worthwhile  a delay  line  between  capacitors  henries,  i n V. r e l a t i v e  with  impedance  with  Improvement  an I d e a l  i n Signal  o f 2000  when C^ = C^, i n d i c a t i n g t h a t when d i r e c t "matched" c o n d i t i o n i s t h e b e s t . f o r maximum i n s t a n t a n e o u s the d e t e c t o r  It i s  f  coupling i n fact,  i s least i s used the the c o n d i t i o n  e n e r g y t r a n s f e r f r o m C^ t o C.*  to the a m p l i f i e r with  c o n d i t i o n c a n be a c h i e v e d  an i d e a l  f o r a l l C, and C . d  f o r m e r has a v o l t a g e  Level  Transformer  The c u r v e above shows t h a t t h e improvement  this  Meg  and i s t h e r e f o r e i m p r a c t i c a l .  Coupling  coupling  Unfortunately,  o f ( s a y ) 10 inductors  value  line  i n signal l e v e l .  o f ( s a y ) 20pf r e q u i r e s  P i g . 1*6  1.3.3  coupled  and shows t h a t d e l a y  increase  characteristic  to the d i r e c t  stepdown r a t i o  transformer,  I f the t r a n s -  I  of r , then the  detector 2  g e n e r a t e s an a p p a r e n t  By  c h a r g e rQ f r o m a c a p a c i t a n c e  r  C•  14 The  voltage  across  &  V.  1  C.  1  = rQ/(C. + *'  V  I  i s V.  w h i c h has  1  r C,)', 2  V  d/ '  max  a maximum V  = Q/2\/C.C *' V I d'  at r  max  max  *  =\/c7/c7 V l d  r max  ...(1.3)  The equal  and  w i t h the is  of  maximum o c c u r s when the t h i s y i e l d s a pulse  l o s s l e s s delay  h a l f as  line.  i n t e r e s t o n l y when C\  r e f l e c t e d capacitances  The  and  great  as  that  transformer are  achieved  coupling  very unequal,  i n p r a c t i c a l t r a n s f o r m e r s w o u l d o t h e r w i s e more  offset  the  Prom t h e s e direct for  coupling  in signal  1.4  general  classes,  preamplifiers "voltage  resistive  amplifiers sensitive o f the that  are  sensitive  capacitive*  be  Voltage  divided  upon  Sensitive -  i n t o the  (b).  stability  integrator  t o the  configuration,  types  I n the  feedback i s a p p l i e d  than d i r e c t l y  two  "charge s e n s i t i v e " ,  feedback i s frequency-independent. or M i l l e r  cases  improved  S c h e m a t i c s o f t h e s e two  shown i n F i g s . 1.7(a) and  stage r a t h e r  i n most  feedback used to o b t a i n  c o n f i g u r a t i o n , the  first  the  or  can  and  s e n s i t i v e " and  d e p e n d i n g upon w h e t h e r the is  seen t h a t  ratio.  C o m p a r i s o n o f Charge S e n s i t i v e Configurations •  Nucleonic  be  t o a m p l i f i e r c a n n o t be  maximum s i g n a l — t o — n o i s e  than  level.  a r g u m e n t s , i t can  of d e t e c t o r  scheme  since  losses  increase  are  voltage  t o the  input  In the  of  to  cathode ensure  charge  capacitive  feed—  15 back i s taken d i r e c t l y  Pig.  from  1.7(a)  the output to the i n p u t *  Voltage  Sensitive  Amplifier  C a l i b r a t i o n Signal tf  P i g . 1.7(b)  1.4,, 1  combination  the  c l o s e d - l o o p g a i n of the v o l t a g e s e n s i t i v e  g i v e n by E q n . 1.4.  cathode  Amplifier  Closed-loop Gain  The is  Charge S e n s i t i v e  of R  c  In t h i s  e x p r e s s i o n R' i s t h e p a r a l l e l  and t h e impedance  of the f i r s t  output v o l t a g e V  tube.  seen  looking  I f a charge  i n t o the  i s dumped on t h e i n p u t ,  i s g i v e n by E q n . 1.5(a) w h i c h  q  amplifier  reduces  t o E q n . 1.5(b) when A ^ i s l a r g e . q  A  cl  ol( fb R  fb  +  R  ') ol  . . . (1*4)  16  (a)  V  o  cl  =  (b)  Y  o  where C, . = t.  =  (C, + d  C.)  (1.5)  F o r the c h a r g e voltage  C  in  is  in  amplifier,  Q gives r i s e  to a  V.  V.  V.  sensitive  where C^  2  =  {C^  + C  ±  + C  f b  )  ...(1.6)  t2  amplified  e x a c t l y by Eqn.  by A -. * so t h a t  the o u t p u t v o l t a g e V  1.7(a) and f o r l a r g e A , by Eqn.  i s given  1.7(b).  Q oi A  ( fb ol C  Comparison  A  o f Eqn.  of the charge  (1.7) +  1.5(b) and  sensitive  1 . 7 ( b ) , shows t h a t  amplifier  depends upon f e w e r  t h a n does t h e o u t p u t o f the v o l t a g e particular  i t i s independent  the  sensitive  (for large  one.  output parameters In  g a i n ) o f the  detector 0  and  tube  sensitive gives  1.4.2  capacitances*  This  characteristic  c o n f i g u r a t i o n makes i t e a s i e r  i t greater  o f the  charge  to c a l i b r a t e  and  also  stability*  System, C a l i b r a t i o n  When the e n e r g y v e r s u s p u l s e - h e i g h t nucleonic  system  C .  of the  i s c h e c k e d w i t h t h e p u l s e g e n e r a t o r , an  a c c u r a t e l y known s t e p v o l t a g e V capacitor  calibration  A charge  Q  i s applied  g i v e n by E q n .  1.8  to the  test  then passes to  1'  17 the  a m p l i f i e r as t h e c a l i b r a t i n g  signal.  C.C V 1 c c (C. + C, ) I c'  ...(1.8)  V  For  the v o l t a g e  capacitance amplifier so C  sensitive amplifer,  C^, d e f i n e d  the M i l l e r  earlier.  capacitance  t h a t C. i s now much g r e a t e r Therefore  c  the t e s t  charge  capacitance.  If C  c  F o r the charge s e n s i t i v e C ^ ^ ( l + A ^ ) i s added t o C Q  t h a n any r e a s o n a b l e is C V  s y s t e m c a n be c a l i b r a t e d w i t h o u t detector  difficult  to obtain very  t h a n l p f so c a l i b r a t i o n requires  1.4.3  f o r this  i s made v e r y  a measure o f t h e i n p u t  provides  type  c a p a c i t o r s o f much  less  of a m p l i f i e r u s u a l l y  capacitance.  closed-loop  gain  of c a p a c i t i v e feedback i s t h a t i t s t a b i l i t y with  b o t h t h e o p e n - l o o p g a i n and t h e d e t e c t o r  by  s m a l l , t h e same  Stability  Another advantage  voltage  c a s e and t h e  s e n s i t i v e a m p l i f i e r ; but i t  accurate  for this  value of  m e a s u r i n g t h e i n p u t and  c o n d i t i o n p r e v a i l s f o r the v o l t a g e is  C^ i s j u s t t h e  feedback s t a b i l i z e s  gain d r i f t s  respect  to d r i f t s i n  capacitance, only.  This  while  c a n be s e e n  c o n s i d e r i n g E q n . 1.9 and t h e d e r i v a t i v e s f o r t h e two t y p e s o f  feedback.  AV  o  ol  +  (1.9)  I t has b e e n assumed t h a t t h e f e e d b a c k components a r e o f  18 high  stability  capacitance For found  and o n l y t h e o p e n - l o o p g a i n o r t h e t o t a l  can d r i f t . the v o l t a g e  QR  v  ^ol  =  C (R + A t  d t  2  V  RM  o l  2  U  C^(R + A R ' )  C  +  C  Q l  Substituting  in  amplifier,  the d e r i v a t i v e s are  f r o m E q n . 1.5(a) t o be  a o  for  sensitive  the worst either A  these  A  o l  o R  R ^  A  , where R = R„, + R ' ="fb  o l  1  t  i n E q n . 1.9 and a d d i n g  absolute  values  case,  g i v e s E q n . 1.10 r e l a t i n g a f r a c t i o n a l change  or  t o t h e r e s u l t i n g f r a c t i o n a l change i n V * Q  AV  0  _  o  For found  ftr) * o l '  ol  the charge  sensitive  amplifier  •••  t  x  +  (  I  -  1  0  the d e r i v a t i v e s are  f r o m E q n . 1.7(a) t o b e :  V  d oi A  =  U  o l  c  o  f b  C  t2  + c  ^ o t 2  )A  o l  '  jc  t  ~  -u  o l  c  V  o  + c )  f b  t 2  ) Therefore  E q n . 1.11 r e l a t e s  g a i n and c a p a c i t a n c e  t h e change  f o r the charge  ••  i n qut.put  sensitive  •  t o t h e change i n  amplifier.  )  C o m p a r i s o n o f Eqn* 1*10 and 1.11 shows t h a t sensitive  c o n f i g u r a t i o n , as c l a i m e d , s t a b i l i z e s  capacitance d r i f t s stabilizes  1.4.4  count the  gain d r i f t s  Input D r i f t  The  average 6  b o t h g a i n and configuration  only*  a t H i g h Count  Rates  i n p u t v o l t a g e shown i n P i g . 1.3 b u i l d s up a t h i g h  rates u n t i l  count  while the v o l t a g e s e n s i t i v e  the charge  rate  count  i t r e a c h e s a maximum dc l e v e l  and t i m e rate  constant.  d e t e r m i n e d by  The maximum s h i f t  a t an  r . c a n be shown t o be V = T. V . r , where ' s in i '  T. i s t h e i n p u t t i m e c o n s t a n t and V. t h e a m p l i t u d e o f t h e in I • input pulses. F o r the voltage s e n s i t i v e a m p l i f i e r , 1  T  For  in  =  t  C  t h e charge  hn  •  '  R  w  h  e  r  e  R  sensitive  B  < A  ol fb C  +  =  B  i  B b  / (  R  i  C  t2»'  V  = RQr, a t a g i v e n c o u n t  by  a maximum amount V rate  v  Q/c  i =  t  case.  V  i= S / ( A  Therefore both configurations  maximum c o u n t  +  rate.  o l  C  f b  + C  t 2  )  have t h e same i n p u t  I f the input bias  , then both a m p l i f i e r s sraax' * r g i v e n by E q n . 1.12.  shift*  c a n change  can handle the  20 r  '= V max  For a maximum  lmev p a r t i c l e s , bias  shift  counts per second. higher too  particle  small  /OR. smax' *  an i n p u t  ...(1.12)  resistance  o f ( s a y ) 0.1 v o l t s , ^ For smaller  energy*  r  l m  a  s  x  f o r some e x p e r i m e n t s .  come w i t h t h e c h a r g e — s e n s i t i v e ,  allowable even  r max  i s 2.2 x 10  bias  d r i f t , and  smaller  This  o f 100 meg., and  and may i n f a c t be  difficulty  but not the v o l t a g e - s e n s i t i v e  c o n f i g u r a t i o n , b y t y i n g R^ t o t h e o u t p u t r a t h e r ground* the  This  adds dc f e e d b a c k  e f f e c t i v e input  rate  t o t h e a m p l i f i e r and r e d u c e s  t o R./A » The maximum 1 ol by a f a c t o r A , t o r = A ,V ol  J  and  i s near the upper therefore  than t o the  resistance  i s then increased  This  c a n be o v e r -  max  c u t o f f f r e q u e n c y o f most  imposes no r e s t r i c t i o n  on h i g h  count /OR..  o l smax' * l preamplifiers  count  rate  operation. 1.4.5  Noise  The be  "charge  superior  stability  not  s e n s i t i v e " c o n f i g u r a t i o n has been shown t o  to the "voltage  s e n s i t i v e " c o n f i g u r a t i o n f o r both To see how t h e i r  compares i t i s n e c e s s a r y t o c o n s i d e r  of feedback  on t h e s i g n a l - t o - n o i s e  It  stated  i s often  that  and t h e n o i s e  explanation  ratio.  t h e S/N r a t i o  o f an a m p l i f i e r i s both the  a r e r e d u c e d by t h e same f a c t o r .  appears  to account  noise  the general  a l t e r e d by the a p p l i c a t i o n o f feedback because  signal this  Amplifiers  and e x p e r i m e n t a l c o n v e n i e n c e .  performance effect  i n Feedback  While  adequately f o r the small  21 effect is  that  f e e d b a c k g e n e r a l l y has  not s t r i c t l y  particularly  true  and must be  on n o i s e p e r f o r m a n c e , i t  applied with  t o wide band systems  caution,  s u c h as n u c l e o n i c p r e a m p l i -  fiers. A more a c c u r a t e s t a t e m e n t g i v e n by the f o l l o w i n g current  ratio  amplifier the  be  theorem^*'''"'"^:  i n a lead  load  short-circuiting  a consequence  of t h i s  theorem,  of the i n s t a n t a n e o u s s i g n a l  The  resolution  but  by t h e r a t i o  find  this  integrated  spectral  changes  the r e q u i r e d  preamplifier system In  preamplifier  S/N  response  noise.  ratio  differs  To  f o r t h e open  Because  and  However, t h e n o i s e p e r f o r m a n c e correctly  from the  frequency response  later  of  open-  i s used.  by t h e p o s t - a m p l i f i e r  causes o n l y a second-order  n o i s e performance be  t o t h e rms  ratio  systems, the p r i m a r y f r e q u e n c y response  are i n t r o d u c e d  It will  the  the f r e q u e n c y response of the  i f the c l o s e d — l o o p  T h e r e f o r e , the o r i g i n a l affect  without a f f e c t i n g  d e n s i t y o f the i n s t a n t a n e o u s  c a n be d e t e r m i n e d  nucleonic  limitations  any f e e d b a c k l o o p c a n  over the f r e q u e n c y pass band.  closed—loop preamplifiers*  loop  ratio i n  to the i n s t a n t a n e o u s n o i s e .  o f t h e peak s i g n a l  feedback g e n e r a l l y amplifier,  voltage  an  i s d e t e r m i n e d n o t by t h e i n s t a n t a n e o u s S/N  q u a n t i t y , the  n o i s e must be  the  the output of  S/N  impedance."  removed f r o m t h e o u t p u t and g r o u n d e d  ratio  of feedback i s  "the i n s t a n t a n e o u s  i s e q u a l t o t h e i n s t a n t a n e o u s S/N  normal As  of the e f f e c t  statement t h a t i s very nearly  shown l a t e r  that  and  the  effect*  f e e d b a c k does  not  correct.  the a d d i t i o n  o f C„,  t o the  ID  input  c a p a c i t a n c e r e d u c e s t h e S/N  ratio  o f the c h a r g e  sensitive  amplifier, the  while  the noise  t o the i n p u t  cathode by  u n b y p a s s e d f e e d b a c k r e s i s t o r , ' does t h e same f o r t h e  voltage  sensitive  amplifier.  However, b o t h t h e s e figurations "charge it  introduced  do g i v e  sensitive"  roughly  effects  are small  t h e same S / N r a t i o .  configuration i s superior  i s most o f t e n u s e d .  and t h e two c o n Because the  i n the other  aspects  2.  SIGNAL. NOISE AND  I n C h a p t e r 1, t h e n u c l e o n i c on p u l s e  height  THE FREQUENCY  RESPONSE  s y s t e m was d e f i n e d and t h e  effect  of noise  r e s o l u t i o n was m e n t i o n e d *  The  effect  o f f e e d b a c k was d i s c u s s e d t o show t h a t t h e c l o s e d - l o o p  s y s t e m c a n be r e p l a c e d by an o p e n - l o o p s y s t e m f o r s i g n a l and noise  analysis.  In t h i s  r e s p o n s e upon t h e s i g n a l will  chapter, and n o i s e  be f o u n d , and t h e c r i t e r i a  formance o f t h e s y s t e m w i l l  2.1  The E f f e c t  The pulses  are  input voltage  i n a variety  of a general  f o r judging  signal  nucleonic  the n o i s e  system  per-  Signals  o f F i g . 1.3 c a n be s h a p e d  a n a l y s i s by l i m i t i n g  the  into  frequency  o f ways - t h e most common o f w h i c h 1  clipping  frequency  be d i s c u s s e d .  double d e l a y - l i n e c l i p p i n g ^ * '  Delay-line  of the  o f F r e q u e n c y Response on N u c l e o n i c  suitable f o r height  response  the e f f e c t  generates  2 # 2  ^  and RC  narrower pulses  clipping^ * )* 2  than  3  RC  i clipping  f o r a given  primarily other  i n high  hand, l e n d s  signal^to-noise ratio;  count-rate  experiments.  i t s e l f more r e a d i l y  hence i t i s u s e d RC c l i p p i n g  to experimental  measurements b e c a u s e o f t h e ease w i t h w h i c h t h e response  c a n be  The  detailed  noise  frequency  altered*  s i m p l e s t RC p u l s e  shaping  network uses  e l e m e n t a r y i n t e g r a t i n g and d i f f e r e n t i a t i n g constants  on t h e  T^ and T  2  respectively.  isolated  networks w i t h  Gillespie  has c a r r i e d  a n a l y s i s o f t h i s n e t w o r k and has shown t h a t t h e  tinie% out a  24  signal-to-noise This  simple  ratio  result  has  been u s e d  by  ( 0 A\ ' .  = Tg = X  i s a maximum f o r almost  a l l authors  527)  (2 5 2 discussing was  the n o i s e o f p a r t i c u l a r  a l s o used  f o r the  experimental  However, f o r t h e o r e t i c a l found  necessary  c o n s t a n t , T^  t o add  f o r unavoidable further.  In the  frequency  cut-off  overall  circuit  2.1(a).  t a k e s the form finding  (  a  )  P  (b)  s  )  =  Upon p u t t i n g  o f the  (1 + s T ^ d  = T  system  + sT )(l 2  -|  xTT  =T  the pass  t o the  i n the  high  three  constant time  the f u n c t i o n  and  T  3  band  noise  i n p u t time  With the  2  account  = xT,  P(s)  P(s)  to a  signal.  + sT )  .*.(2.1)  3  —  ...(2.1)  (s + l / r ) ^ ( s + l / x T )  i n p u t v o l t a g e i s a s t e p , Q/C^,  domain i t i s r e p r e s e n t e d by to u n i t  while  i s g i v e n by  ^  to  time  o f E q n * 2.1(b) w h i c h i s more c o n v e n i e n t f o r  P(s) =  The  system  d e v i c e s i t i s the  response  study*  integration  corresponds  (see S e c t i o n 4 . 2 ) .  the response  (  T^  and,  o f n o i s e i t was  that l i m i t  of the p r e a m p l i f i e r ,  c o n s t a n t s , the f r e q u e n c y of Eqn.  effects  system,  measurements o f i n d i v i d u a l of the t e s t  "parasitic"  to the b a s i c  high frequency  ' ' * ' *  p o r t i o n of t h i s  calculations  a second  than T ) ,  (less  amplifiers  in  S^(s)  and  = Q/sC^..  i n the  The  frequency  signal,  normalized  i n p u t v o l t a g e , i n the f r e q u e n c y domain t h e r e f o r e i s j u s t  t h e d e n o m i n a t o r o f Eqn* 2 * l ( b ) .  Taking  the  inverse Laplace  t r a n s f o r m w i t h the a i d of H e a v i s i d e ' s expansion  results  in  25 Eqn,  2.2(a) f o r s ( t ) , t h e s i g n a l  s(t')  i s plotted f o r several d i f f e r e n t values  where t  -t (b)  Eqn;  the  1  expression  /  ...(2.2)  V  f t - XTZTJ-)  (  1  time  constant  f o r  s m a l l x)  ...(2.2)  respect to than  1 (i.e.  i s much s m a l l e r t h a n X), t h e f i r s t  t e r m c a n be i g n o r e d  and t h e s i m p l e r ,  approximate  2.2(b) w r i t t e n *  Differentiation =  ='^  1  However i f i t i s assumed t h a t x i s much l e s s  parasitic  I n P i g , 2.1,  o f x.  2.2(a) i s n o t r e a d i l y m a x i m i z e d w i t h  exponential  t'  '  s(t) =  time.  i n t h e t i m e domain.  o f E q n , 2.2(b) shows t h a t a t  ( l - x / ( l - x ) ) the signal  reaches  t h e peak v a l u e  S given  by E q n . 2.3.  S  (  x  )  =  XTTxT  e  When x = 0, t h e maximum t  f  and  = 1, t h e w e l l known r e s u l t differentiation  x = 0.3 w i t h  less  increases rapidly, i n P i g . 2.2. and  _  1  /  (  "  x  )  ( f o r x <0.3)  ...(2*3)  i s S(o) = e ^ occuring a t f o r a p a s s band o f e q u a l i n t e g r a t i o n  time c o n s t a n t s .  than  l  E q n . 2.3 h o l d s  up t o  3$ e r r o r b u t f o r l a r g e r x t h e e r r o r  being  The v a l u e s  over  ifo when x = 0.4.  f o r s m a l l x were f o u n d  f o r l a r g e x f r o m P i g . 2*1.  S(x) i s p l o t t e d f r o m E q n . 2.3,  27  2.2  Noise  2,2.1  i n the N u c l e o n i c  G e n e r a l N o i s e Model f o r t h e N u c l e o n i c  Noise of p h y s i c a l pletely  throughout  the  processes but  i t s effect  a t the output  of i t s o r i g i n .  a l l noise results  i n p u t of a n o i s e - f r e e  (a)  n generally one  o f two  i n F i g . 2*3(b) by  case. e  n  and  i  R  t a k e n t o be  n  i s com-  Two  Generator  Model  Models  Y^.  dependent These  are  current generator i  respectively.  are a t l e a s t  at  i n F i g . 2.3(a)*  components, one  a shunt  the f r e q u e n c i e s of i n t e r e s t  can be  as i l l u s t r a t e d  General Noise  a series voltage generator e  general for  consists  a variety  a n o i s e v o l t a g e , n,  (b)  2.3  by  r e a s o n i t was  n o t d e p e n d e n t on t h e i n p u t a d m i t t a n c e  represented and  from  system  system  For t h i s  S i n g l e G e n e r a t o r Model  Fig.  and  System  i s generated  independent  assumed t h a t the  System  partially  n  I n t h e most correlated  i n nucleonic applications*  completely uncorrelated with l i t t l e  or  but they no  error  (28) / .  from  i  With t h i s  and  e  mean s q u a r e  n  add  as"mean s q u a r e s and  the  a m p l i f i e r noise  repap^senting  w  noise  = Vd  a  = 2QeI  2  w  L  total  are  e = w'+  w  w  i  R  i  equivalent -  e  —2  n  +  n  decomposed f u r t h e r .  e  w  resulting  —2 n  and i , and n a input c i r c u i t noise,  %  b  the  i s g i v e n by  sources  generators  d e t e c t o r and  d  w  —2 n  input noise voltage  I n P i g . 2.4 into  assumption, noise v o l t a g e s  other  generators  ic  f  -{^5—Jw^— i . d=£.  G>b  Fig.  As  2.4  f r o m the  D e t a i l e d Noise  a general  predominantly  (}>i  ih  rule,  i n the  s e c o n d and  the  input  a m p l i f i e r noise  stage  subsequent  noise  of the  first  noise  of t h e  subsequent s t a g e s .  e  n  of  and  i  the  active device  a  devices i current,  can  stage  a  stages.  T h i s i s because  taken  i  t o be w,  = 2Q  1^  I s d e f i n e d by  The  I  this  T  t  where Q  expression  adding  to  a m p l i f i e r noise  t o be first  shot n o i s e  so t h a t i t i s c o n v e n i e n t  of  arises  small c o n t r i b u t i o n s  u s e d f o r the  from  System  with  i s a m p l i f i e d before  t h e r e f o r e be  results  Model o f N u c l e o n i c  the  stage.  i n the to take  i s the t o be  noise  generators  generators  leakage  spectral  electronic the  the  I n most a c t i v e  input the  the  density  charge.  equivalent  amplifier/  leakage  current.  leakage  current The  contain  I t i s not and  voltage  two  e v e n be  generator  distinct  "white", e with ' w or  may  n e c e s s a r i l y the frequency  components; one  i s found  s p e c t r a l d e n s i t y w ; and * w'  a second  J  e  w  in a fictitious  noise  R,  input  w  w  The in  = 4kTR  n  noise  i s sometimes lumped w i t h  frequency-dependent  evaluation  of the  overall  separation  o f the  two  they w i l l noise  be  treated  c h a r a c t e r i z e d by  K, t h e n r e p r e s e n t ' .  therefore  as w^  i t s own  R and  =  290°K*  the w h i t e  noise  resistor  the  start,  p a r a m e t e r K, The  noise  three  but  requires  noise  of the  thermal noise  and  the  parameters, active  in this  flicke  i . and  w^  1^,  devices  thesis.  a m p l i f i e r , the  currents  the  Therefore,  which r e l a t e s  o f a l l the  of a l l a m p l i f i e r s considered  contribute  T =  eventually  f r o m the  (K/f).  I n a d d i t i o n t o the resistors  system n o i s e  separately  frequency  and  noise  Therefore  f o r purposes of i n t e g r a t i o n .  t o the  n  equivalent  "equivalent  shown.  , where k i s B o l t z m a n n ' s cons t a n t and  flicker one  as  w^  i s commonly  from thermal n o i s e l o c a t e d a t the  or  "flicker"  a spectral density  t a k e n to r e s u l t  n  to  frequency-independent  i s i n v e r s e l y d e p e n d e n t upon f r e q u e n c y .  resistor"  dc  dependent.  for a l l devices  " e x c e s s " component* e^ . ,*• w i t h  that  measurable  bias  i , with  1 b s p e c t r a l d e n s i t i e s o f w^ = 4kT/R^ and w^ = 4kT/R^ r e s p e c t i v e l y and the d e t e c t o r c o n t r i b u t e s a s h o t n o i s e c u r r e n t 1, w i t h a  spectral current. as the  d e n s i t y w^ I f the  = 2Q I^» e  detector  shown, a l l c u r r e n t  i .  i s the  detector  i s connected d i r e c t l y  generators  s p e c t r a l d e n s i t y Wp o f the  generator  1^  can  be  original  leakage t o the  added t o g e t h e r parallel  amplifi to  current  give  30  v  = 2Q I :where  p  e  This noise spectral  g  = I  L  + ^j-  c u r r e n t causes a s e r i e s  +  SQH^  h  +  input voltage  '•••(2.4)  i /Y, w i t h n x  d e n s i t y Wg g i v e n by E q n . 2.5. 2Q I R  w  I  e  <3•  =  R.R,  2  % o  6  i  t  (1 + » R . C ~ )  b  2  where R =  .  2  —  (R  i  ...(2.5)  —  + R ) b  Prom E q n . 2.4, i t c a n be s e e n t h a t t h e t h e r m a l of t h e b i a s r e s i s t o r s behaves l i k e c u r r e n t 4kT/;2Q R.. meg v a l u e tubes  o f R.  shot noise  in a  noise  leakage  T h i s has a m a g n i t u d e o f 1 na f o r a 49.5  Since  the leakage  and i o n chambers a r e o f t h i s  c u r r e n t s encountered i n order, very  large bias  the thermal  noise  r e s i s t o r s must be u s e d . Eqn. leakage R^ u n t i l  2.5 s u g g e s t s  current noise Wg = 4kTR.  that both  c a n be r e d u c e d The e n t i r e  a p p e a r s as an a d d i t i o n t o R « n  100  i s not excessive.  RC i n p u t a d m i t t a n c e  Since R  noise  reducing  t o such  order  between  so t h a t i t s  s m a l l , however, t h e  an e x t e n t by t h e p a r a l l e l  Therefore,  input thermal  c o n t r i b u t i o n then  i s typically  n  that the net e f f e c t  signal-to-noise ratio.  discussed, very  shunt  I f i t were t h i s  s i g n a l w o u l d be a t t e n u a t e d  the  s i m p l y by r e d u c i n g R^ or  and 500 ohms, R must a l s o be o f t h i s  noise  and t h e  noise  would be a d e c r e a s e i n the f i r s t through  l a r g e b i a s r e s i s t o r s , i s t o be p r e f e r r e d .  method the use o f  31 2.2.2  E f f e c t o f F r e q u e n c y Response  So f a r the a m p l i f i e r in  terms  of s p e c t r a l  p a s s band  To do t h i s ,  and d e t e c t o r n o i s e has been  densities  upon t h e t o t a l the s p e c t r a l  on N o i s e  only.  noise  The  discussed  e f f e c t o f the f r e q u e n c y  o f t h e system w i l l  now  components a r e m u l t i p l i e d  s q u a r e d f r e q u e n c y r e s p o n s e o f t h e system,  be  found*  by t h e  and i n t e g r a t e d  over  —2 the  entire  frequency range.  the  equivalent  substituting  This r e s u l t s  input noise,  Eqn.  2.7  2.6  for n *  i s t h e n f o u n d by  , Wp,  the e x p r e s s i o n s f o r w  i n Eqn.  and w^  f r o m F i g . 2.4*  -oO  -2 n  WJP(CO)|  =  +  2  w  +  Vj  |P(«)|  f  ,(2*6)  2TC  0  2  (a)  (b)  +  Z  n  2  =  4kTR I n  1  e| ( p  — ~ -  2 12  i n t e g r a n d s 1^*  integrals  1  +  2 i x  I^r  ,2TC  I-j a r e f o u n d i n terms Eqn.  2.1(a)  The  of the  f o r P ( s ) i n Eqn*  a l l have t h e f o r m o f E q n .  i n Appendix  2.8  integrals  2,7*  with m are  I*  • 00  m -• os dco  (1 + < o T ) ( l 2  0  00  ,..(2.7)  evaluated  2%  2-, dfa>  ^  f o r e a c h i n t e g r a l as n o t e d *  -H  Pl^|  5- + 2ixK  1  differing  1  t t  t  t i m e c o n s t a n t s by s u b s t i t u t i n g The r e s u l t i n g  1 e  2Q I  +  C  The  e  2  2  1  m  + <o T )(l ^ 2  2  + <* T ) 2  J  2  2 f o r I.  = ° 2 m = 1 for I m  f  o  r  J  3  ...(2.8)  32 When:  = T  =T  2  I  (a)  ±  and  = xT  the  results  are:  (b)  8T(l + x)'  I  2  =  T(l  +  8(1  +  2x) x)  2  ...(2.9) 2x ln(x)  +  2  (c)  I,  (l~x ) 2  4TI(1-X ) 2  The type  effect  of n o i s e  of t h e  (d)  I, 4u(l  2  " p a r a s i t i c " time  i s shown i n P i g * 2.5  by  constant  plotting  each i n t e g r a l .  can be  seen t o be  interest  2.10  n  (  x  be  =  (1  A 1  ^  rms kTR  x)  of  ( x  ^  x  =  0  )  g i v e n by Eqn.  for a l l x  2T  1^  and  I  2  i n Eqn.  equivalent input noise  n  01 T(l + 'e e  4C  2x)  2.7  In to  + § ( l + x)  1.0  -  ,8  -  7  -  Pig.  2.5  Effect  o f T^  on N o i s e  give  voltage  .5  ,9  2.9(d)  of  used i n a l l subsequent e q u a t i o n s .  total  I  f o r m o f 1^  percent  i t i s substituted with  f o r the  )  approximate  w i t h i n a few  so i t w i l l  particular, Eqn.  The  x)  T^ upon e a c h  \ l *k for  +  Voltage  ...(2.10) .6  Components  The of I. • E JLi  this  overall  effect  and K, and c a n n o t  n  time.  Applying  some f o r e s i g h t  dominating upon f * effect  for aUT).  t o E q n . 2*11*  n o i s e term  pre-  and E q n . 2.10 c a n be  T h i s a p p r o x i m a t i o n was f o u n d t o be  f o r determining the n o i s e of the a m p l i f i e r  section  5 . 2 ) ; b u t when a l a r g e  from  the d e t e c t o r , the leakage the e f f e c t  that the  o f i t s i n v e r s e dependence  n o i s e term  (see  before  change  o f x on n c a n t h u s be t a k e n t o be j u s t t h e  o f x on t h e w h i t e  adequate  T^< X  i n the white  over the o t h e r s because  The e f f e c t  simplified  (since  a significant  t o Eqn* 2*10, i t i s a p p a r e n t  of small X r e s u l t s  condition  approximately i f i t i s  enough t o cause  o n l y when X i s s m a l l  any t e r m  size  t h e r e f o r e , be f o u n d e x a c t l y a t  However, i t c a n be f o u n d  assumed t h a t x i s l a r g e in  o f x depends upon t h e r e l a t i v e  c u r r e n t i s added  current noise i s not i n s i g n i f i c a n t  of x i s f e l t *  e x p r e s s i o n f o r n must be  leakage  alone  For this  case the exact  used*  £  +  5  2 - 2  -  (1 + x ) ...(2*11)  2*3  The " E q u i v a l e n t I n p u t NOise  2*3.1  Definition  Charge"  of the E q u i v a l e n t Input Noise  Charge  I n p r e v i o u s s e c t i o n s e x p r e s s i o n s were d e r i v e d f o r t h e . signal  and n o i s e i n t e r m s o f t h e system  parameters  o f t h e g e n e r a l n o i s e model*  time  c o n s t a n t s and t h e  The s i g n a l - t o - n o i s e  ratio  i s the  b a s i c measurement o f the  e x p e r i m e n t can be input  signal level,  c o m p a r i n g the must be  j u d g e d and  is easily  amplifier  since  compared on  of i n d i v i d u a l the  i n t o the  Eqn.  2.10.  t o the  is  as the  the  2*2  Normalizing  and the  charge Q g i v e s  "equivalent  basic  In order  conditions, but  when t h e  rms  normalized as the  two  a m p l i f i e r s be  frequency  Q  n  has  to  charge", Q .  of  definition given  rms  given  Q  n  nucleonic  r e s p o n s e and  n  peak by respect  defined  i s then used  amplifier noise* identical  o n l y the  detector  noise  capacitance  b e e n d e f i n e d h e r e as  the  inverse  of  i t i s often defined  used  the  directly  charge which a p p l i e d i n s t a n t a n e o u s l y output  noise  output  pulse  voltage"  i n w h i c h i t i s measured*  the  noise  of  to  amplitude  5) * v.  i s more u s e f u l f o r e x p e r i m e n t a l  above b e c a u s e i t d e f i n e s  charge  made.  (2 t o the  the  i s i n v e r t e d and  s p e c i f y not  a m p l i f i e r i n p u t p r o d u c e s an  equal  level.  (charge)""^.  compared u n d e r  signal-to—noise ratio,  "that quantity  noise  S/C'^n" i n u n i t s of  measurement o r c a l c u l a t i o n was  While  signal  signal-to-noise ratio with  input noise  i t i s necessary  a l s o the  of the  where S i s the  n i s the  c r i t e r i o n f o r judging  that  normalized  n  T h i s i s seldom used d i r e c t l y but t o be  They  experiment*  in Fig*  input  for  r e s o l u t i o n g i v e n by  signal-to-noise ratio  given  the  amplifiers*  b a s i s o f the  t output  an  i t i s a f u n c t i o n of  This i s independent  converted  with which  a suitable criterion  performance  ratio*  i n any  The  i t i s not  noise  signal-to-noise yet  performed; but  accuracy  This  equivalent  work t h a n t h e charge  i n the  I t does however, have t h e  one  manner  disadvantage  that  the  basic  relationship  noise  r a t i o i s implied  error  of setting  between n o i s e  rather  Q = C,n, n x  than s t a t e d .  ignoring  on the  For  (implied) unit  ease i n c o n v e r t i n g  resolution,  Q  i s generally  n  ' *  noise  expressed  electronic be  charge.  converted  into  the  i neither  typical volts  ion  for  pair  state  the into  resolution* the  Full  This requires the  n  by d i v i d i n g  the  To g i v e  rms q u a n t i t i e s  noise  i  pair  e  can then N by t h e  p e r 30 e l e c t r o n - v o l t s  detector. This  expressed i n energy u n i t s *  The f i r s t  q u a n t i t y N = Q /Q  chamber, o r 1 h o l e - e l e c t r o n  a solid  electronic  o f Q by Q , the n ©  p a r t i c l e energy u n i t s  "detector y i e l d " of 1 ion  for a  p e r 3.5 e l e c t r o n -  i s t h e n the  rms n o i s e  a d i r e c t measurement o f aregenerally  • '  converted  l i n e W i d t h a t one H a l f Maximum  • •  height*  m u l t i p l i c a t i o n b y 2.35* t h e r a t i o o f t h e  standard deviation  to the  charge t o p e r c e n t  dividing  The r e s u l t i n g  lead  .  c h a r g e s o r " e q u i v a l e n t Kev p a r t i c l e e n e r g y " . conversion simply requires  can  ^ o Q\  signal the  This  signal—tc  the e f f e c t of the frequency (o  response  c h a r g e and t h e  of a Gaussian d i s t r i b u t i o n .  FWHM t o  These  conversions (a)  a r e summarized b e l o w i n Eqn. 2.12. C.n Q = —5— ( i n coulombs) n o Q C.n n  (b)  N  =  ^— =  (in electronic  charges) ..•(2*12)  (c)  FWHM =  47 x 1 0 ~ N  (d)  FWHM =; 8.23 x 10"*  ( i n Kev f o r  3  3  N  ion  ( i n Kev f o r  chamber's)  solid-state  detectors)  36 An  alternative  signal-to-noise input  ratio  noise voltage  requires  method o f i s to  n and  Because t h i s  the  o f the  unnecessary  rather  than  amplifier  total  one,  noise  noise  the  use  of  performance  i s not  a  specification.  t o measure, and  s p e c i f y i n g two  of n o i s e v o l t a g e s  This  capacitance,  charge  is difficult  complication  equivalent  input capacitance.  amplifier input  r e q u i r e d f o r the capacitance  normalized  s t a t e s e p a r a t e l y the  a knowledge o f t h e  parameter not  s p e c i f y i n g the  as  because  quantities  a criterion  recommended and  not  of  often  used.  2.3.2  Equations  Eqn.  the  Charge  2.12(b) d e f i n e s the  terms o f the equivalent  f o r Noise  peak s i g n a l  discussed  input noise found  "parasitic"  quantities,  time  the  the w h i t e n o i s e  curve  as  of F i g . 2.5.  S.  upon N  i s just  T h i s can be  i n Eqn.  2.13.  C ( x )  the  represented Using  =  ratio  S M  n(0)  S(x)  and  the  of the by  ^  changes c a u s e d  n as  i s then  shown  in n  of  and C(x')  found  l i - x l */(l-x)  found  i n Eqn.  2.14.  ...(2.13)  e  (l+x) (for x <  by  charge  effect  a "correction factor" N(x)  of  these  noise the  the  effect  both  i n v e r s e l y upon S,  this factor,  ilxl  Since  and  The  to decrease  shown i n P i g . 2.2,  depends d i r e c t l y upon n and x  was  charge N i n  i n s e c t i o n 2.1  i n s e c t i o n 2.2.  constant  signal  equivalent noise  0.3)  37 N(x)  = C(x)N(0) = C(x) C  t  n(o)  Q SCO, ...(2.14)  4  k  T  n  R  = C(x) 2  C(x) for  small  holds, and  i s plotted  i t was f o u n d  f o r m o f S no  .3  .2  directly  longer  of F i g s .  2.6  2.2  and l e a k a g e Tis  1  shown t h a t N(o) i s a minimum when t h e current noise  terms a r e e q u a l .  so l o n g t h a t C ( x ) has n e g l i g i b l e occur  When effect;  a t t h e same t i m e  . , min  ^min  ''' S S  l  v  by E q n . 2.16. u  [  C o r r e c t i o n Factor f o r High F r e q u e n c y E f f e c t s on N  minimum o f N ( x ) and N ( o ) t h e n  J  .4  r-i—I—i—|—r—l—i—i—|—I—I—i—i  c a n be e a s i l y  are equal,  constant T  .  I t was e v a l u a t e d  g r a p h i c a l l y from the curves  .1  white noise  mm  2  2.5.  It  N  K  40?  i n P i g . 2.6.  Fig.  the  ," W ,  x. b u t where t h e a p p r o x i m a t e  1.0  they  r  e  n  k  v  E q n . 2.15 and t h e minimum n o i s e  charge  .6  38 4kTR  X  . =  mm  N  n 20 I *e e  c,  t  ...(2.15)  iV4kTR .2Q I n  mm  'e  e  e  *—  ..(2.16)  For convenience  i n l a t e r c a l c u l a t i o n s , numerical values  f o r the v a r i o u s c o n s t a n t s have been s u b s t i t u t e d i n Eqns. 2.14, 2.15,  and 2.16 t o objtain the e x p r e s s i o n s below.  i n pf, R  i n ohms, T i n [isec, I  is  I n them,  i n nanoamps, K i n v o l t s  /cycle,  and the r e s u l t i n g N's are i n e l e c t r o n i c * charges. 4X10 I T e_  0.198R -n-..  N(x) = C(x) 1.71 C  t  ~2  +  ^ 14 K10 n n  +  ..(2.14')  X  N  . mm  min  = 0.0224 C, t  =  l  e  7  1  C  t  [°"  R 110  1 7 8  V  n I  1 0  (2*15*)  V e  +  I  1 q 1 4  ]  2  --(2.16')  These t h r e e e q u a t i o n s r e l a t e the n o i s e charge of the system t o the v a r i o u s n o i s e parameters and the time  constants.  They were d e r i v e d by assuming t h a t the w h i t e n o i s e term predominates whenever x i s l a r g e enough t o a f f e c t the n o i s e c i a b l y ; they a p p l y t h e r e f o r e , o n l y t o t h i s case.  appre-  P r e d i c t i o n of  n o i s e charge when t h i s assumption does n o t apply can be made  by u s i n g n(xO factoring built  2+3.3  However, i t was f o u n d t h a t  this  study, the approximate  adequate;  Calculation  In theorem noise  C(x).  during  completely  and S ( x ) d i r e c t l y w i t h o u t t h e s i m p l i f i c a t i o n o f  C h a p t e r 1 i t was  on n o i s e  shown by a p p e a l i n g  c a n be f o u n d f o r an o p e n - l o o p  g i v e n because  i s used*  the e f f e c t  been d i s c u s s e d .  Now  represents planned  to the b a s i c the s i g n a l  Miller  that  time an example was n o t  i t has, N w i l l  nucleonic  be f o u n d f o r a system  the e f f e c t  The t w o - l o o p  system  preamplifier.  feedback of the f i r s t  of the p r e a m p l i f i e r  l e a v i n g A-^ and  and  i f the c l o s e d - l o o p  that  stage.  f e e d b a c k has  shown i n F i g *  2*7  ^ f b l "*"  s  charge feedback l o o p d i s c u s s e d p r e v i o u s l y ,  parasitic cutoff  Amplifier  of t h e f r e q u e n c y r e s p o n s e had n o t y e t  and n o i s e *  a typical  that  system  At that  w i t h two f e e d b a c k l o o p s t o c l a r i f y on t h e s i g n a l  exclusively.  of a F e e d b a c k  i n feedback a m p l i f i e r s  frequency response  e x p r e s s i o n s were  hence t h e y were u s e d  o f N o i s e Charge  f o r the a m p l i f i e r s  and C ^ ^ "the  The h i g h f r e q u e n c y  i s a c c o u n t e d f o r by x i n P ( s ) ,  frequency—independent.  Fig.  2*7  Feedback  Loops  of T y p i c a l  Preamplifier  40 ^  ^fbl  E q n s . 2.17 ^  ^ f b 2 ~ ^' ^  =  and 2.18  (note  '-S - -  e  s:  na  that v  1  a  n  ^  n  0  1  s  e  are g i v e n  by  and n have been r e f e r r e d  to  o  the i n p u t by d i v i d i n g by A-^A-,)•  ol  =  V  n  < l > S  = n(x ) =  x  where ' C  x  4kTR I, (x, ) + n 1 1  x  =  tl  + C  ...(2.17)  d  Q e V 2 .< * > l + 2  2TXKI ( 3  'tl ..(2.18)  The  closed-loop  s y s t e m i s most  easily  superposition to a l l instantaneous For  the s i g n a l  this  results  V  Cf^l  +  for Y  C^^2  a n < 1  x  2  A^A  V  o fbl C  V  A  2 t2 C  o fb2 C  C  i n E q n . 2.19,  s  2  the  C  -"-  Generally x <x^.  _  _ t2 ~  results  o  x  ^  o  t2_  i n which  closed-loop  r  1 2 A  = 0^+0^  +  system.  has a g a i n b e e n removed  2  applying  f e d to the input,  A  o  Solving  voltages  by  i n the f o l l o w i n g e x p r e s s i o n :  _Q_  -:  analyzed  to r e f e r V  q  to  input.  QS(x )  QS(x )  2  o2  ( C  fb2  fbll  + C  A  +  0  C  fb2 lV A  ,..(2.19)  41 For  the  series  noise  sources  the  fbl s  C  n  g  =k  ±  k  f o r shunt  noise  lumping these g i v e s Eqn.  2.20  and  f o r the  found  to  integrating  C  over  1  t2  a l l frequencies  noise. 2Q I I (x ) e  n  J  C,,, „n fb2 p  2°t2  4kTR I (x )  +  2  e  2  2  2TXKI ( X  +  3  H2 - /  n  v  From E q n s . 2.17 c a n be  C „, , n, fbl p _ A  rms  't2  C  i tis:  _  t2  total  't2 n„2 ~= C  "t2 -QT  Y  n  total i s :  fb2  C  2 t2  A  source  = A, A,, p 12.  together  "  n  i n  n  2  &  while  instantaneous  v  ...(2.20)  )  x 2  and  2>]  2.18,  the  open-loop noise  charge  be  C  =  N,  t l  n  (  l  x  )  ...(2.21)  S(x )  1  ±  and  f r o m E q n s . 2*19  and  2.20  the  closed-loop noise  charge  is  N  C  2  t2  n  ( x  2  }  ...(2.22)  =  S(x ) 2  The se e x p r e s s i o n s  differ  o n l y i n the v a l u e s  of  and  x.  42  The  difference i n  results  feedback c a p a c i t o r s while  f r o m t h e a d d i t i o n o f t h e two  t h e change i n x r e s u l t s  change i n t h e h i g h f r e q u e n c y The  r e s p o n s e when f e e d b a c k i s a p p l i e d .  calculation therefore v e r i f i e s ,  proof  given  analyzed  earlier  by o p e n i n g t h e f e e d b a c k l o o p s  An that  for this  t h a t the closed—loop  components i n s h u n t w i t h important  from the  case,  the v e r b a l  s y s t e m c a n be  and p l a c i n g t h e f e e d b a c k  the input.  result  of t h i s  a n a l y s i s i s the  t h e n o i s e ^charge depends upon t h e t r u e p a r a s i t i c  a t t h e i n p u t o f t h e a m p l i f i e r and n o t t h e a p p a r e n t observed  when t h e a m p l i f i e r i s i n o p e r a t i o n .  figuration stage is  (see Chapter  because of i t s i n h e r e n t  The N o i s e  2.4.1  of a Nucleonic  The  charge  criterion  noise  i n n u c l e o n i c work.  communications,  T  - T  (F-l) i s  the Noise  usec/  2 - 1 0  erroneous i n d i c a t i o n  performance applying  con-  .  capacitance.  l  for this  the usual  System  f o r judging  In other  system n o i s e i s  a p p l i c a t i o n s such  F i g u r e F, o r t h e N o i s e Why  then  u s e d f o r t h i s a p p l i c a t i o n as w e l l ? an  The c a s c o d e  p r o p e r t i e s and n o t , as  o f i t s low M i l l e r  Figure  q  capacitance  Figure  as e  low n o i s e  The N o i s e  used only  capacitance  5) i s t h e r e f o r e c h o s e n f o r t h e i n p u t  o f t e n s t a t e d , because  2.4  demonstration  i s the noise The r e a s o n  Temperature  f i g u r e not  i s that F gives  o f t h e c o n d i t i o n s f o r optimum  type  of a m p l i f i e r .  definition  noise  T h i s c a n be s e e n by  o f F below t o t h e n u c l e o n i c  system.  43 p A t o t a l o u t p u t n o i s e power w i t h t h e i n p u t t e r m i n a t i o n i n p l a c e ~ O u t p u t n o i s e power r e s u l t i n g f r o m the n o i s e — f r e e a m p l i f i c a t i o n of the s o u r c e n o i s e From t h i s ,  the  spot  n o i s e - f i g u r e F i s g i v e n by Eqn.  t h e b r o a d - b a n d , or i n t e g r a t e d n o i s e - f i g u r e F ^ ^ n  Eqn.  2.23,  while  is given  by  2.24.  F  n  =•  = i + (  2  d^ t| C  T  "  2  W  +  I d  ,  V  4 k T  2 g  t  ,  —  Qe^  2  2 +  2  ^ t C  2e d I  ...(2.23)  (I - I , ) P  int  =  1  +  J  Both these frequencies, not  found e a r l i e r when t h e  the  definition  T  tend  condition  simply  2  noise  I  :  ...(2.24)  T  to a minimum a t i s large.  low This  f o r minimum n o i s e  predominates.  of F t h e r e f o r e r e s u l t s of the  2e d  does  charge  i n d i c a t e s t h a t the n o i s e f i g u r e Literal  i n an  optimum o p e r a t i n g  inherent i n the  , where s  i n the  particle i s the  represents  p r o p e r l y the  ratio.  By  of F t h e  signal  is  a p p l i c a t i o n of  erroneous  conditions for  the  due  denominator i s taken to to s t a t i s t i c a l  noise  associated with noise  degradation  the  input  c h a r g e i s a minimum, i n the  d e f i n i n g F i n t h i s way,  input  a noise  be  fluc-  e n e r g i e s , F i s g i v e n by F = 1  T h i s F i s a minimum when t h e  noise  I  detector noise  i n the d e f i n i t i o n  noise  n /s  Qe d  system.  If  tuations  t o the  source  determination  the  2  expressions  but  low  nucleonic  d  or when the  correspond  4kTR C? 4KC? ^4 + — — -  +  + signal* and  signal-tofigure  for  the  44 s y s t e m has b e e n f o u n d , b u t i t g i v e s no i n f o r m a t i o n n o t a l r e a d y expressed  2.4.2  i n the noise  charge.  The R e l a t i o n s h i p B e t v e e n N and F  Even though the n o i s e f i g u r e specifying  the n o i s e p e r f o r m a n c e  r e l a t i o n s h i p does e x i s t resistively  terminated  i s not s u i t a b l e f o r  of nucleonic  between t h e n o i s e  amplifiers,  figure  a m p l i f i e r and t h e n o i s e  of a  charge f o r the  same a m p l i f i e r when i t i s d r i v e n f r o m a c a p a c i t i v e This r e l a t i o n s h i p noise  figure  a  source.  c a n be d e r i v e d by c o n s i d e r i n g t h e s p o t  F f o r the a m p l i f i e r represented  by t h e n o i s e  model o f F i g . 2.8.  Fig.  F  2.8  Model f o r R e s i s t i v e l y Amplifier  i s g i v e n b y E q n . 2.25,as t h e r a t i o  square i n p u t n o i s e resulting  Noise  t o t h e mean s q u a r e  from the source  noise  Terminated  of the t o t a l  input noise  current  i .  *  voltage  mean  F  4kT R  Z^  n  spot to P  v R 1 + + 2 = 4kT  -2 n R Z.  =  v  1  i  4kT  1  +  +  . ...(2.25)  z.  in  in  noise  complex b u t s i n c e ve a r e c o n c e r n e d w i t h  figure,  i t c a n be t a k e n  . E q n . 2.25  source  minimum n o i s e  P = 1 +  terms i n R  resistance R figure  and  g  are equal.  equal 2.26.  Thus  i s g i v e n by E q n . 2.27  g Q  the  the  and the  by E q n . 2.28(a) and ( b ) .  R  w 2kT  t o be c o n s t a n t  c a n t h e r e f o r e be r e w r i t t e n as E q n .  i s a minimum when t h e two  optimum  R  +  R + Z.  i s i n general  in  R  w  g  +  w  w  Z.  ...(2.26)  4kTR in l  R  w go  w  (a)  |Z.  e I l ml  + z. e in  F  2 w  (note  that  R  -|z.  I)  ...(2.27)  I ml  go  P  - 1 + min ~ ' .  w 2kT  -.— Zm .  ...(2.28)  F  min  -  Solving Eqn.  2.29  general F  . mm  and F  .  mm  2w  w  (b)  1  +  f o r w^  and 2.30  noise  2kT'|Z.  model  (iii)  the i n p u t  i s given. to  and w  relating  from these  g  the n o i s e  equations  generators  to-: ( i ) t h e minimum s p o t  o f an a m p l i f i e r , ' r  4kTR •, go  m  v  ( i i ) the optimum '  impedance  r  Z^  n  source  results' i n of the  noise  figure  resistance R , go'  a t the frequency  f o r which  46  2kT(P w  . -1)|Z.  1  mm  |z. I .+ I ml  2kT(F w  To that  -  R  simplify  the f l i c k e r  Substituting w  go  R _go  1 -  ...(2.30)  m  go  the remaining c a l c u l a t i o n s  P  s u b s t i t u t i n g the r e s u l t  relating  N to F ^ » m  =  g  —2 i n E q n , 2.6 f o r n , i n t e g r a t i n g  f r e q u e n c y p a s s band d e f i n e d by T^ = T^ = T and  i t i s assumed  component c a n be i g n o r e d , so t h a t w and w  ®  ...(2.29)  R  . -1) mm  v  R  i n I. go.  i n Eqn. 2.12(b), r e s u l t s  i n E q n . 2.31  E q n . 2*31 c a n be m i n i m i z e d by c h o o s i n g  n  t o make, t h e two components e q u a l , w i t h the r e s u l t  Eqn.  2.32.  (Here T. = R •  N.  over a  and T^ = 0,  Tallin U  w^.  I  shown i n  C,) go t  C,e V 2 k T ( F . -l.)R " t Y mm go  T L.  8  T  Z.  AZi • I - R  fl_in|  2V i  g£  ml  U  8  T  <l iJ Z  + B K  ogo' »/-  ...(2.31) ^2kT(F N  mm 2Q  mm  -l)C, t  o f an a m p l i f i e r  and t h e n o i s e - f i g u r e source.  I  m|  resulting  relationship  d r i v e n from a c a p a c i t a t i v e  source  I t s h o u l d be s t r e s s e d t h a t even t h o u g h t h e i s used t o f i n d  the n o i s e charge,  e q u a t i o n g i v e s the g e n e r a l broad-band  w i t h the f l i c k e r  between  o f t h e same a m p l i f i e r d r i v e n from a  single-frequency noise figure the  ...(2.32)  |Z. I  2.31 and 2.32 g i v e t h e d e s i r e d  the n o i s e charge  resistive  ~ ^go^ l ^ i n l  1 + R / go'  £  Eqn.  1  term i g n o r e d .  Through  n o i s e charge  t h e use o f t h i s  equation, can be This  a m p l i f i e r s r e p o r t e d f o r communications a p p l i c a t i o n s  rapidly evaluated  i s important  f o r p o s s i b l e use  because  i n nucleonic  i n recent years  l a r g e numbers  p a p e r s have a p p e a r e d i n c o m m u n i c a t i o n s l i t e r a t u r e the  noise  state for  f i g u r e s of a m p l i f i e r s b u i l t  devices.  In a d d i t i o n , the  transistors  u s u a l l y give  c r i t e r i o n f o r the choice  of the  amplifier expected  best  can be noise  As  an  device  2  .*  ' *  transistor  made by  with  manufacturers'  of  standard  f o r the  .  Thus a p r e l i m i n a r y  or o t h e r  u s i n g Eqn.  device  2.32  of Eqn.  n  quantities a solid  f = l k c  = 8 meg.  i n Eqn.  this  The  2.32  for a  nucleonic  to determine  2.32,  the  N  .  The  f.e.t.  I f the  m  The  calculation  work.  has  -F i m  an  case  from -  n  n  be  = 560,  the  • 2'5db =  input  capacitance  of zero  S u b s t i t u t i o n of  detector  these  or FWHM = 4.6Kev f o r  found  in practice.  than  to  exhibit  (See  i n d i c a t e s t h a t the  considerably less  f o r nucleonic  transistor  limiting  2N2386 was  charge  can  mm  specifications.  gives ^ ^  noise  an a m p l i f i e r must be  effect  = 20pf.  state detector.  5.9).  suitable  i n the  i s taken,  approximately Fig.  2N2386 f i e l d  given  so |Z£ |  capacitance  noise  12)  example o f the use  a t B == 1 Meg, 20pf  solid  charge.  f o l l o w i n g data 1.03  reporting  specifications  x  calculated  of  t h e many new  o n l y F as the  (2 11  work.  section  noise  1 db  figure  i f i t i s to  5.3, of be  48 3.  Now the  t h a t the  NOISE SOURCES IN ACTIVE DEVICES  general nucleonic  amplifier noise w i l l  be  s y s t e m has  considered  separately.  g e n e r a l n o i s e model, a m p l i f i e r n o i s e was entirely by  f r o m the n o i s e  t h e p a r a m e t e r s 1^,  R  o f the and  n  A c o n s i d e r a t i o n of a m p l i f i e r noise R  n  and  taken  i n p u t stage  K of the  K f o r each a c t i v e device  been  to  and  was  analyzed*  In  the  result characterized  two-generator noise  therefore entails  t h a t m i g h t be  model.  finding  I^»  used i n a n u c l e o n i c  0  amplifier. This  i s done t h e o r e t i c a l l y  Nuvistors, f i e l d effect These d e v i c e s source  (see  3.1  junction transistors. than  t h e r e f o r e g i v e low  i n the  1 db  noise  at  high  charge  B r i e f d i s c u s s i o n s of the more " e x o t i c " then  given  to  suitable for nucleonic a p p l i c a t i o n s .  i n Tubes and  Noise  and  p a r a m e t r i c j and M a s e r a m p l i f i e r s a r e  they are not  Noise  should  s e c t i o n 2.3).  tunnel diode, show why  transistors  f o l i b o w i n g s e c t i o n s f o r tube  a l l exhibit noise figures less  r e s i s t a n c e and  as w e l l  i n the  Nuvistors  conventional  tube and  i t s modern m i n i a t u r i z e d  (3.1) c o u s i n , the N u v i s t o r frequencies the  shot  noise  less  effect  i n the  completely  than,  , i s p r o d u c e d by say  20 Mc.,  i n plate and'grid  plate current.  uncorrelated  v  the  same p r o c e s s e s .  the most i m p o r t a n t currents  and  flicker  of t h e s e  At are  (excess)  These a r e , f o r a l l p r a c t i c a l  purposes,  49 3.1.1  Shot Noise  i n Tubes and  I n a tube or N u v i s t o r conditions,  the  emission  random e v e n t d e p e n d i n g electrons.  The  statistically current the  rate  noise  can  way  of charge  be  under  upon the  emission,  mean v a l u e  f l u c t u a t i o n known as  shot  operating  temperature-limited  o f an e l e c t r o n f r o m the  i n no  about the  Nuvistors  represented  emission  noise". by  of  is a  other  therefore, fluctuates  giving rise  "shot  cathode  to the  I t can  a current  plate  be  shown t h a t  generator  i  in s  the  plate c i r c u i t with  where Q  i s the  g  w * K/f;  e l e c t r o n i c charge  ^ =  f  .  a power s p e c t r a l d e n s i t y w  203(141 + |l^|)j  w= L  -  ||  (see F i g .  ,  ,  w  s  =  2QI.  3.1).  = 2QeI P  2  p  Plate  'gp  e e„, © H ^ h - ^ A - S f  =r gk C  d  ( f ) SaVg £ r  (j)i8  p  =J=  C  p k  |R  L  ® i a cathode Fig*  This is  result  l i m i t e d by  does n o t  3*1  Triode  Noise  h o l d , however, when the  a p o t e n t i a l minimum between p l a t e  called  space—charge  o f one  e l e c t r o n a f f e c t s subsequent emission*  simply  as  follows.  s t r o n g l y upon the cathode.  Model  limited  The  operation)  depth of  the  opposing f l u c t u a t i o n i n the  and  b e c a u s e now This  current  cathode the  (so-  emission  can be  explained  p o t e n t i a l minimum depends  space c h a r g e d e n s i t y  A f l u c t u a t i o n i n the  plate  i n the  vicinity  Cathode e m i s s i o n  of  therefore  p o t e n t i a l minimum d e p t h .  This  the causes  an  i n turn  induces  cathode e m i s s i o n  t h a t compensates f o r t h e  initial  current 2  fluctuation w  S  = 2Q  and  I  6 .p  and  2  P  f  reduces  where  theoretically  transconductance limited  1  2<  t o be  spectral »n  1*  has  d e n s i t y by been found  so t h a t  To r e p r e s e n t t h i s  i s assumed t o r e s u l t  w  a s  2Q g e  type  m  i s the  f o r space-charge  m  of n o i s e  f r o m the  to  experimentally  m  tube,  P  a factor  p r o p o r t i o n a l t o g / l p where g  of the  operation*  n o i s e model, i  f  the  i n the  noise  general  voltage  s e^ = i / g s  the  a m  t the  input*  equivalent noise • . •  The  shot n o i s e  resistor  R  where R n  i s then c = — . n g m  represented The  by  constant  c  6  v a r i e s between 2.5  and  4 d e p e n d i n g upon tube geometry and  t e m p e r a t u r e and i s most e a s i l y 3.1.2 G r i d Leakage N o i s e  The  second  is  shot n o i s e  is  the  the  and  i n the  a l g e b r a i c sum  positive by  grid  effect capturing  of n o i s e  i n tubes  current I  . The g components I and I . g g grid,  ions l e f t  the g r i d  results  i n the  I  of these  Fig.  I t can be  two  I g.  I  , a  •  g  f r o m the  capture  evacuation,  Grid emission  is a  or o f the p h o t o - e l e c t r i c  on t h e  o t h e r hand, r e s u l t s  f r o m the  e l e c t r o n s f r o m the main p l a t e c u r r e n t .  negative  Nuvistors  observable  tube a f t e r grid.  and  -  dependence  w h i c h the  experimentally.  o f e l e c t r o n s f r o m the  o f i m p u r i t i e s on  3.2.  leakage  o f two  of p o s i t i v e  (3.43.5)  for  grid  source  c u r r e n t f l o w i n g from the  from e m i s s i o n  result  important  found  cathode  two  The  grid  approximate  components upon g r i d b i a s i s shown i n  seen t h a t I  g r i d bias while components a r e  I  +  reduces  very  q u i c k l y to  v a r i e s more s l o w l y .  equal  i s the  potential  The  zero b i a s at  at which  the  51  I(na) -  2  - 1 0  -1 _-2  Pig.  grid  floats  3.2  on  Since smoothed by  open  these the  shot n o i s e .  Typical  by  two  space  the  Curve  circuit. currents arise  independently  charge they both  This noise  represented  G r i d Current vs G r i d V o l t a g e  occurs  at the  current generator  exhibit  and  full,  with  not  uncorrelated  i n p u t so i t can i  are  be  spectral  density  a w^  = 2Q  3.1.3  g  ( jig"! +  Flicker  The excess well  Jl~J  ), i n the p o s i t i o n  i n the  understood  3.1.  Noise  remaining  noise  shown i n F i g .  but  source  of n o i s e  plate current. i t i s thought  i n the  T h i s type to r e s u l t (3  the  emissivity  of t h e  are  g e n e r a l l y s l o w , hence the  triode  cathode m a t e r i a l flicker  is flicker  of n o i s e  or  i s not  from f l u c t u a t i o n s  in  6)  *  Such  fluctuations  noise  spectrum  contains  52 predominately  low  frequency  components.  e x p e r i m e n t a l l y t h a t i t can be frequency  range 1 c t o  frequency  dependent  referred w^  3,1.4  spectrum.  K must be  K = 10~  3  smoothing f a c t o r operation  f r o m the  the  P.  i s the  source  of n o i s e and  triode  P  earliest  field  cathode  as a d e c r e a s e  with  f o r most  tube as  p a r t of the  c  *  .  tying  in  for  This additional  multigrid  where I  This the  cathode  space-charge  anode c u r r e n t s  s i m p l y by a  grid.  i n the  shown t h a t P  smoothing f a c t o r  s  ,•I  c  , and  respectively additional  screen g r i d to  triode.  Noise  effect transistor  semiconducting  tubes,  current results  c a t h o d e and  E q u i v a l e n t C i r c u i t and Transistor  The  e^  Tubes  2 2 = I /1 +1 pVl rn s c p  i s avoided  u s i n g the  inverse  g e n e r a l n o i s e model, i ^ i s  anode t o a p o s i t i v e  I t can be  screen g r i d ,  and P  3.2  regarded  i s g i v e n by  an  the  7  other m u l t i g r i d  be  i ^ with  e x p e r i m e n t a l l y , but  I n p e n t o d e s and i s diverted  over  shot n o i s e , g i v i n g  in Multigrid  n o i s e w h i c h may  plate  the  the  found  50^ * ^.  random p a r t i t i o n i n g of the  are  For  been  represented  generator  P a r t i t i o n Noise  current  I  the  determined  within  1 3  adequately by  t o the g r i d , as was  = K/f.  tubes  50 Kc  I t has  Model  f o r the. F i e l d E f f e c t  ( f . e . t . ) was  devices discussed  one  of  the  i n d e t a i l i n the  (39) literature promising  *  ; but  in spite  s t a r t i t has  of t h i s e a r l y  and.apparently  never achieved widespread use.  The  the  53 principal of  r e a s o n s f o r t h i s have been t h e r e l a t i v e l y h i g h  f,-e.t.'s  c a u s e d by f a b r i c a t i o n  development  o f cheap, v e r s a t i l e  o u t p e r f o r m i n g them fabrication available  f.e.t.'s  and renewed i n t e r e s t  where  i s the low—noise  given f i r s t  analysis  by S h o c k l e y ^ * ^ 3  ).  For t h i s  of  i t s o p e r a t i o n based  to  s u f f i c e because outset  different type  that  as  control  a solid  state  current and  called  of  signals  of t h e o p e r a t i o n o f t h e f . e . t .  was  t h e n i n more d e t a i l by Dacy and qualitative  o f space l i m i t a t i o n s .  transistor  i s one o f v o l t a g e  so t h e f . e . t . i s most analogue  description have  I t s h o u l d be n o t e d a t completely  and i s n o t s i m p l y  and t h e j u n c t i o n  i s carried  carriers.  junction  control  a  special  tube.  transistor  exclusively transistor  rather  than  c o n v e n i e n t l y thought of  o f the vacuum  Another  difference  i s that  current  by m a j o r i t y  i s carried  carriers  by b o t h  F o r t h i s reason, the f . e . t .  a "unipolar" transistor  "bipolar"  transistors.  on t h e work o f t h e above a u t h o r s w i l l  i n the j u n c t i o n  minority  i n t h e i r use f o r  transistor.  between t h e f . e . t . i n the f . e . t .  however,  amplification  the s i s a s i m p l e  f r o m any j u n c t i o n  This process current  c a p a b l e of  i n commercially  t h e f . e . t . o p e r a t e s by a p r o c e s s  of j u n c t i o n  rapid  sources.  A quantitative  the  Recently  they are s u p e r i o r to j u n c t i o n  f r o m h i g h impedance  3 , 1 0  transistors  i n a l m o s t any c i r c u i t .  such a p p l i c a t i o n  Ross^  junction  and t h e  t e c h n i q u e s have i m p r o v e d , r e s u l t i n g  applications One  difficulties,  cost  to d i s t i n g u i s h  whereas  majority  i s sometimes  i t from the  transistor.  Both n-channel  and p - c h a n n e l  f.e.t.'s  a r e made b u t o n l y  54 the p-channel  type  i s described here.  applied  to the n-channel  current  polarities.  - 3.2.1  Theory  Fig.  3.3  changing  shows a s c h e m a t i c p i c t u r e  It consists  heavily  doped p - t y p e  can  a l l voltage  be  and  silicon  " g a t e s " of n-type  and  g a t e f o r m p-n  material.  The  extends  the p o t e n t i a l  given point.  "drain"  into  difference  to a  between c h a n n e l  flow.  current  f l o w s i n the p o s i t i v e  t e r m i n a l s t o w h i c h the names  I n the d e s c r i p t i o n below i t i s assumed  non  and  channel  are a s s i g n e d a c c o r d i n g t o the d i r e c t i o n  current  (a)  channel  of these i s  the c h a n n e l  C u r r e n t f l o w s t h r o u g h the  identical  between  i n t e r f a c e s between  A s s o c i a t e d w i t h each  region that  d e p t h d e t e r m i n e d by  between p h y s i c a l l y  p-channel  o r germanium sandwiched  junctions.  a carrier-depleted  o f the  s i m p l y of a c o n d u c t i n g " c h a n n e l " of  two  " s o u r c e " and  description  of F . e . t . O p e r a t i o n  f.e.t.  g a t e a t any  f . e . t . by  The  x-direction.  pinch-off operation  that  of  55  gate c a r r i e r depleted region  gs  (b)  circuited applied  consider  t o the  t o the  the  source  operation  F.e.t.  Schematic  3.3  Fig.  First  pinch-off  operation  (Vg  S  when the  = 0).  gate i s  A negative  d r a i n causes a c u r r e n t  I  short  potential  to flow  i n the  channel,  d At  any  p o i n t x,  the  approximately V(x) resistance reverse of the high  = I^I^x,  unit length.  bias with  bias  where B (see  carrier-depleted regions  t o meet a t P,  of c a r r i e r s  cause t h i s  the c  channel-gate  i s the  average  Fig. 3.3(a)).  i n t o the  current w i l l  l e a v i n g the  (see  needed t o cause the Since  d i m e n s i o n s and  junction i s channel  The  channel.  increasing  flow  to  cause the  The  current  P and  a l s o by  is  d g  depletion  c h a n n e l f r o m P t o the  F i g . 3.3(b)).  s o u r c e and  penetration  If V  drain  required  s o - c a l l e d " p i n c h - o f f " i s d e t e r m i n e d by  r e s i s t a n c e between the  channel.  on  i n c r e a s i n g x r e s u l t s i n a deepening  enough, s u f f i c i e n t  layers free  per  reverse  the  the  d e p l e t i o n l a y e r s to p e n e t r a t e  average  reverse  the  little  change i n c u r r e n t  bias  whole  b o t h of t h e s e q u a n t i t i e s depend o n l y upon materials*  to  will  be  device-  effected simply  by a f u r t h e r i n c r e a s e  absorbed across  depleted  region  the high  of the  absence the  regions  bias  impedance  current.  and l o w e r d r a i n v o l t a g e  current  penetration,  is relatively  pinch-off  than with  independent  as t h e v o l t a g e  this  e l e m e n t a r y argument, i t i s e v i d e n t  operated V  s  V  ds  c  even i n t h e  c u r r e n t *p$f,n  n  a  with r  a  c  x  zero  occurs  a t a lower  gate b i a s .  i s l a r g e enough t o cause p i n c h - o f f .  the channel pinched  eristics  Again  of the d r a i n v o l t a g e  long  d  of channel  the c a r r i e r  o f t h e d e p l e t i o n l a y e r s i s t h e same as b e f o r e , b u t  current  I  the channel,  The e f f e c t  of the i n i t i a l  is  of the c a r r i e r  i s a p p l i e d to the gate,  because  the  Any s u c h i n c r e a s e i s  e x t e n d p a r t way a c r o s s  of channel  shape  .  channel.  I f now a r e v e r s e depleted  in  as  Prom  t h a t when t h e f . e . t .  off, i tw i l l  ( F i g . 3.4) l i k e  those  exhibit  of a pentode.  Id(ma)  = 0 v  2.0 0.25 1.5 0.50 1.0 1.00 .5  -4  -8  -12 V (volts)  -16  -20  d s  Fig.  3.4  In the r e g i o n not  completely  T y p i c a l S t a t i c C h a r a c t e r i s t i c s of ^ F.e.t.  of operation  penetrate  where t h e d e p l e t i o n  the channel,  l a y e r s do  t h e shape o f t h e c u r v e s c a n  57 be  calculated  the  channel  from  and  a consideration  i t s effect  on t h e  of the p o t e n t i a l carriers  function i n  present there.  This  (3.9) calculation results  i s done c o m p l e t e l y i n S c h o c k l e y ' s p a p e r  i n e x p r e s s i o n s f o r the o u t p u t  transconductance  g', m'  and  the  conductance  * '• and  g^,  the  i / V c u r v e s i n terms o f t h e d e v i c e  &  dimensions  and  applied  characteristic again s i m i l a r 3.2.2  thus  gate p o t e n t i a l .  calculated  to t h a t  of a  equivalent c i r c u i t  g ^ and ideal  o f the l / V  i s shown i n F i g . 3.4  to  be  pentode.  c o n s i d e r a t i o n s o f the f . e . t . o p e r a t i o n ,  shown i n F i g . 3.5(a) can be  g^ a r e the q u a n t i t i e s f.e.t., C , C , , and ' gs' gd' 1  distributed and  portion  F.e.t. Equivalent Circuit  From t h e p h y s i c a l the  The  junction  the g e n e r a t o r s i  the theory of van  c  and  theoretically predicted  T  r  i  (see s e c t i o n s  quantities  because  i t i s i m p o s s i b l e t o extend  "ideal"  l e n g t h o f the  f.e.t.  3.2.4  and  the parameters theoretical  ones;.  The  These  however,  be  fabricated,  the g a t e - c h a n n e l and  and  r,  and  resis-  drain.  These  respectively.  CL  to the i d e a l  f o r the complete  junction for  small bulk  i n s e r i e s w i t h b o t h the s o u r c e  observed  3.2.5).  cannot  channel m a t e r i a l  r ^ supply feedback  and  by  the  S  g  the  together characterize  a r e r e p r e s e n t e d i n F i g . 3 . 5 ( a ) by r  r  of  r e p r e s e n t the n o i s e c a l c u l a t e d  f.e.t.  tances are l e f t  f o r the  C , r e p r e s e n t the e f f e c t sd  "ideal"  the f u l l  Shockley  In i t  c a p a c i t a n c e between the v a r i o u s t e r m i n a l s ,  der Z i e l  The  c a l c u l a t e d by  drawn.  f.e.t.  so  device d i f f e r  observed parameters  that from  are t h o s e o f t h e  the  58  (C*)  \AAA—0 r drain d  c  (a)  Basic Equivalent  w = 4kTr  d  w  s  d  g  = 4kTr  Circuit  source  (b)  Fig.  simplified will  normally  In t h i s to  equivalent  case g  Simplified Equivalent  3.5  »  Circuits  c i r c u i t shown i n F i g . 3 . 5 ( b ) .  be o p e r a t e d m  F.e.t. Equivalent  Circuit  The  f.e.t.  i n the p i n c h - o f f r e g i o n f o r l i n e a r i t y .  g^ and t h e " s i m p l i f i e d "  parameters are r e l a t e d  t h e " i n t r i n s i c " p a r a m e t e r s as shown i n E q n . 3.1.  The  " s i m p l i f i e d " and " i n t r i n s i c "  p a r a m e t e r s may d i f f e r  as much as  20% a t h i g h g ' . .  { } K  a  )  g  g  — ~m ~ 1 + g'r m s  m  g'  (b)  'o  5  1 + g'r m s e  ...(3.1) (c) '  C  = C gs  gs  (1 - g r ) (d) m s B  I t was shown i n s e c t i o n amplifier stage.  (1 4-  C , = C, gd gd  2.4 t h a t  B  the n o i s e charge  depends upon t h e u n f e d b a c k c a p a c i t a n c e  Apparently then '  C  g r,) m  o f the  of the f i r s t  and C ^ must be f o u n d gs gd  from  C' gs 1  i and  C g ^ f o r use i n c a l c u l a t i o n s .  for  the n o i s e parameters of the s i m p l i f i e d  b e e n a l t e r e d by f e e d b a c k  (see s e c t i o n  p a r a m e t e r s o f each c i r c u i t 3.2.3  Noise  Model  Noise  i n the f . e . t .  generators voltage  the  r  g  e  and r ^ .  g  have  also  Therefore the  are s e l f - c o n s i s t e n t .  i s represented i  c  i n F i g . 3.5(a) by t h e  i n the channel  The l o c a t i o n  The c o m p l e t e  of these  i n t h e tube  i s a semiconducting  differently.  3.2.4).  and e^ a s s o c i a t e d w i t h  t h e same as t h o s e  f.e.t.  circuit  however,  of F . e . t .  at the gate,  generators  resistors roughly  i  This i s not necessary,  and t h e t h e r m a l the p a r a s i t i c  generators i s  ( s e e F i g . 3.1) b u t b e c a u s e  d e v i c e , the noise i s produced  theory  of channel  and g a t e  n o i s e has (3 11 3 12)  been p r e s e n t e d There  i n two r e c e n t p a p e r s  b y A. v a n der Z i e l  '  ' *  have b e e n o n l y a few p u b l i s h e d r e p o r t s o f e x p e r i m e n t a l  verification  of t h e t h e o r y  does n o t g i v e as a c c u r a t e  and t h e y  a prediction  as does t h e t h e o r y f o r t u b e s this and  i s the d i f f i c u l t y r , so t h a t t h e i r d  can be c a l c u l a t e d .  g ,  and t h e o b s e r v e d  and  theoretical  channel  discussed e a r l i e r .  (3.13) *  from  performance  The r e a s o n f o r resistors r  n o i s e and  s. • feedback  showed however, t h a t i f r s  t h e maximum g^, t h e z e r o d r a i n v o l t a g e  noise at p i n c h - o f f , then the experimental  results  region.  and g a t e  of the n o i s e  i n measuring the p a r a s i t i c  Brunke  r ^ are c a l c u l a t e d  non—pinch-off  that the theory  c o n t r i b u t i o n s o f thermal  and Q  indicate  c a n be made t o a g r e e Ah o u t l i n e  throughout the  of van der Z i e l ' s  noise i n which noise  sources  theory of  are found  i n terms  of t h e o t h e r p a r a m e t e r s o f t h e f . e . t . f o l l o w s .  3.2.4  white  Channel Noise  i n F.e.t,  Channel n o i s e  r e p r e s e n t e d by i  noise  channel is  i n the f . e . t .  c u r r e n t by t h e r m a l  therefore n e a r l y equal  conductance. spectral  I t results  the  d e n s i t y of i  t o the thermal  modulation  f u n c t i o n of the source  and d r a i n p o t e n t i a l s .  approximately  f o r the  region of operation  and Q i s a c o m p l i c a t e d  t h e o r y was d e r i v e d f o r n o n - p i n c h - o f f  w i d t h , and  noise of the channel  i s the transconductance  bias,  o f the  i n the channel  i n the non-pinch-off  c  t h e same s o u r c e - g a t e  claims that i t holds long  from  The e x p r e s s i o n d e r i v e d by v a n d e r Z i e l  D  varying  i s t h e main s o u r c e o f  fluctuations  i s w . = 4kTg Q where g c max* max for  c  at pinch-off r  but slowly Although  o p e r a t i o n , van der Z i e l  i n t h e p i n c h - o f f r e g i o n as  as t h e d r a i n v o l t a g e i s n o t t o o l a r g e .  61  When the and i  Q  i s short  r ^ adds t o the i n the  by Eqn.  external  3.2.  densities the  gate  circuit.  spectral density  the  circuit  to  expression  = w  o  can  be  w,  w^,  g  currents  s  and  w  due  to r  noise  of i  are  c  r current  is  the  given  spectral  , r,, s d'  + w, + w d c  are  ignored  w r i t t e n by  and  .,.(3.2)  and  pinch-off  operation  i n s p e c t i o n of the  equivalent  be; 4kTr  (a)  noise  capacitors  assumed, t h e s e  The  a total  of  respectively.  w  If  thermal noise  to produce  external  channel noise  the  channel noise  In t h i s  of the  circuited,  w. (l  g ^ m  4kTr, d  1  s  s  -w-  • (b)  =  + g ' r )' m s  6  g» o  2  (1 + g'r )' m s  6  v  5  ...(3.3) 4kT (c)  w^  g^Q  = (1 + g'r ) m s  (note  2  that g  max  = g' m  at  e  &  Substitution Eqn* 3.4  f o r the  pinch-off)  of these  expressions  spectral density  of the  4kT  w  g»' m = (1 + g ' r )' m s' 6  r  6  W i t h the seen t h a t  the  output noise  noise  resistor  expressed R^  is just  i n Eqn. total  Qg' + .—^ g  3.2  noise  r  +  m  in  current.  ,2" d o .,2 m J g  .. .(3.4)  g  i n t h i s way, the term  results  i t can  i n the  be  brackets.  Because the output  conductance g  transconductance  i s much s m a l l e r t h a n the  Q  g , t h e c o n t r i b u t i o n from r i s much s m a l l e r m s t h a n t h e o t h e r s and ban be i g n o r e d . R i s t h e n g i v e n by 1  6  y  n  Eqn*  3.5(a).  R  (a)  n  «  r  +*r g m  s  T  B  ...(3.5)  (b)  . R « r n  (i_Q)+U_«fl-  s  °m  Substitution  o f g = g / ( l - g r ) i n Eqn. 3.5(a) ^m nr m s 1  6  in  (b), r e l a t i n g  expected  6  m  this  to the measurable t r a n s c o n d u c t a n c e .  as was t h a t type  so t h e f i r s t t e r m  of the tube.  of behaviour  i s hot surprising  Gate N o i s e  i s inversely  The e x p e r i m e n t a l  predicted.  This  i n v i e w o f t h e many  approximations resistors.  i n F.e.t.  In a d d i t i o n to the channel n o i s e , there w i l l in l/f  any g a t e  leakage  c u r r e n t * and e x c e s s n o i s e w i t h  f r e q u e n c y dependence i n t h e c h a n n e l  leakage  i n tubes, the gate  independent noise.  results  ( s e e s e c t i o n 4.3) b u t t h e v a l u e  made i n a c c o u n t i n g f o r t h e n o i s e o f t h e p a r a s i t i c  3.2.5  Qis  o f 3.5(b) i s  of the f . e . t .  o f Q was 30% h i g h e r t h a n t h e o r e t i c a l l y discrepancy  results  u  Thus t h e n o i s e r e s i s t o r  tp g  verified  n  t o be n e a r u n i t y ,  negligible. related  R  °m  components I  +  leakage  current.  be s h o t n o i s e characteristic  As w i t h  grid  c u r r e n t i s made up o f two  and I ~ e a c h o f w h i c h e x h i b i t  T h i s n o i s e i s r e p r e s e n t e d as i g » V  "the w h i t e  full  shot  component  of  gate  noise  is  accounted  voltage  f o r which w f o r by  generator  constant  K being  The  noise  howeverj  one  i n the  sources  frequency  that results  noise  to the  this is w  e x h i b i t e d by tube.  I t resembles  when r e p r e s e n t e d 2  the  by  For  uncorrelated with  the  the  R  n  the  The  direct  There i s  f . e . t . w h i c h has  i s the  correlated  no gate  o f the  channel  g r i d noise  that  power s p e c t r u m  i s near 0 . 4 ^ * 3  channel  little  of  a t the  1 2  ^.  i  gate, is  noise  error  v  but  i t can be  assumed  124 *<  «  With t h i s  assumption,  model o f the f . e . t . c o n f o r m s t o t h e g e n e r a l model i n u n c o r r e l a t e d noise sources represent a l l n o i s e .  f.e.t.  then;  I  =  T  | l  = r (l-Q) + s  +  ++  |  |LLl ~ |g  I g  L and  the  g  correlated with  the n o i s e w h i c h two  tubes,  circuits.  a current generator  where H ( z )  2  noise  noise  have a l l had  induced  (3 t o be  excess  with  from c a p a c i t i v e feedthrough  = H(z)4kTB w C g n gs  partially  now  This  i n tubes at h i g h f r e q u e n c i e s .  noise  i t was  Nuvistor noise  of n o i s e  gate.  The  experimentally.  a n a l o g u e i n the  noise  occurs  same.way as  discussed u n t i l  t u b e and  type  11~| ) .  (|lg| +  g  f r e q u e n c y - d e p e n d e n t p a r t of t h e  determined  a n a l o g u e s i n the  low  the  = 2Q  t i( l z 7 )14 4 KkIT ' tRt w Ctf " ++ H /2Qe* n gs * * 2  2  2  2  Q/g . m  2 The source  is  important  In n u c l e o n i c  input  input,.  a white The  t h e r e f o r e to  C^;  so t h i s  of t h e an  term  i n 1^ makes  at high frequencies  spectral  effect cause  final  amplifiers,  capacitance,  voltage with the  dependence o f t h e  of n o i s e  edance. net  to  however, 1^ term  and  high  this input  i s s h u n t e d by  contributes a s  frequency-dependent gate  apparent  increase  in R  n  to  the  noise  d e n s i t y of H(z)4kTR (Cg /C^.) n  imp-  noise  to  64  B ' = B ( l + H(z)C /C,)» n n gs t'  The  because H(z)  «  =0.4,  and  C  3.3  i s generally O  .  J  small  C, .  gs  '  increase  t  Noise Model f o r J u n c t i o n T r a n s i s t o r s  j u n c t i o n t r a n s i s t o r s . 1^  For referring  the w h i t e n o i s e  (see F i g . 3 . 6 ( a ) ) t o the circuit.  sources input  I n the b a s i c n o i s e  and  B  r  clan be  found  of the b a s i c T n o i s e  o f the  common e m i t t e r  model, i  represents  by model  equivalent  shot  noise  in  e  the  emitter  resistor,  current,  and  i  The  transistor  the  collector  i n p u t by  the  e^  thermal noise  partition  noise  i n the  i n the  also e x h i b i t s l / f noise leakage  flicker  current. constant  This  t r a n s i s t o r s , K v a r i e s widely^-*^*^ experimentally;  hence i t w i l l  and  n o t be  collector i n the  can be  K as w i t h  base  the  spreading c u r r e n t ^ * "'"^ •  emitter  current  represented other  must be  discussed  at  devices.  and  the 1  For  determined further.  collector  emitter O  o  base  base  (a)  B a s i c J u n c t i o n T r a n s i s t o r N o i s e Model  base  /  65 collector  2L  vyv  a. e e  Ve  =  emitter  (b)  Common E m i t t e r N o i s e M o d e l f o r Loop A n a l y s i s  Pig.  For noise  the  3.6  T r a n s i s t o r Noise  c a l c u l a t i o n of  model i s m o d i f i e d  as  equivalent  on  base has the  collector source  are  been t a k e n as  assumption that current  the  f «l/2-n;r C  found  as  follows:-  Let  e  = e  + e  n l  x l  external voltage  respectively,  and  sources.  loop  e  l  and  e •= e 2  s o u r c e s i n the  e^  and  e  n 2  equations  are  and  .  has  g  s i g n a l and  x 2  + e  first  the  f o r the  C  ;  n 2  IT  are  <r ) e  sources,  been  ignored  circuit,  the  from each  e  second  respective  basic  A l l current  where  and  circuit  the  voltage  From t h i s  r e s u l t i n g f r o m the  be  The  equivalent  input,  can  ±  input noise,  shown i n F i g . 3 . 6 ( b ) .  s o u r c e s have b e e n changed t o t h e i r the  Models  x l  noise  and  e  x 2  loops  internal  noise  then:  " ...(3.6)  (  (r  + Z e  (1-a)) c  Solving  for i  e  I  = ( Z  If e  xl  a  ^  ^  this  e  (a)  i n  2 s  by C r a m e r s r u l e  ( Z  s  +  r  _b + e  +  r  r  ^C e r  +  Z  -  }  c  U  e  -  a  l_ D  ( r  +  e  r  a  then i  u  can be e x p r e s s e d  where Yl  l i e -. f xl  =  f  e  c  Z  )  ..(3.7)  e o Z  c u r r e n t i s assumed t o r e s u l t  P ^'  i  gives*  T  — xl  from  a voltage  as,  'x2  nl  e  n2  = °> ...(3.8)  ( Z  (b)  (Note  e., -  f  t h a t Y| d i f f e r s  because found  i  e ^  f r o m Eqn.  (a)  3.7  to  (c)  b  +  *+)  the t r u e f o r w a r d t r a n s c o n d u c t a n c e  Y  f ^ r  TI ^ — f r  T a k i n g now the E q n s . 3.10  source impedance).  Y£  can  Y^ be  be;  •:(•!•• - ocZ ) e c + r ) pr + Z (l-tx)l + r Z s e L e c 'J e (  TJ. = f ~ Tz v  b  from  r  i s i n s e r i e s w i t h the  x  < >,  s  +  (1 f Z /Z ) + Z /8 s' c  (when ^  p  « r  e  « Z  Uben  c  and  r  Z  e  s  « Z  « Z  c  )  c  ...(3.9)  )  e  r  the s i g n a l  and e a c h n o i s e s o u r c e s e p a r a t e l y *  f o r the c o l l e c t o r  c u r r e n t can be  found.  67 (a)  signal  (b)  0  e. : e, in'  emitter  noise  (c)  base  (d)  partition  e  noise  e  noise  l  = e  l  ~ b  5  6  e  5  e, = 0 1  e  2  0  2  : e ' 2  0  cs  = T' e. f xn  ce  = T' e (1 f e  i  = e  e  e  i  + Z /Z ) s' c  i . = f • e, cb f b  =-i Z i p c ce  - T ' i (2 e + r + r ' f p s e . b  ...(3*10)  (In equations  ( b ) , ( c ) and ( d ) , i t was assumed t h a t r , r , « Z ). e  From t h e s e of n o i s e  c a n be r e p r e s e n t e d  generators Z  g  expressions  as r e q u i r e d .  f o r t h e shunt  i t i s evident that the three  a t the i n p u t of the a m p l i f i e r  I f one c o l l e c t s  current generator  c sources  by two  a l l terms t h a t depend on  and a l l terms t h a t do n o t  depend on Z , f o r t h e s e r i e s v o l t a g e g e n d r a t o r , spectral  o  the r e s p e c t i v e  densities are: 2kTr  (a)  w  L  = a  a  o_ ...(3.11)  (b)  w  = 4kTr* + 2kTr + w b e  Considerable effected best  exhibits impedance  simplification  i f a particular  low-noise  2Q I — e| e 2 a  a noise f i g u r e  than  a  (r + r ' ) ' e b'  expressions  i s considered.  at present  of l e s s  -  a  of these  transistor  transistors  1  c a n be  One o f t h e  i s t h e 2N930 w h i c h ldb^ *"^^.  o f t h e 2N930 i s 8 p f s h u n t e d  3  The  collector  by a p p r o x i m a t e l y  20 megohm;  68  so  the  will  s e c o n d t e r m of 3.11(a) can be  be  operated  w e l l below the  p a r t i t i o n n o i s e ; hence i n the e x p r e s s i o n s  (a)  w  Jj  T  2Q I * = — ( b ) p  cut-off  The  frequency  to l i m i t  the  Q  and  w  gives:  g  2Q w  transistor  zz*. <X * I n c o r p o r a t i n g t h e s e m o d i f i c a t i o n s  |oc|  f o r w^  ignored.  w  «  4kT(r» + 2r ) + u e  I e  ' • ( r + r») •. e u  e  p  ...(3.12)  Since  r ^:kT/Q I , e  e  2kTr /p  L T  the  ^  junction transistor  I /3 e r  and  R ^ n  I t must be the  transistor  either  are  section  3.6  constants  b•  course  of t h e  resistor  t h a t even w i t h  istors  theoretically  o f the  d e v i c e s d i s c u s s e d so f a r .  3.4 3.4.1  1^' and  estimated  R  n  term  ignored. are  then,  parameters f o r  a l l t h e t e r m s t h a t were  apparent  ignored.  these  can be  c a l c u l a t i o n w o u l d have  or the  l / f n o i s e was  and  This  as  + 2kT/Q I . . ' *-e e  o p t i m i s t i c because  the n o i s e  I n a d d i t i o n , the  =  expressed  of magnitude.  first  s t r e s s e d that these  i g n o r e d d u r i n g the to  the  the  r ' + 2r b e  (b) can be  same o r d e r  t h e r e f o r e much s m a l l e r t h a n  For I  second term of  + terms i n r ^ o f the  g  is  the  e  helpful  g i v e much p o o r e r  leakage  It will  be  added  current. seen i n  approximations,  trans-  noise performance than  any  Modern " E x o t i c " Low—Noise A m p l i f i e r s The  Tunnel  Diode  The  tunnel  or E s a k i d i o d e  has  o f t e n been m e n t i o n e d i n the  69 literature of these  as  a u s e f u l low-noise  claims, noise  amplifying device.  f i g u r e s o f 4 to  5db  (3 17 communications  a m p l i f i e r s are  cited  *  figures obtainable  are  this  so  is  a "low—noise"  high  minimum n o i s e  that gives  the  lowest  ),  noise 3  t r a n s i s t o r s ^'"''^ . a l l  nucleonic diode  they  resistance amplify 3.4.2  has  of the  the  diode  effect  tunnel  \  2 0  the s o u r c e  Since  junction low  tunnel diodes  for  argument, the  tunnel  and  and  even more b a s i c  therefore  provides  load r e s i s t a n c e .  resistive  upon the  diode  and  u n s u i t a b l e f o r an  the  device  at  resistance device  sources  the  p o r t i o n of  system g a i n .  the  The  c a n n o t t h e r e f o r e , be  .With.,  negative  used  to  signal.  Parametric  Two  no  from t h i s  as b e i n g  with  f i g u r e s below 1 db  s u p e r i o r to  Apart  "cancelling"  nucleonic  terminations  tunnel  transistors  r e g a r d l e s s of f r e q u e n c y * 3  are v a s t l y  dismissed  power g a i n by  high  that for nucleonic  i s obtained  1  I t i s a negative  capacitive  figure  give noise  applications.  can be  reason.  charge  Nuvistors^ * ), f . e . t . ' s * '  frequencies,  At  f r o m t u b e s and  shown i n s e c t i o n 2.3  the  1 9  .  t h a t i n c o m p a r i s o n the  amplifiers  3  frequency  device.  However, i t was  tubes^ *  support  18)  *  the n o i s e  at l e a s t  for high  3  frequencies,  In  other  considerable  A m p l i f i e r s and  types  interest  Masers  of low-noise of l a t e  are  a m p l i f i e r s t h a t have  the  parametric  caused  amplifier^ * "^ 3  (3*22) and  the Maser  amplifiers proper  *  .  Like  the  are u s e f u l mainly  tunnel diode,  at frequencies  o p e r a t i o n of t u b e s o r t r a n s i s t o r s .  both  of  these  too h i g h f o r I f they  are  to  the be  2  70 useful to The  f o r a m p l i f y i n g p u l s e s , then,  convert  t h e low f r e q u e n c y  m o d u l a t o r must add l e s s  w o u l d i f t h e low n o i s e  pulse noise  a m o d u l a t o r must be d e v i s e d signal  than  capabilities  to a modulated r f s i g n a l .  a conventional a m p l i f i e r  of the parametric  amplifier  •or Maser a r e t o be r e a l i z e d . One  m o d u l a t o r t h a t shows p r o m i s e f o r s u c h l o w - n o i s e  combines m o d u l a t i o n w i t h  parametric  work  a m p l i f i c a t i o n through the (3 • 23  use *  o f two v a r i a b l e c a p a c i t o r s ' *  constant  •.  The b r i d g e  amplitude  lower than  i s pumped a t r f and g i v e s  until  modulates the output. the input  (varactors) i n a bridge  a signal  impedance  i s considerably  so power g a i n as w e l l as m o d u l a t i o n i s a c h i e v e d .  published  *  .  circuit  cps and i n d i c a t e t h a t t h e c i r c u i t  l/f  type  of the  at least other  then,  that while  shows g r e a t p r o m i s e f o r l o w - n o i s e  amplifiers  noise  i s relatively  I K w h i c h compares u n f a v o u r a b l y  frequencies,  fact  have r e c e n t l y been  However, i t has an e q u i v a l e n t n o i s e  c a n be c o n c l u d e d  amplifier  The  The r e s u l t s o f  with  below  f r e e from resistor  t h e B^s f o u n d f o r  devices.  It  low  signal;  The measurements were made a t f r e q u e n c i e s  100  noise.  an o u t p u t o f  s e e n by t h e l o w - f r e q u e n c y  n o i s e measurements made on t h i s  *  u n b a l a n c e s t h e b r i d g e and  The r f o u t p u t impedance  circuit  at frequencies  of interest  a conventional  negative-resistance application too.  modulator-  a m p l i f i c a t i o n at  i t c a n n o t compete y e t w i t h more  conventional  f o r nucleonio  t h a t m o d u l a t i o n c a n n o t be a c h i e v e d  than  the b r i d g e  without  amplifiers. adding  more  a m p l i f i e r r u l e s o u t t h e use o f  parametric  a m p l i f i e r s , and Masers f o r . t h i s  '  71 The p p s s i b i l i t y the  p-n p a r t i c l e  parametric  of u s i n g the n o n - l i n e a r  detector  capacitance of  as t h e v a r i a b l e r e a c t a n c e  a m p l i f i e r was c o n s i d e r e d  early i n this  study.  i d e a had t o be .abandoned however, b e c a u s e t h e b i a s f o r d e t e c t i o n and a m p l i f i c a t i o n a r e n o t e a s i l y energy r e s o l u t i o n of d e t e c t e d layer  capacitance  voltage  curve  conditions  compatible.  bias.  a m p l i f i c a t i o n requires a high  versus  This  Linear  r e q u i r e s a deep d e p l e t i o n  i n t h e d e t e c t o r hence a l a r g e r e v e r s e  hand, p a r a m e t r i c  3.5  particles  ina  On t h e o t h e r  slope  hence a s m a l l  of the  reverse  bias.  Summary o f T h e o r e t i c a l R e s u l t s  With the b r i e f  arguments o f t h e p r e v i o u s  s e c t i o n , the  modern " e x o t i c " a m p l i f i e r s have b e e n shown t o be u n s u i t a b l e f o r nucleonic  applications.  The c h o i c e  r e d u c e s t o one o f t h e f o u r in  3.5.1  Choice  expected noise  o f Tube, N u v i s t o r  The p a r a m e t e r s I  T  i-i  summarized  The n o i s e  sources  i n the n o t a t i o n of the general  a comparison of t h e i r  i n Table  3.1.  therefore  "conventional" active devices  s e c t i o n 3.1 t h r o u g h 3.3.  been e x p r e s s e d  o f an i n p u t d e v i c e  and R  f o r the four noise  model  c a n now be made.  and F . e . t .  Types  f o r the four devices are n  discussed have  so t h a t  72  —  .  R n I  Tubes  +  +  g  + I g" 1  1 g  f.e.t.  I  +  +  June.. Trans,  (.4)4kTB toV n  Ig  g  for  equations  (2.5<C<4)  fl-  ^  3.1  of Table  Theoretical  nucleonic amplifiers.  (.67<Q<1)  r ' + 2r o r r / + b e p 0 1 T *e e  Noise  3.1 g i v e a n o t h e r  reported noise f i g u r e ) f o r choosing low-noise  C/gm ^  r  Table  The  (2.5<C<4)  s  Ie/P  ^  C/gm g  1  Nuvistors  from  I  Parameters  criterion  suitable  active  (apart devices  I f i t i s assumed t h a t t h e  (34) grxd  leakage  quality  currents *  tubes, then  transconductance, latter  affects  when C_j. ^  a r e r o u g h l y t h e same f o r a l l h i g h  the b e s t tube  and t h e l o w e s t p a r a s i t i c  the n o i s e mainly  The t u b e s  the h i g h e s t t r a n s c o n d u c t a n c e with  a g  a g  o f 60ma/v.  is for  also this  triode^  single  currently  Besides having  c o n s i d e r a b l y cheaper study. 3 i 2 6  ^,  Other  The  parameter i s the  available  that  exhibit  a r e t h e WE 416B microwave  o f 50ma/v, and t h e P h i l l i p s  m  capacitance.  a t low d e t e c t o r c a p a c i t a n c e  ; so t h e most i m p o r t a n t  transconductance*  m  i s t h e one w i t h t h e h i g h e s t  E810P  slightly  (7788) p e n t o d e  t h e E83F p e n t o d e ^ * 3  were n o t c o n s i d e r e d b e c a u s e t h e i r  2 7  ^  with  h i g h e r g » t h e E810F m  t h a n t h e 416B so i t was  commonly u s e d  triode  tubes  such  chosen  as t h e 417A  and t h e 6AK5 p e n t o d e ^  n o i s e performance  3  has a l r e a d y  73 j  been s t u d i e d that  and  extensively  and  cannot  o f the newer E 8 1 0 F . '•' The c r i t e r i o n of h i g h e s t g also ° m f,e.t*'s*  Hence t h e  gave t h e h i g h e s t g  a t the t i m e  m  theoretical  and  the  experimental  2N930 was  chosen  However, the f a c t  v e r y low  c u r r e n t * a f e a t u r e not  3.5.2  i n T a b l e 3*1  r£ and  g  C, » t  C  gs  available  on t h e  in transistors,  the extreme v a l u e s f o r c and gate  73il  term  other parameters  T a b l e 3.2  C.  Q are  taken;  are i g n o r e d  (assume are  Bias Condition  I  25pf  I = 30 ma p  lOna  45  Nuvistor (7586)  lOna  225  t o 400.O-  8pf  I = 8 ma P  f.e.t. (2N2386)  lna  225  t o 333.fl.  20pf  I = 2 ma s  g = 55 m  g =10 . m g m 6  =3  >  lua Table  3*2  5000 -rt250  Theoretical  SL  taken  results:  Tubes (E810F)  June. Trans (2N930) 55na  to  could  Performance  (range)  n  noise  criterion.  specifications, R  ( e . g * 2N2498).  s t r e n g t h o f i t s low  o f t e n found  t y p i c a l v a l u e s f o r the  from m a n u f a c t u r e r s '  F.e.t.'s  i t e x h i b i t s h i g h c u r r e n t g a i n at  the frequency-dependent  ) ; and  started*  also.  as an a l t e r n a t i v e  Comparison of Noise  If r ,  that  the 2N2386 w h i c h  c o n s i d e r a t i o n given, f o r the  mainly  figure.  have b e e n u s e d  t o compare w i t h  a p p l i e s to the N u v i s t o r s  s t u d y was  are now  2N2386 a p p l y t o t h e s e newer t y p e s The  expected  c h o i c e o f t h e 7586 and  with higher transconductance The  be  6pf  I = .01 e  ma  r  6pf  I = 0*2 e  ma  r  Comparison of Noise  S =  180  8 =  200  Parameters  ma/v ma/v ma/v  74 T h i s t a b l e g i v e s an that the  can be  expected.  devices  is  In s p i t e  can be r a n k e d  minimum n o i s e  levels.  b e s t because  i d e a o f the  magnitude o f n o i s e  of the  i n the  u n c e r t a i n t y i n c and  order  shown f o r  F o r most d e t e c t o r  i t has  the  lowest  R  •  N u v i s t o r may  be  capacitances,  s u p e r i o r because  Q,  expected  However, as '  n zero, the  parameters  the  E810F  C, t e n d s d  of i t s low  to  parasitic  capacitance. The because  f . e . t . might be  i t s product,  1^^  However, i n p r a c t i c a l detector noise current is  added  i s lower  as  to o u t - p e r f o r m (see  Eqn.  a p p l i c a t i o n s 1^ has ( c . f . s e c t i o n 2.2)  i s a l w a y s swamped and  roughly  l a r g e as  the  f o r the  comparable t h e o r e t i c a l l y the  expected  except  net  2.16  the  for N ^  the  f.e.t.  shunt c u r r e n t  f o r the  The  ).  m  bias resistor  so  Nuvistor.  Nuvistor  two  and leakage  generator  are  therefore  lower capacitance  of  Nuvistor. The  two  transistors  s e t s of p a r a m e t e r s f o r t h e  are v a s t l y  inferior  t o any  2N930, show t h a t j u n c t i o n  of the  other  devices  e x c e p t when the d e t e c t o r l e a k a g e c u r r e n t i s l a r g e . By e q u a t i n g the p r o d u c t R ( l + I,) f o r the 2N930 and the 2N2386, i t can be n L d ' T  r  shown t h a t t h e I-. ^ d  two  devices  0 « 0 5 / S R iz£ l u a n r  r  (R n  g i v e the  i s f o r the  same n o i s e f.e.t.).  c h a r g e when S i n c e most  detectors  (3 29 ) have l e a k a g e  c u r r e n t s much s m a l l e r t h a n  t r a n s i s t o r was nucleonic  r e j e c t e d as  amplifiers,  A more d e t a i l e d the I^'s  end and  o f C h a p t e r 4. R 's n  and  a suitable device excluded  t h a t time the  have been d i s c u s s e d  v a r i o u s parameters i s reduced*  * for  from f u r t h e r  c o m p a r i s o n of the By  lua,  so t h e  devices  ' the  junction  low-noise study. i s given  experimentally  at  determined  u n c e r t a i n t y i n the  75  4.  From t h e o r e t i c a l g ^ s , B's, and I  typical relative  noise  accurate  t o be  c o n s i d e r a t i o n s and a knowledge o f *Sf  i t was  p o s s i b l e to estimate  performance of tubes,  junction transistors. not  MEASUREMENT OF NOISE PARAMETERS  However,  the  N u v i s t o r s , f.e»t.'s and  the parameters found  enough f o r use i n d e s i g n i n g a m p l i f i e r s ,  i n t h i s way and had  s u p p l e m e n t e d by t h e measurements d e s c r i b e d i n t h i s  chapter. The m e a s u r i n g t e c h n i q u e s described literature  in detail  The measurements  that  are d e s c r i b e d i n d e t a i l f o r  o n l y , b u t t h e same methods were u s e d f o r N u v i s t o r s  f.e.t.'s with  4.1  b e c a u s e t h e d e s c r i p t i o n s g i v e n i n the  do n o t e x p l i c i t y m e n t i o n a l l t h e p r e c a u t i o n s  must be t a k e n . tubes  were n o t o r i g i n a l , b u t t h e y a r e  the m o d i f i c a t i o n s  Tube and N u v i s t o r  4.1.1  noted.  Parameters  G r i d C u r r e n t Measurement  Techniques  I  f o r t h e E810F and  +  g  and I ~ were e s t i m a t e d g  the n e t d . c . g r i d  and  leakage  current I  7586 f r o m  measured w i t h t h e  circuit  shown i n F i g . 4.1. The m e a s u r i n g s e q u e n c e circuit  open and t h e g r i d  s t a r t s w i t h the key i n the g r i d  at a potential V g  condition, flows the  the potentiometer  i n the galvanometer.  - I R . g g  P^ i s a d j u s t e d u n t i l The k e y i s t h e n  r e s i s t a n c e of P-. i s much l e s s  Under  this  no c u r r e n t  c l o s e d and, s i n c e  than R , the g r i d  potential  we  76 AVQ  50K  (cours£) 2  v o  P;  * K IK  V  P  AVO  t  VEVM 27K,  GND  P i g . 4.1  changes t o V^. the  tube  until The  Current Test  T h i s change i n g r i d  the galvanometer reads  grid voltage  Circuit  potential  and d e t e c t e d by t h e g a l v a n o m e t e r .  impedance I  Grid  i s a m p l i f i e d by  Adjustment of P^  z e r o a g a i n makes V^ e q u a l t o  c a n t h e n be measured a c r o s s t h e r e l a t i v e l y low  o f P^ and t h e g r i d  leakage  current calculated  t o be  = V /R .  4.1.2  Grid  C u r r e n t Measurement R e s u l t s  Values  of I  region of u s e f u l plotted  plate  against V . g  i n P i g . 4.2.  were o b t a i n e d  i n t h i s way t h r o u g h o u t  c o n d i t i o n s by v a r y i n g V ^  Typical  From t h e s e  the  and R^, t h e n  cur/ves f o r t h e E810F a r e shown  curves  +  —  I and I c a n be e s t i m a t e d b e c a u s e g g (4 1) of t h e known e x p o n e n t i a l b e h a v i o u r o f I a t low c u r r e n t *•«:..  77 - 2.0na  -2.0  -1.0  -1.5  V (volts) g  P i g , 4.2  For d a t a was i n the  convenience  plane  the  7586  4.1.3  The  the  curves  gives  the  constant  I  and I,  (Note:  grid  current  constant = I  1^  4 I  8  &  f o r the E810F and  Fig.  ; &  4.4  Nuvistor.  K Measurement  parameters R  were f o u n d by  the  q  and  Technique  K representing  resistive  s y s t e m shown i n F i g . 4.5*  tube b e i n g  of  curves  Curves  b i a s p o i n t s , the  of p l a t e c h a r a c t e r i s t i c s .  and  noise  i n choosing  t h e n p l o t t e d as  F i g . 4.3 for  T y p i c a l Grid Current f o r E810F  shot  and  s u b s t i t u t i o n method  This  s y s t e m c o n s i s t s of  t e s t e d , w h i c h a c t s as a p r e a m p l i f i e r , a  post—amplifier  which d e f i n e s  the  flicker  p a s s band and  using the  high-gain  a Hewlett-Packard  J _  50  J  I 60  I  I  70  l_  I  80  I  I  90  t  I  ,  100  Eb(volts) F i g . 4.4 Grid Leakage Current f o r the 7586 Nuvistor  I  110  79 400D VTVM w h i c h s e r v e s  as a d e t e c t o r .  VTVM i s , f o r a l l p r a c t i c a l flicker  noise  resistor small  R^.  purposes,  o f t h e tube p l u s This i s ensured  t h a t the g r i d  and  by u s i n g  a low-noise  I Pig.  circuiting e^ the  new n o i s e v o l t a g e  spectral of the  GND  circuit;  spectral  4.5  noise  making  so  R^  i n the load i s n e g l i g i b l e ,  R e s i s t i v e S u b s t i t u t i o n Test System  procedure  c o n s i s t s of f i r s t  and o b s e r v i n g  e *2  resistor  R^ g e n e r a t e s  a noise  with  n  ^/  B x  *  y  raan  i t i s assumed  t o the i n p u t o f t h e t u b e .  voltage  R^ and o b s e r v i n g current  the i n p u t  so t h e a d d i t i o n a l n o i s e  d e n s i t y 4kT |z^ j  short-  t h e rms n o i s e  i n s e ^ i n g the t e s t  s u b s t i t u t i o n measurements* thermal  resistor  |  d e n s i t y 4kT/R^ i n p a r a l l e l  the t e s t  of the t e s t  post-amplifier.  the i n p u t g r i d  on t h e VTVM, t h e n  noise  i s negligible,  current  to the  due t o t h e s h o t and  by making the g r i d  noise  I  The e x p e r i m e n t a l  entirely  the thermal  current noise  so l a r g e t h a t t h e t h e r m a l  The n o i s e p a s s i n g  with  impedance  added by R^. h a s resistive  t h a t R^ d e l i v e r s However,  i t was  full found  80  i n these  measurements t h a t t h e s h u n t i n g  appreciable Miller  effect  even a t moderate f r e q u e n c i e s , b e c a u s e of t h e l a r g e  capacitance  of the t r i o d e s being  tested. —2  taken  o f Z. was in  i n t o account,  When t h i s i s  —2  t h e n o i s e v o l t a g e s e^ and  measured a r e  g i v e n by E q n s . 4.1 and 4.2*  -o©  if-  (4kTB  + |)  n  |A(f)|  0  e  +  5-^5—'  + f ) | A ( f ) | df 2  U"*> T )  n  2  2  n  0  (where T. = R , C ) in tin  The and case  measurements were a l l made w i t h  differentiation  •••(4*1)  4kTR,  (4kTR  =  (where A ( f ) i s  the g a i n f u n c t i o n )  -oo -2 2  df  2  time  constants,'!'.  ...(4.2)  single,  equal  The i n t e g r a l s  have b e e n e v a l u a t e d p r e v i o u s l y ( s e e C h a p t e r  integration  for this  2.2) so t h a t  —2 ' —2 e^ and c a n be w r i t t e n a s ;  -2 l e  kTR =  n 2f  „ K 2  A  (where A i s t h e n o m i n a l mid-band i  -2 2 = e  By  kTR  n  2-r  kTR,  —  2lT(l+x) 2  taking the r a t i o  4^ r  2  of these  ...(4.3)  A(where x = T. /T) in  equations  R  gain)  n  c a n be f o u n d  (4.4)  to be:  81  U  )  n  (b)  K  (l~y)(l+x)  =  = —^-2 (1+x)  " M  2  U  - If  h  (c)  e  r  \  e  Y  =  = a  e  l  -  n  / , e  2  }  H  I n E q n . 4 . 5 ( b ) R^ i s t h e a p p a r e n t n o i s e correction for flicker  o r i n p u t time  Eqn* 4 . 5 ( c ) R^ i s t h e combined s h o t Taking  constant, and f l i c k e r  the d i f f e r e n c e b e t w e e n two v a l u e s  different  frequencies  g i v e s Eqn* 4.6  >^(4*5)  resistance  without  while i n noise  resistor*  o f R^ measured a t  f o r K.  AR"kT K =  With the r e s u l t s R  n  is  Af -  expressed  and K p r o c e e d s as f o l l o w s . found  ...(4*6)  n  i n this  From t h e v o l t a g e  arid c o r r e c t e d f o r t h e i n p u t  o f R" measured a t d i f f e r e n t n E q n * 4.6  t o f i n d K.  way,  time  time c o n s t a n t s  the c a l c u l a t i o n ratios,  constant.  of  R^  Values  are then used i n  F i n a l l y R^ i s c o r r e c t e d f o r t h e  flicker  c o n t r i b u t i o n to give R . n The measurement calibration  i s independent of the g a i n  o f t h e s y s t e m ^ making t h e r e s i s t i v e  method  s u p e r i o r t o any d i r e c t  4.1*4  R  n  and K Measurement  measurement  and  absolute  substitution  method.  Results  The measurements were made t h r o u g h o u t t h e u s e f u l r e g i o n o f operation  f o r two E810F t u b e s and f o r two 7586 N u v i s t o r s  as at selected biases f o r 8 other ESlOF's.  as w e l l  Two test r e s i s t o r s were used as  82 a c h e c k , and t h e measurements were made a t t h r e e v a l u e s o f T*j  0.08, 0.8, and 8 u-sec.  Prom t h e s e measurements, R  were computed as i n t h e f o l l o w i n g c a l c u l a t i o n  R  and K  f o r one o f t h e E 8 l O P  tubes. Table  4.1 below shows t h e measured d a t a .  column g i v e s t h e p l a t e l o c a t e s the data  s u p p l y v o l t a g e and p l a t e  i n the plate  The  first  current which  characteristics,  e^ and e^ a r e  t h e rms n o i s e v o l t a g e s i n a r b i t r a r y u n i t s measured w i t h t h e VTVM, the In  second this  value  case,  t h e two v a l u e s u s e d  e^ i s t h e n o i s e circuit  o f e^ b e i n g f r o m  the second  were 100 and 200 ohms,  c o n t r i b u t e d by t h e p o s t a m p l i f i e r w i t h t h e t e s t  r e p l a c e d by i t s a p p r o x i m a t e  most o f t h e measurements, t h i s s m a l l , b u t when t h e p l a t e resulting  impedance.  In  c o n t r i b u t i o n t o t h e n o i s e was  gain,  circuit  was l o w ,  a c o r r e c t i o n h a d t o be  factor too.  v  In  output  c u r r e n t i n the t e s t  i n a low f i r s t - s t a g e  made f o r t h i s  resistor substituted.  bb  Y  h  e  l  e  2  e  0  200v  20ma  100  1.50  2.18  .30  200v  20ma  200  1*50  2.56  .30  T a b l e 4,1  D a t a f o r E810P  T=  R_  .08 usee  T a b l e 4.2* t h e c a l c u l a t i o n s  R  R  Calculation  = 4k  are performed  i n sequence.  First  the p o s t - a m p l i f i e r noise  i s subtracted to give the true  — 2 — 2 values  o f e-^ and  values  of  n  -  w h i c h a r e t h e n u s e d t o d e t e r m i n e t h e two  The e f f e c t  of d o u b l i n g  i s e v i d e n c e d by t h e l a r g e r v a l u e ohm t e s t r e s i s t o r . The estimate the  t h e i n p u t time cases.  nl (1+  l  and  capacitance  X ; L  )  used*  used w i t h R^,  n2 (l+x )  2  = l y r ^ i  1  of the t e s t test  v  h  e  r  e  r  = - n l / n2  >**  B  circuit  ( 4  resistor  and a c a l c u l a t i o n o f T ^ and time  n  constant  b o t h methods o f d e t e r m i n i n g  consistent results* shot  thus;  f r o m a d i r e c t measurement o f t h e  I n most c a s e s  t h e combined  ...(4 2  2  x f o r the p a r t i c u l a r  being  o f R ' c a n be u s e d t o n  R*  x c a n a l s o be d e t e r m i n e d input  o b t a i n e d w i t h t h e 200  That i s ,  = 2x^, x^ c a n be f o u n d  x  constant  c o r r e c t i o n s i n c e R ^ must be  constant  R',  2  of  d i f f e r e n c e i n t h e two v a l u e s  same i n b o t h  Since x  t h e i n p u t time  x were  I n t h e f i n a l column o f T a b l e 4.2,  and f l i c k e r  noise r e s i s t o r  i s given.  2 The  correction factors  measurements o f R ^ . R^  e x a c t l y equal  sample  alone.  l/(l+x)  u s e d were o b t a i n e d  f r o m many  Hence t h e y do n o t make t h e two v a l u e s o f  as t h e y w o u l d i f t h e y were o b t a i n e d  from  this  84 -2  -2 l  -2 2  2.25  4.75  2.25  6.55  e  -2 l  -2 2  .06  2.19  4*69  ,467  .467/.533  88  1.1  80  ,06  2.19  6.49  ,338  .338/.662  102  1.2  85  e  e  0  e  Table  After  4.2  c o n d i t i o n s , K was e s t i m a t e d the r e s u l t s  Calculation  R ^ was c a l c u l a t e d  were r o u g h l y  R" n  2  way f o r a l l o p e r a t i n g  The r e s u l t s  t h e same f o r b o t h  g i v i n g K ^ 10~  i n this  (1+x)  o f R" f o r E810F n  from the frequency  u s i n g E q n . 4.6,  R' n  y/(i-y)  y  e  dependence o f  of this  tube t y p e s  calculation  and f o r t h e N u v i s t o r s ,  , as l o n g as t h e p l a t e c u r r e n t and power  d i s s i p a t i o n were w e l l below t h e r a t e d maximum. This analysis  i s i n accord with  the theory.  o f t h e dependence o f f l i c k e r  v o l t a g e was n o t a t t e m p t e d b e c a u s e study  the f l i c k e r  noise  A more  detailed  n o i s e upon p l a t e c u r r e n t and  i n the cases  of i n t e r e s t  to this  formed o n l y a s m a l l p a r t of t h e t o t a l  noise  —13 and  c o u l d be a d e q u a t e l y Using  equivalent  t h i s value  noise  a t t h e time  r e p r e s e n t e d by the c o n s t a n t  does n o t a f f e c t  R  N  *  The c o r r e c t i o n was o n l y 1.5 ohms  o f 0,08 s e c , j so t h a t t h e u n c e r t a i n t y i n K  a p p r e c i a b l y the a c c u r a c y  I n F i g s . 4.6, and 4.7, t h e v a l u e s E810Fj  and 7586 N u v i s t o r r e s p e c t i v e l y  constant leakage for  R  N  The v a r i a t i o n  t h e E810F b u t a l m o s t  inR  of R  N  »  o f R f o r the best n  are p l o t t e d  i n the p l a t e c h a r a c t e r i s t i c  currents.  .  o f K, R ^ was a d j u s t e d t o g i v e t h e t r u e  resistor  constant  10  r  plane,  as c u r v e s o f  as were t h e g r i d  was f o u n d  t o be l e s s  7 5 % f o r t h e two N u v i s t o r s t e s t e d .  than 20%  I  80  »  I 90  '  I  100  <  I 110  I  I I I I 120 130 (volts)  I 140  I—I—I 150  1 160  F i g . 4.6 Equivalent Noise Resistor f o r the E810F Tube  Bk(volts) Fig.  4.7  Equivalent Noise Resistor f o r the  7586  Nuvistor  I  I 170  86 This  could indicate  t h a t the  f o r N u v i s t o r s than f o r tubes such  n  to g m  was  &  w i t h the  determined  c u r r e n t s between 5ma by  and  i n parameters  b u t w i t h o n l y two  a c o n c l u s i o n i s r a t h e r premature.  measured a g r e e d R  spread  To  f o r t h e E810P.  samples t o  see  p r e d i c t e d behaviour,  i s greater  i f the the  I t was  study,  shot  noise  constant  3.5  + 20% —  relating  for plate  20ma» w h i c h i s w i t h i n the r a n g e p r e d i c t e d  theory.  4.2  Measurement  of F . e . t .  Extensive  Parameters  measurements o f the  f . e . t . n o i s e and  admittance  p a r a m e t e r s were made i n o r d e r t o become a c q u a i n t e d w i t h relatively  new  d e v i c e , and  d e s i g n of f . e . t .  performance,  4.2.1  so t h e y  F.e.t. Static  The  static  were measured and f.e.t. and  admittance  importance  t o the  are  source  f.e.t.  and  o f the two  shown i n F i g . 4.8. as  claimed  inverted with  large difference a difference  study  measurements  of'f.e.t,  noise  Characteristics  Most o f t h e  d r a i n are  parameter  i n the  are r e p o r t e d i n A p p e n d i x I I .  i n the  d r a i n were i n t e r c h a n g e d w i t h no  w i t h the  from  The  characteristics  i s symmetric*  characteristics.  The  t o o b t a i n i n f o r m a t i o n f o r use  circuits.  are of o n l y secondary  this  i n channel  o f f . e . t . p a r a m e t e r s has  available  check t h a t  theory,  change  the  the n o m i n a l  i n the  the  same r e s u l t ,  and  for this  indicates  not y e t been a c h i e v e d .  checked  indicating type  of  zero b i a s c u r r e n t probably width  source  static  o t h e r p a r a m e t e r s were s p o t  indistinguishable i n the  To  f.e.t.'s  the  f.e.t.. results  t h a t good For  that  control  low-noise  F i g . 4.8(b)  S t a t i c Characteristics of F.e.t. #2  88 amplifier be  circuits this  i t a tube, or an  but  f o r any  this  f.e.t.,  crucial  because  the  input  device,  i s u s u a l l y s e l e c t e d f o r minimum  noise,  c i r c u i t where s e l e c t i o n o f components i s n o t d e s i r a b l e *  limits  4.2.2  i s not  the  design  considerably*  F . e . t . Gate Leakage Measurements  To measure the  gate leakage  c o n n e c t e d as  shown i n F i g . 4.9.  grid  current  leakage  test  current,  This  circuit Fig.  the  f.e.t.  was  c i r c u i t operates  like  the  4.1.  2.5K  Fig.  The useful and  leakage  region  (b).  reverse  For  4.9  current  Gate Leakage T e s t  I  was  of o p e r a t i o n w i t h the  bias  measured t h r o u g h o u t  the  conditions  results  shown, I  leakage because, u n l i k e tubes,  significant For  this  not  be  forward  reason  the  found unless  current u n t i l separate  Circuit  p-n  a slight  shown i n F i g s . 4.10(a) i s equal  the  gate  to  the  j u n c t i o n s e x h i b i t no forward  components of g a t e  operation with  the  bias  current  forward  i s applied, need  biased  is  V (volts) d  F i g . 4.10(a) Gate Leakage Current f o r F.e.t. #1  V (volts) d  F i g . 4.10(b)  Gate Leakage Current f o r F.e.t. #2  90 anticipated.  I n any c a s e ,  the leakage  i s so s m a l l  will  noise  and f u r t h e r c a l c u l a t i o n s o f t h e p o s i t i v e and n e g a t i v e result  4.2.3  i n no u s e f u l  F.e.t*  The  than the d e t e c t o r  that i t s  noise  ents  g e n e r a l l y be much s m a l l e r  current  compon-  information.  N o i s e R e s i s t o r Measurements  noise  resistor  and f l i c k e r  constant  measured i n t h e same way f o r t h e f . e . t . however, n e c e s s a r y  measurement o f g a t e resistive  leakage  Itis,  to i n c l u d e the  This noise  current  f o r t h e f . e . t . were  as f o r t u b e s .  now t o m o d i f y t h e t h e o r y  frequency—dependent gate n o i s e .  the  leakage  does n o t a f f e c t t h e  and need o n l y be i n c l u d e d i n  s u b s t i t u t i o n measurement o f t h e c h a n n e l and f l i c k e r  noise. The  short  circuit  output  t u b e , b u t t o e2> t h e o u t p u t — contribution e  e  «  n  2  =  where x =  /T  The this the  noise  J  T V  i n place, a  2  2  d  a  + <A T ) 2  Cl » T ) ( 1 2  +  i s evaluated  2  '  i n A p p e n d i x I as 14,  meaning.  Taking  and s u b s t i t u t i n g i t i n E q n . 4.9 g i v e s Eqn* 4.10 f o r  due t o t h e f r e q u e n c y - d e p e n d e n t g a t e kTH(z)R R C (2+x) = V * 9 2xt (l+x) 2  0  e  2 g  To  resistor  and t h e o t h e r v a r i a b l e s have t h e i r u s u a l  integral  result  the t e s t  f  s  *  with  —2 e i s given by:  i s added.  4kIH(z)R cg R^  -2  e^ r e m a i n s t h e same as f o r t h e  compare t h i s w i t h  2  noise.  2  ...(4*10)  2  the c o n t r i b u t i o n f o r channel"noise,  91 the is  ratio  —O  — O  e /e i s t a k e n . n' g  kTR /2T(l+x) n  The c o n t r i b u t i o n f r o m c h a n n e l  noise  , so t h a t t h e r a t i o i s :  e e  2xT  2  n  2  (2+x)H(z)R C t gs  2  2  g  2  ...(4,11)  X  T.  if  x « 2  H(z)R C t gs 2  Substituting C  gs  *  t y p i c a l values  o f H ( z ) = 0.4, R^. = 2K,  T. = C. R, = 2K x 4 0 p f , r e s u l t in int * *  = 8 p f ,7  Tis  2  i n e /e ^10 T, n g 2  2  where  3  i n (xsecs. As  l o n g as t h e measurements a r e made a t time  than  ( s a y ) 0.1 [xsec., t h e n  will  not a f f e c t  The  calculation  gate  noise  the frequency-dependent gate  the determination  built.  theoretical  of the channel  noise  and f l i c k e r  component o f t h e n o i s e  noise*  i n the  T h e r e f o r e * no a t t e m p t was made t o c o n f i r m t h e  e x p r e s s i o n f o r i t by extending  s t i t u t i o n measurements t o s h o r t e r time large  longer  i n s e c t i o n 3.2»5 showed t h a t t h e f r e q u e n c y - d e p e n d e n t  i s n o t an important  amplifiers  constants  the r e s i s t i v e sub-  constants  —2 where e w o u l d be g  enough t o d e t e c t . The  circuit  circuit  o f F i g . 4*11, w h i c h i s e q u i v a l e n t t o t h e t e s t  used f o r tubes  ( s e e F i g . 4.5) was u s e d f o r t h e r e s i s t i v e  s u b s t i t u t i o n measurements on t h e f«,e*t»  The d a t a  obtained  a t time  c o n s t a n t s o f 0.32, 1.6 and 8.0 |j,secs w i t h t h e two t e s t r e s i s t o r s , IK and 2K, was r e d u c e d t o R and K b y c a l c u l a t i o n s l i k e t h o s e ' n J  described  i n S e c t i o n 4.1 f o r t u b e s .  I n F i g s . 4.12(a) and (b)  92 AAAr  ss  5K  =j=10^f '15K(ww)  •lftf  itkT t  Et  F i g . 4.11  curves  to post-amp,  —O  2N2386  F.e.t. Resistive Substitution Circuit  of constant R  are p l o t t e d  n  i n the d r a i n  Test  characteristic  plane.  f .e . t .  I (ma)  #1  R (K) n  d  .2 .4 .6 .8  3.3 1.45 1.15 1.0  V  f .e. t . #2 V  = 3v  d g  g (ma/v) m  0.5 1.0 1.3 1.5  R n gm  I (ma)  1.6 1.45 1.5 1.5  .2 .4 .8 1.0  d  &  T a b l e 4*3  In drain  = 2v  d s  R (K) n  g (ma/v) R g n m m  1.5 1.15 .80 .78  T a b l e 4.3, t h e p r o d u c t  R^^Q  approximations channel  this  Q i s roughly  i s probably  50% and 3 0 %  a result  made i n a c c o u n t i n g f o r t h e e f f e c t  resistors.  1.20 1.38 1.28 1.40-  i s formed f o r d i f f e r e n t  h i g h e r t h a n p r e d i c t e d f o r f . e . t . #1 and #2 r e s p e c t i v e l y . i n the theory,  .8 1.2 1.6 1.8  F . e . t . Noise R e s i s t o r s  c u r r e n t s i n f . e . t . #1 and #2.  mentioned  to  .As was  of t h e  of the p a r a s i t i c  P i g . 4.12(b)  Equivalent  Noise R e s i s t o r f o r F . e . t .  #2  The is  25% v a r i a t i o n  i n Q with  current  n o t e x p e c t e d t o be a c o n s t a n t  f u n c t i o n of the b i a s The  flicker  but i s rather  Below t h e s e  make t h e d e t e r m i n a t i o n very  4.3  varying  10 t i m e s  so t h a t K c o u l d be d e t e r m i n e d more  +10% for a l l drain  currents,- R  n  of K d i f f i c u l t ,  becomes l a r g e  that  accurately.  + 10%, f o r a l l d r a i n c u r r e n t  1 3  0.2rna; i n f . e . t . #2, K = 6 x 10~  at  a slowly  was f o u n d t o be r o u g h l y  I n f . e . t . #1, K = 8 x 1 0 ~  above 0.4rna.  because Q  voltages*  noise  observed f o r tubes  i s not excessive  above  currents  enough t o  but apparently  K  increases  low c u r r e n t s .  Summary  of Experimental Noise  At t h e end o f chapter expected noise made u s i n g  performance  Parameters  3, a b r i e f  comparison of the  of tubes, N u v i s t o r s  the t h e o r e t i c a l l y  determined noise  and f . e . t . ' s was parameters.  Because  of t h e u n c e r t a i n t y  i n t h e s e p a r a m e t e r s , t h e c o m p a r i s o n was  and  t h a t t h e E810F was e x p e c t e d t o be t h e b e s t  i n d i c a t e d only  device. for  Now  that  the n o i s e  a l l possible operating  of t h e n o i s e  4.3.1  Choice  The  parameters f o r the d e v i c e s  be made.  Points  minimum n o i s e  charge f o r a n u c l e o n i c  system  when t h e p r o d u c t P = R I = R ( I , + I ) i s a minimum. n e n L ex r  -the  sum o f e x t e r n a l  point*  The e f f e c t  a r e known  c o n d i t i o n s , a more d e t a i l e d p r e d i c t i o n  performance w i l l  of B i a s  brief  v  leakage  currents  of changing  a c o n s i d e r a t i o n of F i g . 4.13*  occurs I  ex  is  n o t a f f e c t e d by.changes i n b i a s  the b i a s p o i n t  c a n be s e e n  from  95  I (m4) D  Rn = 80  25  = 2.5 + l e x 20  2.0 + I e  X  15 le = 1.25 f l e x  10 -  t lex  • 1-0  5 75  100  150  125  V (volts) b  P i g . 4.13  In t h i s  diagram,  superimposed, the I  jj T  curve If  B i a s P o i n t F o r Minimum  some R  and I  i s i n c l u d e d by i n c r e a s i n g  the I  the b i a s p o i n t  of A a l o n g t h e R  n  hence P i n c r e a s e s . and  and 1^ c u r v e s f o r t h e E810F a r e  Q  c u r v e s as shown. intersects  Noise  T  A t t h e p o i n t s A and B where  i s moved  to the r i g h t  = 80 c u r v e , t h e l e a k a g e  =80  + 2).  current increases;  Between A and B however, the l e a k a g e c u r r e n t until  a minimum  1  the constant leakage  p o i n t X " as a n o t h e r p o i n t of equal  n  of B or to the l e f t  i s reached  p o i n t X , where t h e two c u r v e s a r e t a n g e n t .  points  the R  = 2 c u r v e , P i s e q u a l t o 80.(1  the product decrease  argument f o l l o w i n g  the value of  o f minimum  slope t h e r e f o r e form  P.  a t the  A complementary :  current curves gives the The l o c u s o f a l l  the curve  of optimum  bias  96 Locating  the  optimum b i a s p o i n t  measurements i s d i f f i c u l t I  &  i n t o i t s two  adjustable  because  components.  bias  circuits  of the  Therefore,  (see  at f i x e d  sufficiently  I  is neither  negative  bias  t h a t where the  to reduce I  grid  to (4  is floating  to f l o a t ,  grid bias resistor  reduced.  This  t h o u g h the I the  .  could  However, two  detector  attributed ment i n I  biased  amplifiers built The  current  bias  argument  grid  is  biased  .  By  allowing  i s eliminated  and  the  I  i n a decrease  i s small.  the  i n P,  even for  fractional  S e c o n d l y , i n moving f r o m p o i n t X  fixed  Firstly, that  improvet o A,  I  ex increases  o f the  exponential  opposes the improvement i n I . I n T a b l e 4.4, R and G1^X v a l u e s n  optimum b i a s  line  are  c o l l e c t e d and  for external  I (ma) b  leakage  Table  the  R (K)  I (na)  .22  .4  L  increase  for different  currents  n  5  in I  points  and along  the  product P = R I is n e of 0, 1, and l O n a . p  o  P  l  P  10  .088  .306.  2.28  10  .125  1.2  .15  .275  1.39  15  .090  1.75  .16  .248  1.06  20  .070  3.0  .21  .280  .91  4.4  T  L i  r a p i d l y because  evaluated  p)  *  is  c u r v e of optimum b i a s  so t h a t  (4  grid  i s g e n e r a l l y much l a r g e r t h a n  resistors,  had  i t s p o s i t i v e component, 3) *  the  separating  c o n d i t i o n f o r minimum  result  on  in  current  f a c t o r s combine t o make t h i s u n l i k e l y .  leakage  t o the  noise  conceivably  tube i s not  the  t h a t where the g  nor  uncertainty  s e c t i o n 5.2.1).  above does show however, t h a t the noise  e x a c t l y from g r i d  C o l l e c t e d N o i s e D a t a f o r Optimum B i a s Tube  Points  f o r the  E810P  97 It  c a n be seen t h a t t h e a d d i t i o n o f an e x t e r n a l  current  of only  l O n a moves t h e optimum b i a s p o i n t  current  o f 20 ma.  Since  most s o l i d  t h i s much l e a k a g e , t h e tube w i l l a current  above 20 ma, so R  n  increases that  the transconductance  does n o t c o n t i n u e  bias  point  Nuvistor  Collected bias It  shows r o u g h l y  indicates the  that  b  the f l i c k e r  increases.  o f 10  P apply  t o the  and 1 ^ c u r v e s .  n  a r e shown i n T a b l e  4.4.  as t h a t f o r t h e E810F and f o r most a m p l i f i e r s i s a t  ma.  R  Z  n  L  V  P  l  P  10  1.000  *8  4  .650  1.6  1.04  1.69  7.5  6  .425  3.0  1,27  1.70  5.55  8  .370  6.0  2.22  2.59  5.9  10  .320  9.0  2.88  3.20  6.1  1.8  10.8  C o l l e c t e d N o i s e D a t a f o r Optimum B i a s the 7586 N u v i s t o r  f.e.t.  noise  c u r r e n t of  2  4.5  slowly,  The n e t r e s u l t i s  minimum  i n the R  f o r the N u v i s t o r  t h e same b e h a v i o u r  currents  110 v o l t s .  t h e optimum b i a s p o i n t  I (ma)  The  Also  for finding  of the s i m i l a r i t y  maximum c u r r e n t  Table  of roughly  point data  a t as h i g h  At plate  f o r t h e E810F i s a t a p l a t e  considerations  because  have a t l e a s t  o f t h e E810F, i n c r e a s e s  to decrease.  20 ma and p l a t e v o l t a g e Similar  state detectors  system n o i s e .  as t h e p l a t e d i s s i p a t i o n  the best  to a p l a t e  g e n e r a l l y be b i a s e d  as p o s s i b l e f o r minimum  leakage  has l e a k a g e  currents  Points f o r  o f f r a c t i o n s o f 1 na  so  t h a t the n o i s e  Therefore,  L  will  a l w a y s be swamped by d e t e c t o r  the f . e . t . i s b i a s e d  minimum R » drain voltage  o f 6 v o l t s was  a bias  data  capacitances  i n Tables  obtained  current  o f 2.3 ma  at a  c h o s e n , g i v i n g R^ = 600 ohms.  C a l c u l a t e d C u r v e s o f Minimum  The  noise.  a l w a y s a t maximum c u r r e n t f o r  F o r f . e . t . #2, t h e n *  n  4.3.2  of I  4*3  Noise  and 4.4  Charge  and t h e p a r a s i t i c  from the m a n u f a c t u r e r s '  specifications  were  u s e d i n E q n . 2.16 t o f i n d N . , and i n E q n . 2.15 t o f i n d T • . ^ min min C u r v e s o f N . v s . T • a r e shown i n F i g . 4.14. The c u r v e s were min min 7  11  6  extended to s h o r t time-constants highest noise  current  i n E q n . 2.14  by u s i n g  f o r N»  The e x t e n d e d  c h a r g e t h a t r e s u l t s when t h e time  than " f ^ m  curves  n  ( f o r high  count r a t e s  were c a l c u l a t e d e n t i r e l y  bias point  i s assumed f i x e d .  the data  or other  constant  f o r the curves  i s made  reasons).  The  show t h e shorter  f.e.t.  f r o m E q n . 2.14, b e c a u s e t h e  D a t a f o r t h e 2N930 c u r v e s  was  taken  f r o m t h e m a n u f a c t u r e r s ' s p e c i f i c a t i o n s a n d t h e c a l c u l a t i o n made ignoring  r J , the f l i c k e r  n o i s e , and h i g h  frequency  effects  in i *  p The  N's p r e d i c t e d f o r t h e 2N930 a r e t h e r e f o r e o p t i m i s t i c ,  particularly  a t s h o r t time  constants.  In a d d i t i o n to the curves curves curve  shown f o r C^ = 20pf,  similar  were c a l c u l a t e d f o r C^ = O p f , 60pf, and l O O p f . the absolute  minimum N was f o u n d and t h e c u r v e s  From  each  of N .  mm vs  C^ p l o t t e d ( s e e F i g . 4 . 1 5 ) . The  information displayed In Figures  self-explanatory section  3*5 were  4*14  and 4.15 i s  and shows t h a t t h e t e n t a t i v e c o n c l u s i o n s substantially correct.  The E810F and  of  Nuvistor  e x h i b i t e d p a r a m e t e r s w i t h i n t h e p r e d i c t e d r a n g e . As e x p e c t e d ,  lna ^  Detector leakage Detector leakage I  I  0*1 Fig. 4.14(a)  ^sain  V 3  I  I I  » I'min  f o r  ~  I  - E 8 1 0 F  I  10  1.0 --  1 n a  Detector Leakage Current  FWM(KEV)  10  1.0  0.1 Fig. 4.14(b)  N  m i n  vs.  for 10 na Detector Leakage Current  100  2000 N(e.c,)1500-  2N2386^^  1000—  /  7586^-^  /  E810F^-  500/  -20  1  0  20  40  I 80  60 C (pf)  I  1  1100  1 120  d  Fig. 4 . 1 5 ( a ) N  m i n  vs. G f o r 1 na Detector Leakage Current d  2000 -  2N930  N(e.c.) -  2N238>^  1500 7586 1000  -  /  ^ ^ ^ ^  .^-""""^ ESIOF^,  '  / >  r  v  /-20 i |/,  r  1 0  I I 20  I I 1 40 60 C (pf)  I I 80  100  ( I I I 120  d  Fig. 4 . 1 5 ( b )  N . vs, C, f o r 1 0 na Detector Leakage Current  101  the n o i s e  of t h e E810P was  capacitance* more f l i c k e r inferior  The and  to the  however, s t i l l  f.e.t. channel  Nuvistor  less  on t h e noise  at a l l but  the  lowest  o t h e r hand, e x h i b i t e d c o n s i d e r a b l y than  expected,  e v e n w i t h no  much s u p e r i o r t o t h e  and  as t h e b e s t  device.  devices  as a r e s u l t  external noise.  are r e q u i r e d t h e  low  There-  power  f.e.t.  is  It i s ,  junction transistor.  f o r e , f o r a p p l i c a t i o n s where t h e r u g g e d n e s s and sumption of s o l i d - s t a t e  detector  con-  emerges  102 5.  In Chapter  PREAMPLIFIER DESIGN AND  PERFORMANCE  2 i t was assumed t h a t a m p l i f i e r n o i s e  reduced t o the n o i s e  of the i n p u t s t a g e .  c a n be  On t h e b a s i s o f t h i s  assumption, the e q u i v a l e n t  noise  then discussed  3 and 4 i n terms o f p r e d i c t e d and measured  noise  parameters o f v a r i o u s  of t h e n o i s e built is  i n this  charge m e a s u r e d .  s e n s i t i v e " type  using  2N2386 f i e l d  comparison w i t h  the  superior noise  the  tube c i r c u i t s  open—loop g a i n s .  performance amplifiers  the  performance  sensitive"  The f o u r t h , configuration  B e c a u s e of  o f t h e E810F, time was t a k e n t o make  into practical The N u v i s t o r  7586 N u v i s t o r s ,  stages.  s e n s i t i v e E810F s t a g e .  nucleonic  and f . e . t *  the noise  preamplifiers with stages,  theory  g a i n f o r use i n n u c l e o n i c  on t h e o t h e r  large hand,  o f t h e t h e s i s and do n o t  systems.  The good  tube a m p l i f i e r s i n d i c a t e d t h a t t h e Other  c o u l d be s i m i l a r l y m o d i f i e d  f o r use as p r a c t i c a l  The m o d i f i c a t i o n s were n o t c a r r i e d  time and component l i m i t a t i o n s ,  conjunction with  (7788) t u b e s ,  i n the "voltage  t h e charge  of the m o d i f i e d  preamplifiers.  were o f t h e " c h a r g e  t r a n s i s t o r s f o r the input  p r i m a r i l y to t e s t  sufficient  three  r e s p e c t i v e l y E810F  effect  for  and p e r f o r m a n c e  of P r e a m p l i f i e r s  a l s o u s i n g E 8 l O F ' s , was b u i l t  have  Their design  the four p r e a m p l i f i e r s b u i l t ,  were b u i l t  To c h e c k t h e v a l i d i t y  chapter.  D e s i g n and C o n s t r u c t i o n  Of  and  active devices.  a m p l i f i e r s was  c h a r g e s p r e d i c t e d i n t h i s way, f o u r p r e a m p l i f i e r s were  and t h e i r n o i s e  described  5.1  i n Chapters  charge o f n u c l e o n i c  but they  the c i r c u i t d e s c r i p t i o n s .  nucleonic  out because of  are discussed i n  103 The  p r e a m p l i f i e r s a l l use  grounded-grid noise  input  amplifiers  stages.  because  " c a s c o d e " , or  This  circuit  i t gives  the  grounded-cathode-  i s commonly u s e d f o r  lowest  noise  of any  low-  two  (5 l ) stage high  corifiguration current  4.3.1.  The  noise, the  and  levels noise  i l l u s o r y because  is are  t h a n the  added.  discussed  derived  A l l the  input  i n accordance with  case  the  low  lower b i a s  one  d i s c u s s i o n of  and  absence of  c u r r e n t s w o u l d have  amplifiers when the  p r e a m p l i f i e r s are only b r i e f l y  the  were b i a s e d  improvement o b t a i n e d  current  current  stages  measured i n the  However, any  high  The  * '.  charge was  in this  performance.  noise  v  of  give  conventional  expressions  improved  i n t h i s way  detector  gain  Cfb « 2pf  lOOM Note: a l l resistors i n Kobms, a l l capacitors i n yUf, unless noted. 5.1  system  design;  for their  is  so  noise they  are  -vW-O 220-a. 340v  i n Appendix I I I .  Fig.  section detector  higher  inevitable  at  E810F C h a r g e - S e n s i t i v e  Preamplifier  104  5.1.1  E810F Charge S e n s i t i v e P r e a m p l i f i e r  Pig. circuit. and (T^)  5.1 shows t h e E810P " c h a r g e  The i n p u t  t h e ac l o a d  the  dc l o a d .  for  excessively high  provided  The c i r c u i t  circuit the  by t h e o u t p u t  but P  2  gives  only  a fine  o f R^, R  2  r ^ r e f e r t o T^,  = R  L  + r  ¥ith a cascode so t h a t A voltage =  without  resistors.  c  s e e  2  2  +  +  l)R p l  2  to d r i f t  i n the b i a s  2  tube t o  f o r a l l possible of the plate  With the values  plate  current  of these  i s 20ma. has a v o l t a g e  i n Appendix I I I . p  C^  feedback through the  "bootstrapping"  and r  r (A  current  = 208.  gain  ^2 (  p  impedance a r e  of the input  current  t h e need  Feedback through  adjustment  cascode  Jas g i v e n b y E q n . 5.1 d e r i v e d  range  and R^»  cascode stage without  [A ([j,  ^1'  t h e dc c o n d i t i o n s  P^ has s u f f i c i e n t  ]L  (T^).  s e n s i t i v e " , while  shown, t h e n o m i n a l  The  c  and l o a d  The p o t e n t i o m e t e r s P-^ and P  are used to a d j u s t  resistors  A  increased  stage  increasing  reduces the tendency of the input  optimum v a l u e .  and  voltages  cathode f o l l o w e r  resistor  d e f i n e d by t h e c h o i c e  c  supply  "charge  count r a t e s .  voltages,  A  i s therefore  o f t h e dynamic c a s c o d e l o a d and a low o u t p u t  input g r i d high  seen by the cascode w i t h o u t  gain  plate  renders the c i r c u i t  at  E810P's  " b o o t s t r a p p e d " b y t h e E810P p e n t o d e  2  Isolation  preamplifier  c a s c o d e o f two t r i o d e - c o n n e c t e d  T ) has i t s l o a d  to increase  sensitive"  In this  gain  expression  t o T^.  L  2  +  1)  o f 20ma; r  ^  p  ^= r  g  m L R  p  2  f  o  r  l  a  r  g  e  *2  — ( 5 . l )  =-1.3K and u.^ = |^ = 50, 2  When t h e l o a d i s d i v i d e d and b o o t s t r a p p e d , the  i s given  by E q n . 5.2 f o r w h i c h t h e maximum o c c u r s  Appendix I I I ) .  C h o o s i n g R^ = R  2  when  105  A  cb  - B{  + B  ^ 2 + r  ?  + 1 .+ r ( l 1 ) R  p 2  p  ( 1  l  gm3 2 ^) + R J g ^  +  R  +  .  )  V  h  1 3 1 = B R  p t e  r  6  R  R3  ; +  ...(5.2)  approximates t h i s R ^ by  only  condition f a i r l y well*  a small  amount.  t u b e p a r a m e t e r s and A  for  A^  and  c  being  1600  increases  the  g a i n o f the  o f T^  affect  be  respectively*  i n a cascode  i s added t o t h e  w i t h two  the  noise  The  charge  only  5% f o r d e t e c t o r  input  i n chapter  capacitance t h a t the  term n u c l e o n i c necessary, and  t h a n was  and  reduces various  measured  predicted  values  values,  dynamic  cascade  above the  value  of u n i t y i t  t h a t the M i l l e r  capacitance  The  load  also  a n a l y s i s o f the  amplifier  2 showed, however, t h a t t h i s  1.11  100 10  between Opf  i s r e d u c e d by of the The  the  =  the  circuit Eqn.  1.7  charge d i f f e r s  and  150pf,  does  not  closed-loop  gain  open-loop g a i n i s 300pf.  The  same amount*  can  However, t h i s use  be  can shows by  indicating stability  stability effect  of  These f i g u r e s  a m p l i f i e r i s adequate f o r  stability  increasing C^.  special  1.J1,  t i m e s b e t t e r when  stability  required with  input  times b e t t e r than the  drifts  o f the  of s e c t i o n 1.4.  for fixed  Prom E q n .  m i g h t n e c e s s i t a t e the  W i t h no  the  and  f o r the  The  gain s t a b i l i t y  capacitances  experiments. by  and  amplitude  sensitivity.  i s 30pf and  indicate  signal  pulse  f o u n d t o be  when  so  values  = 1750.  capacitance.  sensitivity  the  c a n be  tube  circuit  c a l c u l a t e d f r o m E q n s . 1.7 output  The  i s 20K  performance.  that  if  first  input  feedback loops  good c h a r g e  gives A^  were i n good agreement w i t h  and  has  S u b s t i t u t i n g the  resistors  200  normally  since  long-  increased further^  d e c r e a s e s the  of a lower-noise  post  output  amplifier  2pf.  precautions  t a k e n to improve  the  high-frequency  106 response  of the c i r c u i t * r i s e  5pf f e e d b a c k c a p a c i t o r s reduce the r i s e resulted  time  i n large  r e s p e c t i v e l y a r e measured.  f u r t h e r by i n c r e a s i n g  basic  c i r c u i t , t h e minimum r i s e  For  a l l but the v e r y f a s t e s t  an a d e q u a t e  rise  circuit  time  c a n be t a k e n t o be 10 n s .  i n t h e charge  an o u t p u t c a t h o d e  Preamplifier  stage, the v o l t a g e  sensitive  the o v e r a l l  pentode  capacitor  voltage  i s applied to the input  sensitive  and r i s e  voltage  i s followed g a i n , and  s t a g e a g a i n o f 50 so  from the output t h r o u g h R ^ cathode,  preamplifier  The  g a i n i s 4000. and t h e phase  thus f o r m i n g the c o n v e n t i o n a l  2) * '.  The c l o s e d - l o o p v o l t a g e  gain,  time a r e d e t e r m i n e d by t h e amount o f f e e d b a c k , hence by t h e  o f Rfk*  ^  o  r  frfb  =  IK "khe c l o s e d - l o o p g a i n was 130 and t h e r i s e  time 4 0 n s .  (Note t h a t  formed  10 ohms s h u n t e d by l / g ^ * )  from  the e f f e c t i v e  decrease r e s u l t e d  voltage  sensitive  i s 7.5 ohms t o 220 ohms  t i m e t o 12ns, b u t a f u r t h e r  then, the voltage  are equivalent.  resistor  Decreasing R ^  i n the c i r c u i t o s c i l l a t i n g  timing purposes  amplifiers  cathode  m  r e d u c e d t h e g a i n t o 30 and t h e r i s e  the  This  stage t o boost the open-loop  (5  For  E810F  f o l l o w e r t o p r o v i d e a low o u t p u t impedance.  open-loop  Feedback  size  sensitive  preamplifier.  c a s c o d e has a g a i n o f 80, and t h e p e n t o d e  lead  gives  shown i n F i g . 5.2 employs a m o d i f i e d v e r s i o n o f t h e i n p u t  a grounded-cathode  that  so t h a t f o r  time*  a low—noise input  cascode used by  t h e amount o f f e e d b a c k  c o i n c i d e n c e work t h e n , t h e c i r c u i t  E810F V o l t a g e S e n s i t i v e  For  Attempts t o  o v e r s h o o t and e v e n t u a l o s c i l l a t i o n ,  the  5.1*2  t i m e s o f 42 ns and 10 ns f o r 2 p f and  at high frequencies.  sensitive  and c h a r g e  sensitive  However, t h e l o n g - t e r m g a i n s t a b i l i t y o f  amplifier  c a n n o t be e x p e c t e d t o be as good  since  107  7-45pf "  ' W V  Rfb  a  470-a  Note: a l l r e s i s t o r s i n Kohmsj a l l c a p a c i t o r s I n | J f ; unless noted. Fig.  5.2  E810F V o l t a g e S e n s i t i v e Preamplifier  f e e d b a c k compensates o n l y f o r d r i f t s changes i n c a p a c i t a n c e in gain s t a b i l i t y  a t the i n p u t *  i n open l o o p g a i n and n o t f o r The amount of improvement  i s 30 t i m e s and 75 t i m e s f o r l k and 200  ohm  feedback r e s i s t o r s r e s p e c t i v e l y *  5*1*3  Nuvistor  Test A m p l i f i e r  The N u v i s t o r two N u v i s t o r s  t e s t a m p l i f i e r consisted simply  and an o u t p u t  cathode f o l l o w e r  of a cascode of  (see F i g . 5 . 3 ) ,  As i t  108  stands  the  Nuvistor  c a s c o d e has  f e e d b a c k c a p a c i t o r does not except f o r very intended the  low  f o r use  charge  source  only  as  a voltage  make the  circuit truly  capacitance.  a noise  g a i n of 90,  test  t h a t the  charge  However, the  c i r c u i t , and  so  2pf  sensitive  circuit  for this  was  purpose  s e n s i t i v i t y i s adequate*  i  1|  —<  °fb= P * 2  Pig.  To  convert  nucleonic the  the  5*3  Nuvistor  p r e a m p l i f i e r , the  input g r i d  resistor  and  must be and  appropriately.  tube  amplifier into increased  t i e d to the tubes,  input with  c i r c u i t s so  relatively  high Nuvistor  by  practical  considerably  and  Because of  the  output.  a Nuvistor  junction transistors  t h a t the  a  c i r c u i t could scaling  A n o t h e r p o s s i b i l i t y would be  T h i s mixed c i r c u i t would r e q u i r e the  Preamplifier  d i r e c t l y f r o m t h e E810P c i r c u i t s i m p l y  voltages  Nuvistor  test  Test  g a i n must be  s i m i l a r i t y between N u v i s t O r s designed  Nuvistor  a somewhat d i f f e r e n t  transistors  supply  e l s e w h e r e i n the  voltages.  c a n be  the  currents  t o use  a  circuit*  design  isolated  be  than  from  the  109 5.1.4  F.e.t.  The and  Preamplifier  manufacturing  t h e maximum c u r r e n t  differed Since  considerably  the noise  tolerances  o f t h e two a v a i l a b l e f o r t h i s  resistor  stage  low-noise  f.e.t.  Use o f t h e " b e s t "  i s t h e one w i t h t h e low-noise  c a n n o t be b i a s e d  off  impedance the  The f i r s t  a very  stage.  In a d d i t i o n to these  these  this  circuit  for practical An  design  roughly  t h e u s e o f two  p r o b l e m s c a n be overcome t h r o u g h t h e use o f a  Bootstrapping  cascode  circuit  o f the cascode  i n an a t t e m p t  to increase  of the type  shown  l o a d has b e e n u s e d i n  the gain to a s u i t a b l e  u s e , b u t i t r e s u l t e d i n a maximum g a i n  a n a l y s i s of the c i r c u i t  given  problems  s u b s t i t u t e c a n be f o u n d .  mixed f » e . t . - j u n c t i o n t r a n s i s t o r i n P i g . 5.4.  cut-  t o t h e low  expense o f f . e . t . ' s makes i t d e s i r a b l e t o a v o i d  All  i n noise.,  i n t h e low f r e q u e n c y  l a r g e c a p a c i t o r i s used to couple  common-gate  when an a d e q u a t e  high  Therefore,  s o l u t i o n r e s u l t s i n an i n c r e a s e  t h e s e c o n d r e s u l t s i n an i n c r e a s e  unless  as t h e  c u r r e n t must be l o w e r e d , o r ac c o u p l i n g must be u s e d  between s t a g e s . while  f.e.t.  at a current  enough f o r optimum p e r f o r m a n c e o f t h e i n p u t f . e . t . the b i a s  i s a maximum  o f a c a s c o d e o f two f . e . t . ' s p o s e s a p r o b l e m  b e c a u s e t h e common—gate f . e . t .  either  experiment  i s a minimum when t h e c u r r e n t  maximum c u r r e n t .  common—source  poor,  (as i t p r e s u m a b l y would f o r any o t h e r t w o ) .  (see P i g . 2 . 2 l ) , t h e " b e s t " highest  f o r f . e . t . ' s are r e l a t i v e l y  level  o f o n l y 230.  i n A p p e n d i x I I I shows t h a t t h e g a i n i s  by E q n . 5.3.  g P3 l 2 R  R  A -  m  R  l  +  r  eP  (if r  c2  is very  large)  3  (5.3) =c g R - . R / r . m 1 2' e 0  (if  P ^eO) 3  110 GND  Note: a l l r e s i s t o r s i n Kohms; a l l capacitors i n |^f; unless noted. Fig,  Thus A can resistance,  T^  be  5.4  F.e.t*  increased  t o have h i g h  8*  W i t h good t r a n s i s t o r s , t h i s possibility An  of  large  this  Phase—lead  bootstrapped The  too  interstage  overcome t h i s  type  stages,  c i r c u i t was  rise  but  ,  by  using  i t was  large  t o have l a r g e c o l l e c t o r  2  i n c r e a s i n g b o t h R-^  does, t h e r e f o r e ,  coupling the  the  f.e.t;  found t h a t  f o r the  offer  R. 2  the  use. followed  the  phase  by  two  shift  through  f e e d b a c k to be e f f e c t i v e .  and  t r a n s i s t o r s with higher  circuit  f^,  could  showed l e s s p r o m i s e t h a n  time o f the  2N1305's the  f*e*t* well  rise  preamplifier  as  the  time was  depended upon  amount o f f e e d b a c k . 0.5  and  0.7  \isec,  arid 5 p f f e e d b a c k c a p a c i t o r s  r e s p e c t i v e l y , while  the  and  time  [xsecs.  2N706 s r e d u c e d the T  and  the  circuit.  of t r a n s i s t o r s u s e d as  •2N1304 s and  and  circuit  built  drawback b u t cascode  choosing T  enough g a i n f o r p r a c t i c a l  a m p l i f i e r was  common e m i t t e r  by  Preamplifier  rise  t o 0.3  and  0.1  use  the With  f o r 2 pf of The  2N705's rise  Ill  times are s t i l l  considerably  t u b e and N u v i s t o r  stages^  s u i t e d m a i n l y to "slow"  5.1.5  Construction  The  choice  longer  i n d i c a t i n g t h a t the f . e . t .  this  the  and o t h e r  input  below w i t h  the  p r e a m p l i f i e r s has  o f a m p l i f i e r noise*.  levels  and c i r c u i t been  stages  isolate  consimplified  However, t o a c h i e v e  i n p r a c t i c e , the c o n d i t i o n s component n o i s e  o f complete  w h i c h was assumed i n the  used t o do t h i s  r e f e r e n c e , t o t h e E810F p r e a m p l i f i e r s o n l y ,  t u b e s were  remainder  point,  The c o n s t r u c t i o n t e c h n i q u e s  the other To  bias  i n t h e c a l c u l a t i o n s , must a l s o be r e p r o d u c e d  amplifiers.  to  studies  i s o l a t i o n and l a c k o f e x c e s s  implicitly  circuit is  T e c h n i q u e s f o r Low-Noise P r e a m p l i f i e r s  of input device,  predicted noise  with the  experiments.  f i g u r a t i o n f o r low—noise nucleonic by  than those obtained  are discussed  but they  apply-  as w e l l •  t h e E810F p r e a m p l i f i e r from s t r a y s i g n a l s ,  shielded with  of the c i r c u i t  conventional  was b u i l t  tube  i n a closed  s h i e l d s , and t h e copper  I n p u t s i g n a l s a n d d c power were f e d i n t o t h e c h a s s i s  chassis. i n shielded  c a b l e s , a l l dc l i n e s were d e c o u p l e d w i t h i n  t h e c h a s s i s , and t h e t u b e  f i l a m e n t s were  supply  s u p p l i e d f r o m a dc f i l a m e n t  In a d d i t i o n t o these p r e c a u t i o n s , shielded (see  F i g . 5.5(a)).  shield was  separately  to isolate  t h e base o f t h e i n p u t t u b e T^ was  the input  The s i g n a l and t e s t  through the r f connectors  capped t o p r e v e n t p i c k u p  (see A p p e n d i x I V ) .  shown.  of noise  from t h e r e s t o f t h e c i r c u i t inputs  enter  this  inner  When one was n o t i n u s e i t  on t h e i n p u t .  (a)  S h i e l d Used  (b)  Pig.  Since impedance  the  5.5  I n p u t Tube  p u r p o s e of the  i n p u t from n o i s e  w i t h i n the  shown i n F i g . 5.5(b) m i g h t b e ' s u p e r i o r excludes  the  which could  cathode  back l e a d passing t o be is  recommended f o r use  using are  of the  only  are is  The  circuit built* i n other  noise*  the  swamped by  the  circuit,  leads  and  shield  plate  only  the  feedfound  the more s e l e c t i v e  shield  of t h i s  f o r R^,  type.  R »  R^  2  carries  overcome and  R^»  by which  appreciable  portion  essentially  no  the  remainder  i n a l o c a t i o n where t h e i r  noise*  lead  o f F i g . 5.5(a) was  c o u l d f o r m an  or occur  high  It  the  has  the  the  one.used.  excess n o i s e , while  amplified input  isolate  i n components was  others*  hence g e n e r a t e s no  a l l e i t h e r ac b y p a s s e d  but  circuits  wound r e s i s t o r s  Of  i s to  i n p u t and  shield  r e s i s t o r s whose n o i s e  output  c u r r e n t and  to the  problem of excess n o i s e  a x i a l - l e a d wire  the  noise  through i t .  adequate f o r the  The  t o the  components, f i l a m e n t  a l l introduce  Shields  inner shield  sources  Recommended S h i e l d  noise  113  5*2  Measurement o f P r e a m p l i f i e r N o i s e  The evaluated  noise  performance  standard  procedures  2  noise  c h a r g e was t h e n  and system time  constants  3}  * *  the i n p u t and t h e o u t p u t The  o f t h e f o u r p r e a m p l i f i e r s was  f o r various detector capacitances (5  by  Performance  •  A test  i n p u t c h a r g e was a p p l i e d t o  signal—to-noise ratio found  from Q  S/n was  - Q n/S»  n  c  observed.  During  these  measurements, t h e d e t e c t o r c a p a c i t a n c e s were  s i m u l a t e d by p l a c i n g  a capacitor  (see F i g . 5*6),  time  across the p r e a m p l i f i e r i n p u t  c o n s t a n t s were s e t by t h e D y n a t r o n p u l s e  n o i s e broad-band post to c o u p l e noise  A low-  a m p l i f i e r d e s c r i b e d i n A p p e n d i x IV was u s e d  the p r e a m p l i f i e r to the Dynatron a m p l i f i e r  of the l a t t e r  overall  amplifier.  (^.Iv rms a t t h e o u t p u t )  so t h a t t h e  d i d not a f f e c t the  signal—to-noise ratio.  HP  400D  CDC K.S.  CRO  VTVM Fig.  The V  and t h e  5.6  Noise  Charge M e a s u r i n g  mercury-relay  pulse  generator  applies a voltage  t o t h e c a p a c i t o r C , so t h a t t h e t e s t  c.  + c,  amplifier  m d isQ = V C (C, + C. + C ) . c c c_ d in c.  amplifier  input  capacitance.  System  charge passed , where C. m  When ( C ^ + C^) i s > n  step  to the  i s the t o t a l 200 p f ,  (as i t  114  is  f o r a l l the charge  sensitive  can be takjbn t o be V C w i t h c c voltage  sensitive  expression  forQ  c  charge  However, w i t h a must be  used.  b a s i c i n p u t c h a r g e was d e t e r m i n e d by m e a s u r i n g t h e  mercury-^relay  supply voltage with  B o o n t o n Q—meter.  Since  C  measurement was e s t i m a t e d p u l s e s were in  a t most 1% e r r o r .  p r e a m p l i f i e r , the input capacitance  d e t e r m i n e d and t h e complete The  p r e a m p l i f i e r s ) , the i n p u t  a dc VTVM and C  was o n l y  c  £  with a  2pf, the accuracy  t o be a b o u t  5%.  Latere  of t h i s  the input  compared t o t h e a c c u r a t e l y known c h a r g e p u l s e s  a solid—state  d e t e c t o r by Polonium a l p h a  particles.  generated  This  c h e c k s t h e c h a r g e measured w i t h t h e m e t e r s and a l s o g i v e s a d i r e c t energy—unit estimated  c a l i b r a t i o n of the system*  was  o f the system^ t h e s i g n a l - t o - n o i s e r a t i o can  measured d i r e c t l y w i t h  height  the accuracy  t o be 5%.  At the output be  Again  spectrum w i t h  b e c a u s e o f t h e time  an o s c i l l o s c o p e and a VTVM, o r as a p u l s e  a kicksorter*  B o t h methods were u s e d , b u t  r e q u i r e d t o accumulate  an apcurate  pulse  height  s p e c t r u m a t 60pps* t h e k i c k s o r t e r method was u s e d o n l y t o c h e c k some o f t h e d i r e c t When n o i s e  measurements* i s measured w i t h  t h e HP 4000D VTVM, t h e v o l t a g e  i n d i c a t e d b y t h e meter must be m u l t i p l i e d b y 1*13 t o o b t a i n t h e t r u e rms n o i s e to r e a d  output ^ * ^ »  T h i s i s because the meter i s c a l i b r a t e d  t h e rms o f s i n u s o i d a l , n o t random s i g n a l s .  correction i s necessary high frequency  a t s h o r t time  l o s s e s i n the meter*  t h e VTVM was measured and f o u n d by  (approximately)  observed  constants  t o account f o r the  The f r e q u e n c y  t o be l i m i t e d  a double time c o n s t a n t  An a d d i t i o n a l  response of  at high  frequencies  o f 0.02 ^ s e c .  n o i s e must be i n c r e a s e d f u r t h e r by t h e f a c t o r  Thus t h e ( l . + x')  115  where x*  = 0.02/T.  t o t h e "raw  any  frequency none was  ~t  in  e r r o r t h a t might r e s u l t  response available  f o r the  1.76  Table  R e s u l t s of N o i s e  Using  experiment  .16  .32  1.43  1*28  5.1  and  time  the  constants.  so the HP  For  of  noise charge v e r s u s  58 C  show the  curves  effect  be for  used*  1.6  3.2  8.0  1*18  1*15  1 .14  1.13  T(with detector  capacitance  four preamplifiers.  F i g . 5.10  f o r the  5.9(b) and  theoretical  5.9  f.e.t.  5.10(b),  pre-  the  as the v a r i a b l e  o f a change i n d e t e c t o r c a p a c i t a n c e  e a c h p r e a m p l i f i e r , the  previous  f o r t h e E810F c h a r g e - s e n s i t i v e  In P i g s , 5.7(b),.(5.8(b),  broken l i n e s , C h a p t e r 4.  t o be  *8  charge i s p l o t t e d w i t h d e t e c t o r c a p a c i t a n c e  t o show t h e  high  Charge Measurements  f o r t h e N u v i s t o r p r e a m p l i f i e r , and  noise  use  However  400D had  and v o l t a g e — s e n s i t i v e p r e a m p l i f i e r s , r e s p e c t i v e l y , P i g ,  amplifier*  The  B  the d i r e c t measurement method d e s c r i b e d i n the  curves  5.7  below  Meter High Frequency C o r r e c t i o n s  as a p a r a m e t e r ) were o b t a i n e d f o r the Figs.  5.1  from approximating  o f the m e t e r w i t h two  • 08  a-sees.  section*  " c o r r e c t i o n f a c t o r s " t h a t were a p p l i e d  band VTVM f o r the n o i s e measurement would have  correction factor  5.3  net  n o i s e v o l t a g e s are g i v e n i n Table  of a b r o a d e r avoided  The  curves,  more  clearly.  shown as  were c a l c u l a t e d f r o m the n o i s e p a r a m e t e r s g i v e n i n  The  c a l c u l a t i o n s were s i m i l a r  f o r a l l the  circuits  e x p l a i n e d b r i e f l y w i t h t h e a i d of t h e f o l l o w i n g sample the E810F p r e a m p l i f i e r .  and  can  calculations  116  "( (psecs) F i g . 5.7(a) N vs. T f o r E810F Charge Sensitive Preamplifier  20  40  60  80  100  d  140  160  180  c ( f) f o r E810F Charge Sensitive Preamplifier d  F i g . 5.7(b) N vs. C  120  P  FWHM (KEV)  1.0 "C  (jJeecs)  F i g . 5.8(a) N vs. X f o r E810F Voltage Sensitive Preamplifier  20  100  40  120  160  180  c (pf) d  F i g . 5.8(b)  N vs. C  d  f o r E810F Voltage Sensitive Preamplifier  20  40  60  80  C (pf) d  F i g , 5..9(b) N vs,  C  d  f o r Nuvistor Preamplifier  100  119 N(e,c)  FWHM(KEV)  G = 68pf d  14 -  12  10  3  GJ*  \- _ o - — « -  Opf  Measured with Meters Theoretical Curves I  I — J  1—i_  0.1  10  1.0 X F i g . 5.10(a)  20  (jC/secs)  N vs. f f o r F.e.t. Preamplifier  •"  40  60 C (pf) d  F i g . 5.10(b)  N vs. C  d  f o r F.e.t, Preamplifier  0  &  100  120  \ For  a cascode  are found K = 10~  is  f r o m P i g s . 4.8 .  1 3  current  c u r r e n t o f 20 ma t h e n o i s e p a r a m e t e r s i n t h e E810F  The g r i d  and 4.3  resistor  N = C(x)l.71(27  If  these v a l u e s  o f T^t  t  f r o m F i g . 2.6 t o be respectively  T  T^  t  h  (27  3  circuit.  +  .86, .91, and .95 a t  .(5.4)  + 5  2  d  response  of t h e  c a l c u l a t i o n s by t h e (xsec.  C ( x ) can be X = 0.1, 0.2  at a l l longer .T's.  of C ( x ) t h e c a l c u l a t i o n  out i n Table  o )  = t r i s e / 2 . 2 = 0.18  "correction factor"  and n e g l i g i b l e  values  Flicker  e  T  results  3  r  d  then  leakage  of t h e tube  13. 5 x l 0 T  13.8  C )  c a n be a p p r o x i m a t e d f o r n o i s e  time c o n s t a n t  these  c h a r g e o f t h e E810F  +  = 3na and  L  q u a n t i t i e s i n E q n . 2.14  i t i s assumed t h a t t h e h i g h f r e q u e n c y  preamplifier  carried  c o n t r i b u t e s an a p p a r e n t  S u b s t i t u t i o n of these  i n Eqn. 5.4 f o r t h e n o i s e  and  = 70 ohms, I  n  o f 1\ = 0.5na and t h e n e t i n p u t c a p a c i t a n c e  25pf.  single  t o be R  found and 0.4  Using Eqn.  of N f o r C  d  With  fxsecs  5,4  = lOpf i s  5.2.  - Shot  Grid  Sum  N(o)  Corr. Fac.  N(x)  .i  5  138  .96  144  758  .86  "™65o"  .2  5  69  1.92  76  552  .91  502  .4  5  34.5 .  3.84  43.3  417  .95  394  1.0  5  13.8  9.68  28.4  338  338  2.0  5  6.9  3 52  352  Table  5.2  19.2  31  a  C a l c u l a t i o n o f N f o r E810F P r e a m p l i f i e r (C, -  lOpf)  121  The  validity  o f the  assumption that white noise  f o r x l a r g e enough t o a f f e c t calculation,.  As  the  noise  charge  the d e t e c t o r c a p a c i t a n c e  were o b t a i n e d similar  f o r the  i n v e r s e square other  Device  Tube (E810F)  Config.  Ch»  sens«  o f C^*  Vol.  the  Ch.  20  20  8  R  70  80  370  3  3  6  2  1  n  (ohms)  I^(na) Ii(na)  ,5 IO"  K(v /c) 2  t  r  (ixsec)  T^(usee)  C.(pf) c  f b  ( f) P  c a n be  c h a r g e f o r any divergence  1 3  Ch.  sens. 2  2  IO"  1 3  6 x  10"  *04  .*06  .3  .018  .018  .027  .136  25  25  8  16  2  0  2  2  5*3  1 3  Data f o r C a l c u l a t i o n o f N f o r Preamplifiers  s e e n f r o m a l l the  of the  by  f.e.t. (2N2386)  .04  Table  It  io-  1 3  devices  5.3.  sens.  I (ma) h  other  Nuvistor (7586)  sens*  leakage  T h e o r e t i c a l curves  data In Table  Tube (E810F)  the  assumption  dependence o f t h e  c o n d i t i o n s and  c a l c u l a t i o n s u s i n g the  i s d e m o n s t r a t e d by  i n c r e a s e s , the  becomes even more a c c u r a t e b e c a u s e o f t h e c u r r e n t n o i s e upon t h e  predominates  three devices  between t h e e x p e r i m e n t a l  curves  t h a t the  theoretical  noise  can be v e r y n e a r l y a c h i e v e d . and  theoretical  curves  is in  The  122  most c a s e s are  w i t h i n the  some s y s t e m a t i c  follows* that  Firstly,  expected  the minimum n o i s e  some s e c o n d - s t a g e ,  Secondly,  t h a t the  were  to the h i g h f r e q u e n c y show t h a t o b s e r v e d  noise  charges  indicating  experimental  f o r the  of t h e meter and  can be  than  constants  effect  U n d o u b t e d l y a more d e t a i l e d  response  noise  i n t e r p r e t e d as  lower  measured a t s h o r t time  theoretical values  perhaps inadequate.  be  there  stray input noise i s  c o r r e c t i o n s a p p l i e d to the  meter l o s s e s , o r to t h e  However,  i s never achieved,  p o s t - a m p l i f i e r , or  t h e o r e t i c a l values were  indicating  accuracy.  d i f f e r e n c e s which can p r o b a b l y  added to that c a l c u l a t e d . the  experimental  . values f o r  of  T^  approximation  p r e a m p l i f i e r s would  p r e d i c t e d a c c u r a t e l y at a l l  frequencies* The  results  predictions noise  o f the  o f s e c t i o n 4*3*2.  device  except  at  N u v i s t o r i s supferior* the  noise  very Of  c h a r g e — s e n s i t i v e one  c h a r g e measurements v e r i f y That  low  the  i s , the  the  E810F i s t h e b e s t  d e t e c t o r c a p a c i t a n c e , where  two  low  the  c o n f i g u r a t i o n s u s e d f o r the E81.0F,  e x h i b i t e d lower  noise, p a r t i c u l a r l y  at  h i g h f r e q u e n c i e s , b e c a u s e i n the V o l t a g e - s e n s i t i v e a m p l i f i e r s a d d i t i o n a l noise increases B sensitive u s e d was  grid  f r o m 70  t o 80  p r e a m p l i f i e r was 22 meg  sensitive the  n  generated  by  resistor  the  At  inferior 100  Decreasing  meg the  low  resistor  f r e q u e n c i e s the  voltage  mainly  because the g r i d  as was  used i n the  feedback r e s i s t o r  resistor  charge  and i n c r e a s i n g  s h o u l d t h e n make t h e v o l t a g e - s e n s i t i v e a m p l i f i e r  more n e a r l y c o m p e t i t i v e w i t h  alone,  unbypassed feedback  ohms.  r a t h e r than  circuit.  the  the  All  the  curves  and  t h e minimum n o i s e  the  charge—sensitive  show the n o i s e  optimum t i m e - c o n s t a n t s  levels  f o r the  e x h i b i t e d by i n these  one. the  curves  amplifiers  do  a m p l i f i e r s when t h e y  not  indicate  are u s e d  with  123  detectors. that  The d i f f e r e n c e s were d i s c u s s e d  time i t was p o i n t e d  noise,  t h e optimum time  those given  here.  i n S e c t i o n 4.3.2  and a t  out t h a t t h e a d d i t i o n o f t h e d e t e c t o r constants  are c o n s i d e r a b l y  shorter  than  124  6.  The the  study  many r e c e n t  reported advances  tube a m p l i f i e r s s t i l l triode—connected detector types  CONCLUSIONS  i n this  i n solid-state  and t h e 7586 N u v i s t o r Of  nucleonic  found  t o be t h e  amplifiers.  Below t h a t ,  tube f o r a l l some o l d e r  d e v i c e s , the f i e l d  most  s u i t a b l e f o r use i n  The 2N2386 n o i s e  l e v e l s were 8 0 % h i g h e r  those  obtained  with  t h e E 8 1 0 F , b u t t h e y were s t i l l  half  those  expected  with  junction transistors.  a p p l i c a t i o n s where minimum s i z e  preference more to  to the j u n c t i o n t r a n s i s t o r s diode  Apart merit  from these  of v a r i o u s  results*  now  and p a r a m e t r i c  be u n s u i t a b l e f o r l o w - n o i s e general  Therefore, i n  nucleonic  commonly u s e d . a m p l i f i e r s were  regarding  p r o d u c e d many  P r e l i m i n a r y d i s c u s s i o n s of the " t y p i c a l "  n o t g e n e r a l l y improve t h e n o i s e p e r f o r m a n c e .  effect  of feedback i n r e d u c i n g  a cathode Of sensitive"  one has g r e a t e r  experimental  convenience.  shown  the r e l a t i v e subsiduary  counting and a m p l i f i e r A l s o the  the i n p u t capacitance  of (say)  f o l l o w e r c a n n o t be u s e d t o r e d u c e t h e n o i s e the a l t e r n a t i v e  The  work.  conclusions  a m p l i f i e r s j . t h e study  be u s e d i n  s y s t e m showed t h a t m a t c h i n g n e t w o r k s between s o u r c e will  roughly  and power d i s s i p a t i o n a r e more  t h a n minimum n o i s e j t h e f » e , t , s h o u l d  "exotic" tunnel  tube  effect  than  important  A  are s u p e r i o r .  t h e ("modern" s o l i d - s t a t e  t r a n s i s t o r was  conventional  resolution.  t o be t h e b e s t  above l O p f .  i n spite of  electronics,  give the b e s t n u c l e o n i c  E810P was f o u n d  capacitances  t h e s i s shoved t h a t  charge.  feedback c o n f i g u r a t i o n s , the "charge stability  and p r o v i d e s  greater  I t has b e e n s t a t e d i n o t h e r  reports  125  t h a t the charge because found  c o n f i g u r a t i o n a l s o has p o o r e r  i s added t o t h e t o t a l  capacitance.  i n noise  sensitive  charge.  The  noise  generators, writing  theory  aspect  t h e charge  account  sensitive configuration  c a n be r e p r e s e n t e d by two n o i s e  and one i n shunt  the s p e c t r a l d e n s i t i e s  with  the i n p u t .  of the generators,  cutoff  derived f o r a frequency  response  and d i f f e r e n t i a t i n g  f a c t o r " was s m a l l * b u t i t r e s u l t e d t h e o r y and e x p e r i m e n t t h a n The  noise  charge  d e f i n e d by s i n g l e , time  constant.  The  equations  equal "correction  i n b e t t e r agreement between  i s u s u a l l y obtained*  c h a r g e i s a minimum when t h e " w h i t e "  o f t h e two g e n e r a t o r s  To  of the p r e a m p l i f i e r , a  " c o r r e c t i o n f a c t o r " has b e e n a p p l i e d t o t h e n o i s e  integrating  the " c l a s s i c a l "  c a n be a p p l i e d t o a l l a m p l i f i e r s .  f o r the high-frequency  By  i n t h e same  of the u s u a l tube n o i s e g e n e r a t o r s , ,  of G i l l e s p i e  change  too*  of each d e v i c e  one i n s e r i e s  f o r m as t h o s e  n o i s e added i n  c o n f i g u r a t i o n causes an even l a r g e r  Therefore  superior i n this  resolution  However, i t was  f o r i»he E810F t h a t t h e f e e d b a c k r e s i s t o r  the v o l t a g e  is  sensitive  are equal*  components  B e c a u s e o f t h i s , t h e minimum R^^*  n o i s e c h a r g e f o r any d e v i c e i s d e t e r m i n e d  by i t s product  where R ^ i s t h e e q u i v a l e n t n o i s e r e s i s t o r  and 1^ i s t h e e q u i v a l e n t  input leakage  current*  the d e t e c t o r leakage i n determining  I n most a p p l i c a t i o n s *  1^ i s swamped b y  c u r r e n t so R ^ i s the most i m p o r t a n t  t h e minimum n o i s e *  parameter  To be c o m p e t i t i v e w i t h t h e  E810F, a d e v i c e must have an e q u i v a l e n t n o i s e  resistor  less  than  80 ohms* B Instead,  n  and 1^ a r e n o t u s u a l l y g i v e n i n d e v i c e the n o i s e f i g u r e , F i s quoted.  specifications*  U s i n g E q n . 2.32, t h e  126  noise  charge  f o r judging  c a n be f o u n d f r o m F , g i v i n g an a l t e r n a t i v e  w h e t h e r an a m p l i f i e r i s s u i t a b l e f o r t h i s a p p l i c a t i o n ,  To compete w i t h t h a n 0*2 It f*e*t**s  R  n  must e x h i b i t a n o i s e t u b e s , l e s s t h a n 0.1  i s possible to p r e d i c t R  performance i n the order and p r e d i c t t h e i r  the f l i c k e r  noise  exact  constant  noise  to rank  However,  to  performance, R  K must be f o u n d  1^ f r o m dc measurements o f l e a k a g e  Nuvistors,  enough a c c u r a c y  given.  a n d K c a n be f o u n d by t h e r e s i s t i v e  figure less db.  and 1^ f o r t u b e s ,  n  and j u n c t i o n t r a n s i s t o r s w i t h  amplifiers and  f . e . t . ' s a device  d b . and t o compete w i t h  their noise  criterion  n  design and 1^  experimentally.  s u b s t i t u t i o n method, and  current.  By p l o t t i n g t h e  measured p a r a m e t e r s i n t h e p l a t e c h a r a c t e r i s t i c s ( s o u r c e characteristics different  f o r t h e f . e . t * ) , t h e optimum b i a s p o i n t s f o r  detector  leakage  f o r t u b e s and N u v i s t o r s  t h e optimum b i a s stage of a general  be b i a s e d  a t as h i g h  As t h e d e t e c t o r  p o i n t moves t o h i g h e r  as p o s s i b l e .  effectively  the p r e d i c t e d noise  eliminate  therefore  S i m i l a r arguments  the b a s i s  levels,  second stage n o i s e .  c a s c o d e c o n f i g u r a t i o n does t h i s .  a m p l i f i e r s must  I t was  However,  c a s c o d e i s n o t l a r g e enough t o make c h a r g e  effective,  so i t s l o a d i s commonly  g a i n as r e q u i r e d , w i t h o u t  the g a i n  the g a i n  of the f * e * t *  circuit  g a i n of  feedback  "bootstrapped".  a f f e c t i n g the n o i s e  can a l s o be u s e d t o i n c r e a s e  Increasing  shown t h a t t h e  the v o l t a g e  E810F p r e a m p l i f i e r d e m o n s t r a t e d t h a t b o o t s t r a p p i n g  it  leakage  current.  purpose a m p l i f i e r should  a current  shown  f o r the f . e . t . To a c h i e v e  fully  I t was  are near the p o t e n t i a l  on open c i r c u i t .  The i n p u t  apply  c a n be f o u n d .  that these points  at which the g r i d f l o a t s increases,  currents  The  i n c r e a s e s the  performance.  of the N u v i s t o r requires  Thus  circuit*  the use o f  127  junction transistors With the on  low—noise  the  latest  has  completion  nucleonic  t u b e s and  t h e E810F and  the  been a s s e s s e d  that noise  of h i g h e r  8 than  of t h i s  study,  a m p l i f i e r s has  solid-state  those  "classical"  devices.  The  work  include  potential  of  2N2386 f o r l o w — n o i s e  nucleonic amplifications  f o r the  The  i s required, while low  the  been updated to  first  time.  the E810F i s s u p e r i o r to a l l o t h e r  when b o t h  used.  noise  and  the  field  solid-state  assessment  showed  d e v i c e s when minimum  effect  transistor  circuitry  are  i s superior  required.  128 APPENDIX I  Evaluation  o f I n t e g r a l s Used  The  four  integrals  i n Theory  used  i n the t h e o r y  (i-^I  C h a p t . 2; 1^ i n C h a p t . 4) a l l have t h e g e n e r a l so  t h e y c a n be expanded  to  give  and 1^, i n  f o r m o f E q n . 1.1, '  i n p a r t i a l f r a c t i o n and i n t e g r a t e d as shown  Eqn* 1*2.  to da> m  i 2%  (l4<o T )(l*o T )(l4to T ) 2  2  2  2  2  2  m  2 f o r I.  m  0 f o r I,  * ... I«1  m = 1 f o r I,  0 -oo  I =  B  1 ^  271  _(l+a T ) 2  dco  (l*o T )  2  2  (1-K0 T ) 3'  2  2  0  2  J CO  OO  Atan^CtoTi )  I =•  , Btan T 2 fo=0  Ctan  (<oTo,  l  T  2  4,  The  constants  substituting relates  [ T ,  + 3_ + T  2T  2  to=0  <o=0  -.1.2  3  A* B, and C c a n be f o u n d f o r 1^, I 2 2 2 2 s u c c e s s i v e l y to = -T^, , to = ~^2  f  W  2  2  separately  1*3  n  to the o r i g i n a l  P o r I ^ , when m i s o d d , t h e c o n s t a n t s  one i n t e g r a l must be t r e a t e d  and 1^ by  2 ~^3 •^1 '  =  t h e n u m e r a t o r o f t h e expanded i n t e g r a n d  expression* this  r  (toT-Q T  a r e i m a g i n a r y so  ( s e e E q n . 1.5 and  following), <..1.3 to = A ( l - K * T ) ( l - k o T ) n  2  2  2  2  + B(l-W> T )(l-Ko T ) + C(l-Ko T ) (l+co T ) 2  2  2  2  2  2  2  2  129 For  I , , I - and I . t h e d e n o m i n a t o r s o f t h e c o n s t a n t s 1' 2 4  same and a r e g i v e n by E q n . 1.4. and  each constant  - T )  [C] = ( T - T ) ( T  2  - T )  (c)  Den  (T  2  2  2  2  m  -T  0  T  Table  Upon s u b s t i t u t i n g  V  a  ;  Num.(B)  T  4 1  -T  4  1  -1  1.1  I  2  -T ) 2  constants  2  3 A  T  3  l  1 Numerators  i n E q n . 1.2 and s i m p l i f y i n g ,  result.  + T )(T  2  2  L  F r a c t i o n Constants'  T  X  _T  2  . .'  1 ~ 4(T 4 T )(T  - T ^ T  Num.(C)  l  these  and I ^  2  2  Partial  2  ...(1.4)  2  4  4  E q n . 1 . 5 f o r 1^, I  ( b ) Den [B] = ( T  2  Num.(A)  2  h  1.1.  are g i v e n i n Table  2  Den [A]  (»)  The n u m e r a t o r s f o r e a c h i n t e g r a n d  - T )(T  (a)  are the  3  X  + T ) 3  440 T *° > 2 X  T _  j  ( T  l 2 + lV, 2 3 T  T  T  T  4 (T- +T ) ( T + T ) (T-,+T ) L  2  2  3  3  T (T + T + T ) 2  X  (c)  I,  =  3 "  2  3  4T T T (T +T )(T +T )(T +T 1  2  3  To e v a l u a t e  1  I  2  3  2  3  1  , the o r i g i n a l  i n E q n . 1*6, so t h a t A, B and C w i l l  ..(1.5) 3  integral  i s expanded  be r e a l .  can be e v a l u a t e d by i n s p e c t i o n t o be E q n . 1 . 7 *  as shown  The expanded  integral  This expression  vanishes  130 at  the lower  letting found  to—>- oo  A t t h e upper l i m i t  after  substituting  as b e f o r e by e q u a t i n g  unexpanded the  limit.  integrand.  same as f o r  i t c a n be e v a l u a t e d by-  A, B and C.  the numerators  F o r I ^ and t h i s  and r e s u l t  The c o n s t a n t s  were  o f t h e expanded and  new e x p a n s i o n ,  A, B and C a r e  i n Eqn. 1.8 f o r 1^,  DO  B  (H<o T ) 2  T£  2~ 2T A  2%  C  2 2(l-k^Tp  B  ln(l-Ko T ) 2  dW  2, 2.  ...1.6  ( l - r t on ^ )  m  2  2  oo +  ln(l-K0 T ) 2  2  2  2T  ln(l-Ko T )  2  2  2  2T  0  0 .1.7  T T ln(T /T ) 2  2  1  I„  =  2n  2  (T  + T T ln(T /T 2  3  - T )(T  2  2  + T T ln(T /T3][  2  2  1  - T )(T  2  2  2  2  2  - T ) 2  ...1.8  E q n s . 1*5* and 1.8 a r e t h e e x p r e s s i o n s for  arbitrary  T-^ = T case,  2  = T,  T^, T  2  and T^.  and T^ '= xT < "T*  the f o l l o w i n g  simplified  of the f o u r  In the theory the s p e c i a l i  s u  s  e  (  i  exclusively.  integrals  case  when  For this  e x p r e s s i o n s f o r the i n t e g r a l s  c a n be  found.  (a)  (b)  I-, =  (b)  8 T(l+x)'  2x  2  lnx +  i 3li±2sl 2  (l-x)  47t(l-x ) 2  2  2  (2+x)  2  (c)  8(l+x)  I 4  8xt (l+x) 3  2  131 APPENDIX I I  F«e»t» A d m i t t a n c e The recommended  admittance  parameters  Parameters  were measured i n t h e manner  by the manufacturer.  I n t h e case o f t h e i n p u t  a d m i t t a n c e s Y, and Y , a s e c o n d d i r e c t on a H e a t h k i t Q-meter» straightforward outline  graphs  a)  Forward The  The measurements were a l l r e l a t i v e l y  so t h e d e s c r i p t i o n h e r e w i l l  of the r e s u l t s  be l i m i t e d  of the t e s t  forward transadmittance^ Y ^  signal  100 ohm l o a d r e s i s t o r *  circuit,  Y^  causes  f  was measured w i t h t h e c i r c u i t  the d r a i n current a voltage  f  d r a i n c u r r e n t f o r t h e two f . e . t . t s  Curves  a r e shown i n F i g *  ments were made a t f r e q u e n c i e s o f 10 k c ^ l O O k c , v a l u e o f Y^ h a s s t a r t e d t o f a l l  be p r e d i c t e d i f t h e p a r a s i t i c  f r o m g* b u t t h a t  or instructive  b)  Transadmittance Y  Reverse  The  .  J i g of F i g *  slightly*  11*5. Measure-*  and 1 mc.  calculation  A t lmc  This behaviour can i n the  i s not p a r t i c u l a r l y  and w i l l be e m i t t e d ,  £  11*2 g i v e s Y^ (whiiijh: i s s C  c i r c u i t ) only I f the input  The  o f Y^ v s .  capacitances are included  interesting  —  ( i n mv)*  2  t h e o u t p u t c a n be c o n s i d e r e d t o be s h o r t  c i r c u i t e d as i s r e q u i r e d f o r a measure o f Y^*  of g  resulting  = v^Y^'100 i n t h e  Hence Y | ( i n M i l l i m h o s ) = V  i s s m a l l enough t h a t  ^calculation  jigs,  Transadmittance  f r o m t h e 10 mv g a t e  the  to a b r i e f  obtained.  shown i n F i g . I I . 1 . I n t h i s  load  measurement was a l s o made  o f t h e e x p e r i m e n t a l p r o c e d u r e * diagrams  and  and o u t p u t  g d  i n the equivalent  c a n be c o n s i d e r e d t o be s h o r t  circuited*  132  P i g * 11*1  • J i g t© Measure I  f  i of F.e*t«  To see t h a t t h e 10K gate r e s i s t o r e f f eetiAfely s h o r t c i r c u i t s the i n p u t , c o n s i d e r t h e e x p r e s s i o n f o r t h e gate c u r r e n t i n terms of the 4 admittance parameters. t h a t I ( l ^ 10^1^) g  Itisf I  = Y Y * r  2  =  + ^r^2'  V  l  =  I  g  1  G  ' ^°  Now 1 0 I ^ i s much l e s s t h a n u n i t y and 4  the 1OK gat6 r e s i s t o r a c t s as an e f f e c t i v e ' s h o r t c i r c u i t , as i s r e q u i r e d * The 1 v o l t s i g n a l V causes a c u r r e n t T t o f l o w i n t h e 4 /' gate r e s i s t o r g i v i n g r i s e t o a v o l t a g e Y- « 10 T so t h a t I ( i n 0  umhos) = *1V^ ( i n mv)*  I t was assumed t h a t I  r  can be approximated by  the s i n g l e c a p a c i t o r C ^ which was c a l c u l a t e d and p l o t t e d i n the s t a t i c c h a r a c t e r i s t i c plane (see F i g * II«6)« can be seen t h a t  Prom these c u r v e s , i t  i s r e l a t i v e l y iiijdepen^lent o f t h e d r a i n c u r r e n t  i n t h e pinch«-*eff r e g i o n *  c)  Input Admittance 1^ Because o f t h e importance o f 1, = s(G _ + C, ) i i . t h e p r e d i c t i o n i gs , as .  of n o i s e , i t was measured i n two s e p a r a t e Ways*  F i r s i d i r e c t l y on a  H e a t h k i t 0>meter u s i n g t h e t e s t c i r c u i t <*£ P i g * 1 1 . 3 ( a ) , t h e n  133  GND P i g . I I . 2 J i g t o Measure T  i n d i r e c t l y u s i n g the j i g of P i g . 1 1 . 3 ( h ) .  r  of F.e.t.  The d i r e c t method i s  obvious w h i l e t h e i n d i r e c t method c a n be u n d e r s t o o d by c o n s i d e r i n g the e q u a t i o n I  8  above. W i t h t h e source s h o r t c i r c u i t e d t o the d r a i n ,  V £ i s nov zero and 1^ - T^Y^ where Yj, «=  - lOOmv.  Substituting  t h i s i n t h e e q u a t i o n and s o l v i n g f o r Y^ g i v e s  Y.^  (v" i n mv, Y^ i n umhos) o r , a p p r o x i m a t e l y  = 0*1V *  2  Y^  = 10 v" /(lOO-V" ), 2  2  2  Both methods  gave s u b s t a n t i a l l y t h e same r e s u l t s , and these are d i s p l a y e d i n P i g . 11*7 as cualwes o f c o n s t a n t c a p a c i t a n c e i n the d r a i n c h a r a c t e r i s e plane*  F i g * 11*3(a) J i g t o Measure Y^ of P*e«t» D i r e c t l y  134  VTVM  F i g . 11,3 (b)  d)  Output Admittance X  and  i  Q  and r e a l p a r t s Of t h e output a d m i t t a n c e . X  The i m a g i n a r y were measured  J i g t o Measure I o f F . e . t . Indirectly  Q  ,  s e p a r a t e l y u s i n g the two c i r c u i t s shown i n F i g s . 11.4(a)  (b)» The o p e r a t i o n o f t h e d i r e c t method i s a g a i n s e l f - e v i d e n t ,  w h i l e t h e i n d i r e c t method f o l l o w s from t h e e x p r e s s i o n I , = X„\T d i gs - Io Y gd,» I n t h i s case V gs = 0, ' so t h e d r a i n c u r r e n t i s e n t i r}e l y due t o t h e a f f e c t o f V and X . Nov V- = 100 I , and V , = i v - V gs o 2 d gd \ Z r  0  which upon s u b s t i t u t i o n i n t h e equation, f o r 1^ g i v e s X = 10V /(lO0Oi*Y ) = 1 0 V , where V 2  2  2  2  i s I n mv  #  Q  ( i n umhos)  The r e s u l t s o f t h e  d i r e c t measurements showed t h a t t h e c a p a c i t i v e component of X i s q  i n d i s t i n g u i s h a b l e from output conductance g  Q  i n d i c a t i n g t h a t C^  g  can be i g n o r e d .  The  o b t a i n e d from t h e o t h e r measurement was checked by  comparing i t w i t h t h e slope o f t h e s t a t i c c h a r a c t e r i s t i c s tlteh p l o t t e d i n F i g s . II«8(a) and (b) a g a i n s t t h e d r a i n c u r r e n t .  135  Fig*  II*4(a)  J i g t o Measure I  of F . e . t ,  Directly  F i g . 1144(b)  J i g t o Measure T  o f F.e#t«  Indirectly^  Fig.  11.5(a)  Y  of F.e.t.  f  #1  ^(aa) Fig.  11.5(b)  I  f  of F . e . t .  #2  1.0 .8  /  .6 .4  8pf  6pf  3pf  4pf  5pf  .2  F i g . 11.6(a)  C  d g  of F.e.t* #1  2.8 (2.4 2.0 _  V  =  0  /  1,6 6pf  8pf  1*2  3pf  4pf  5pf  .8 .4  _t_ -2  -4  .6  J -8  I -10  L_ -12  -14  -16  V (volts) d  F i g . 11.6(b)  C,  of F.e.t. #2  -18  138  -2  -4  -6  -a  -10  -12  -H  -16  -18  -20  Y (volts) d  Fig.  11.7(a)  F i g . 11.7(b)  C. = C  C±  g s  = C  + C^  of F . e . t .  d  + C  g d  of F .e.t. r  #1  #2  139  Pig.  11.8(a)  I  Q  o f F . e . t . #1  140 APPENDIX I I I  D e r i v a t i o n of P r e a m p l i f i e r Gain  a)  Gain  o f Tube C a s c o d e w i t h  The by  the  "Bootstrapped"  cascode of F i g *  III*l(b)*  Fig*  Cascode  111*1(a)  Boostrapped  various grid voltages  ~ = ix, V , — I r , , V - = — I R^,* g2 ^ l gl p pl g3 p 2 T  i n the Fig*  c a n be  (b)  values  simplified  represented  Equivalent  seen to be 5 V  ¥hen these  e q u i v a l e n t c i r c u i t , i t c a n be  Load  111*1(a) can be  e q u i v a l e n t c i r c u i t of F i g *  The V  "bootstrapped"  Expressions  ^  =  ^in*  are s u b s t i t u t e d  t o the  form  I I I 2 below* a  Hi* Fig,, 111*2  Simplified  Equivalent  Circuit  Circuit  shown i n  141  The c u r r e n t I  around the l o o p i s :  P  V T  P  =  R  I  +  R  2  +  2  r P  t  i n H^2 * p l  +  U  ^  ^  +  TTT + R  l*m3 2  -J  *  R  The output v o l t a g e i s ;  T  Therefore  _ -I RJ(l + g B )  Q  p  m 3  ...111.2  2  the g a i n i s : u ( i 1  A  cb  = B{  + R  2  +  r  p  t  2  + 1)R|(1 + g R )  2  m 3  r  +  p  l  U  +  ^  +  2  R ^ ^  "-  1  1  1  '  3  !  To f i n d the g a i n of the unbootstrapped cascode, l e t R R  l ~ L* ^ R  v  e  r  "k^e l o a d r e s i s t a n c e *  e  +  A  c  =  R  L  +  r  p2  +  r  p l  U  1  )  R  2  = 0 and  The cascode g a i n i s then:  L  + *2>  ...111.4  The optimum v a l u e s of R^ and R > flan be found by maximizing 2  the approximate e x p r e s s i o n III«5 w i t h r e s p e c t to R^ l  been assumed t h a t \i »  and the sum o f  t  and R  2  8  I n 111*5 i t has  has been t a ^ e n t o  be R.  D i f f e r e n t i a t i o n with respect t o dA  ^ ^ gm3  c b  JT|  1  =  1  2  ( R  ~  2 B  i>  r e s u l t s i n j ''  [Denominator - g ^ R ^ R - R ^ ] n  (Denominator)  •*«lll O a  142  The gain  b)  derivative  i s z e r o o n l y v h e n B^  i s a c h i e v e d vhen the  two  l o a d r e s i s t o r s are  G a i n of F * e * t , - J u n c t i o n To  consider current  determine the F i g * 111*3  gain  below*  (a)  The  o f the  I n 111*3(b) the  voltage  gain  of the  B^  apparent l o a d r e s i s t a n c e  I d i v i d e s between R^  e q u a l s the  resistance  voltage  r /(!-<*).  and  drop across Thus,  T^  transistor  r  o  circuit  (b)  circuit*  been r e p l a c e d  i n accordance  so t h a t  f o u n d as the  by  with  i s then;  Simplified  Circuit  111*3  can be  the  Circuit  c a s c o d e has  F*e*t»-junction T r a n s i s t o r C i r c u i t  t h e i maximum  equal.  f*e*t •function  Fig*  The  therefore  T r a n s i s t o r Combination  g e n e r a t o r g V. with internal resistance ° °m i n  Norton*s theorem.  current  = B/2,  follows.  voltage  drop  The across  (approximate) base-emitter  a  143  I (B 1  The v o l t a g e  + r / ( l - a ) ) = IB^  1  .111.8  e  change c a u s e d b y t h e c u r r e n t I s *  V  o *  I  1 3 2 P  (assume P  R  Therefore the apparent l o a d  \  = r  3  » l j  R  2  Eqn. the  =  B  t  r  + r ^ / ( i -«)  ...III.?  r  B  1  2  This w i l l  ^  n  e  1  + p^) ^  o  r  ^  n e  tube  circuit.  Q  l"k S a  transfer  e  i n g e n e r a l be l a r g e r  e x p r e s s i o n Eqn* I I I . 1 1 c a n be  ^ ^  t h a n R ^ l so t h e a p p r o x i m a t e  1  In  becomes  r a t i o f o r the junction t r a n s i s t o r  T * 3  gain  used*  g p.,R,R~ g 0,R,R„ nv3 1 2 w»> m 3 1 2 R + r e / U - a) '^ + rep 6  6  1  1  0  c a n be s e e n by i n s p e c t i o n o f  c a s e r ^ becomes l / g o f t h e f*e*t«, and  y o  T  .111.10  e  of the cascode r  T  R  Q  111*4 t o be a p p r o x i m a t e l y p i ( l  e2^ e2*  that  0  output r e s i s t a n c e  transistor  )  gm P3 l 2 = P R R + r R^ + r / ( l - c ) 3  The  3  r e s i s t a n c e R^ i s j  Upon s u b s t i t u t i o n o f 111*9 i n 111,7* i t i s s e e n  ,  « R  III.11  K  3  144 A p p e n d i x IV  Subsidiary Electronic A)  Post—Amplifiers  Two amplifiers  low-noise  p o s t - a m p l i f i e r s were b u i l t  to the Dynatron a m p l i f i e r during  measurements^ ring-of—three by  Equipment  an o u t p u t  The t u b e c i r c u i t c i r c u i t , with  f o r minimum n o i s e .  The  feedback i s taken the  followed  to the cathode of the  t h e g a i n f r o m t h e open l o o p v a l u e o f  p o s t - a m p l i f i e r shown i n F i g . IV.2 i s o f s i m i l a r  gain being  provided  by two g r o u n d e d e m i t t e r  impedance by an e m i t t e r f o l l o w e r . from the second stage  g a i n i s a d j u s t e d by v a r y i n g  gain i s roughly  stages  conventional  o f 10.  transistor  t h e low o u t p u t  charge  shown i n F i g , I V , 1 , i s a  Feedback from the output  design, the voltage and  the p r e -  The i n p u t tube i s t r i o d e - c o n n e c t e d  i n p u t t u b e c a n be u s e d t o v a r y 5000 t o a minimum  the n o i s e  two g r o u n d e d — c a t h o d e  cathode f o l l o w e r .  to couple  2000 w h i l e  rather than  In t h i s  stages  case  the output,  the f e e d b a c k r e s i s t o r .  and  The open  the c l o s e d l o o p g a i n i s a d j u s t a b l e  loop  from  20 t o 220.  B)  DC F i l a m e n t  The amplifiers  Supply  dc f i l a m e n t s u p p l y  i s shown i n F i g . I V . 3 .  reduce the r i p p l e The  first  ripple  stage  without  t o 50mv  the s e c o n d s t a g e  t h e E810F and N u v i s t o r  Cascaded  series regulating  precircuits  t h e u s e o f l a r g e chokes o r c a p a c i t o r s .  reduces the v o l t a g e  f r o m 0.5 v o l t s  set with  used w i t h  from 15 t o 9 v o l t s  ( a t 2 amps, o u t ) .  and t h e  The o u t p u t  which reduces the r i p p l e  voltage i s  f u r t h e r t o 2mv ( a t  145 2 amps)*  The power t r a n s i s t o r s a r e operated w e l l below t h e i r  maximum r a t i n g s * but they are bypassed by t h e r e s i s t o r s t o p r o v i d e a f u r t h e r margin Mt - r e l i a b i l i t y *  A t output c u r r e n t s below 1 amp, the  c u r r e n t drawn by the r e s i s t o r s i s l a r g e enough t o a f f e c t a d v e r s e l y t h e regulation circuit  circuits*  They can t h e r e f o r e * be " s w i t c h e d  when o n l y s m a l l c u r r e n t s are r e q u i r e d *  o u t " of the  The e f f e c t o f changes  i n t h e output c u r r e n t upon t h e r i p p l e and the output v o l t a g e are shown i n F i g * IV.4*  146  Bote:  a l l resistances in Kohms, a l l capacitances In Pig, IV.1  yt,  unless noted.  Tube Post-amplifier WD  Note: a l l resistances in Kohmsj a l l capacitances In |Jf, unless noted. Pig. IV.2  Transistor Post*-amplifier  147 4-  Note: a l l resistors in Kohmsj a l l capacitors i n f J f unless noted. Pig.  IV.3  D-c  Filament  Supply-  Output Current (Amps) Fig.  IV.4  R i p p l e and Output V o l t a g e  o f D-c  Filament  Supply  148  REFERENCES  Chapter  1  1.1  Secre** E*> e d . , E x p e r i m e n t a l N u c l e a r P h y s i c s * J o h n W i l e y and Sons I n c . , New Y o r k * (1959)*  1*2  B r o m l e y , D*A*, " N u c l e a r E x p e r i m e n t s w i t h Semiconductor D e t e c t o r s " . I»JB*E. T r a n s . on Nuc 1 * S c . * V o l . 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" C o n s i d e r a t i o n s i n the D e s i g n o f P u l s e A m p l i f i e r s f o r use w i t h S o l i d S t a t e R a d i a t i o n D e t e c t o r s " , I.R,E. T r a n s , on N u c l . Sey* V o l . NS-8* ( J a n . 1 9 6 1 ) , p . 129. "  2.6  C o t t i n i * G** G a t t i , E . , G i a n e l l i , G, and R o z z i * G., "Minimum N o i s e P r e a m p l i f i e r f o r F a s t I o n i z a t i o n Chambers", NUovo Cimento* V o l * 3* (Feb* 1 9 5 6 ) , p . 473* Chase•*• e t * a l * , op*  ' 2.7  cit*  2.8  van der Z i e l ,  2.9  T s u k u d a , M a s a h i r o , "The E f f e c t o f P u l s e S h a p i n g on t h e S/N R a t i o o f P u l s e A m p l i f i e r f o r use w i t h S o l i d S t a t e R a d i a t i o n D e t e c t o r s " , I*R«E* T r a n s * on N u c l * S c * * V o l . 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N o i s e , C h a p t e r  3.3  Robinson* F*N»H,, Noise i n E l e c t r i c a l C i r c u i t s * Oxford U n i v e r s i t y P r e s s (1962)* C h a p t e r V and V I , pp* 35-48*  Chapter  3.4  3.5  Noise, Chapter  3  -  5*  F a i r s t i e n * E*, "Grid Current i n E l e c t r o n T u h e s % Rev* S c . I n s t r . , V o l . 29 (June 1 9 5 8 ) , p * 524. Valley*  G*E«* and V a l l m a n , H., Vacuum Tube A m p l i f i e r s , M c G r a w - H i l l Book Co., I n c * , New Y o r k , ( 1 9 4 8 ) , p . 418.  van der Z i e l *  N o i s e , pp.  3.7  Robinson*  c i t . , p*  3*8  R o b i n s o n , op*  .3*6  5*  op*  flf'j*,  p.  224-232*  47. 41.  150 S h o c k l e y , ¥ * * "A U n i p o l a r 'Field Effect Transistor'", £roc> I.R.E., V o l . 40, (Nov. 1 9 5 2 ) . p*. 1365. Dacy* G*C* and R o s s . I.M., "The F i e l d - E f f e c t T r a n s i s t o r " , B e l l Syst. Tech. 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