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Millimeter-wave radiometer for the measurement of temperatures in hot transient plasma Carter, Charles Ruskin 1966

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A MILLIMETER-WAVE RADIOMETER FOR THE MEASUREMENT OF TEMPERATURES IN HOT TRANSIENT PLASMA  CHARLES RUSZIN CARTER B.A.Sc, University of B r i t i s h Columbia, 1962  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF APPLIED SCIENCE  i n the Department of E l e c t r i c a l Engineering  We accept this thesis as conforming to the standards required from candidates f o r the degree of Master of Applied Science  Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA March, 1966  In p r e s e n t i n g  this thesis  in p a r t i a l  f u l f i l m e n t of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y Columbia, for  the Library  r e f e r e n c e and s t u d y .  tensive by  I agree that  s h a l l make  I f u r t h e r agree that  copying of t h i s thesis  i t freely  cial  gain  that  available  pe rm i ss i on ' f o r e x -  f o r s c h o l a r l y p u r p o s e s may be g r a n t e d  t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s .  understood  of B r i t i s h  copying o r p u b l i c a t i o n  of this thesis  s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n  Itis f o r finan-  permission.  Charles Ruskin Garter  Department o f  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a Date  Snf/^t/-/^  t/^cft/cJ  vH>*vt 3°  Columbia  I %4>.  Abstract A superheterodyne Dicke type radiometer suitable f o r the measurement of radiation from a high temperature plasma i n the 35 GHz range has been developed^  The radiometer employs  a balanced mixer at the radiometer frequency, a 3.5 GHz parametric amplifier using a varactor diode as the f i r s t IF amplifier, a broad-band transistor amplifier at the second IF of 7Q MHz  and  a commutator detector. The performance of the radiometer has been measured by conducting hot load tests and by using an S-band argon noise source.  The minimum detectable temperature change was found  from the hot load tests to be 11 deg K f o r an output bandwidth of 0.32 Hz.  However,; from,argon noise source measurements, a •5  minimum detectable temperature change of 1.4 x 10  deg K was "I  determined f o r an output bandwidth of 6.4 KHz and 9.5 x 10- deg K for an output bandwidth of 160  KHz.  The equation f o r the minimum detectable temperature change f o r the Dicke radiometer has been deduced following conventional analysis.  It has been found that there are two  errors i n Goldstein's derivation the effects of which cancel out and h i s f i n a l formula i s correct. by Ring does not appear to be v a l i d .  Thus, the change suggested For the two channel subtrac-  t i o n radiometer i t has been found that the expression given by Graham should be multiplied by\/~2 . 1  The d.c. radiometer has also  been analysed and i t has been found that i t s minimum detectable signal power i s independent of both the radiometer bandwidth and the output  bandwidth.  The effect of noise at the radiometer input before the modulating switch has been investigated and i t i s shown that t h i s noise could produce a cutoff condition i n the Dicke radiometer and the two channel subtraction radiometer.  iii  CONTENTS Page . I i I S I OP SYMBOLS  vii  LIST'" OF ILLUSTRATIONS  x .  LIST OF TABLES  xi  ACKNOWLEDGEMENTS  xii  CHAPTER I -INTRODUCTION  1  CHAPTER II THEORY OF THE DICKE RADIOMETER 2.1  Introduction  6  2.2  Superheterodyne Dicke Radiometer  7  2.3  D.C. Configuration  10  2.4  Comparison of Radiometers  11  2.5  Noise Temperature, Minimum Detectable Temperature Change and Radiometer Noise Figure  12  CHAPTER I I I DESIGN OF A SUPERHETERODYNE DICKE RADIOMETER 3.1  Design Data  14  3.2  C i r c u i t Diagram^  16  3.3  Power Input to the Radiometer  16  3.4  Calibration of the Radiometer  21  3.5  Balanced Mixer  22  3.6, Reduction of Local O s c i l l a t o r Noise  23  3.7  Radiometer Noise Figure  25  3.8  Modulation Frequency  28  iv  Page 3.9  Choice of the P i r s t IF Amplifier  • 3.10 Varactor Diode Parametric Amplifier  28 29  3.11 Second Mixer  34  3.12 Second IF Amplifier  35  3.13 Band-pass Amplifier  36  3.14 Coherent Detector  36  CHAPTER IV RADIOMETER PERFORMANCE 4.1  Radiometer Tests  39  4.1.1  Preliminary Tests ....................  39  4.1.2  Hot Load Test  41  4.2  Radiometer Improvements  42  4.3  Plasma Measurements  43  ....  CHAPTER V CONCLUSIONS  45  APPENDIX I ANALYSIS OF THE DICKE RADIOMETER WITH ONE NOISE SOURCE  47  APPENDIX II ANALYSIS OF THE DICKE RADIOMETER WITH TWO NOISE SOURCE®  49  APPENDIX III ANALYSIS OF THE D.C. CONFIGURATION  59  APPENDIX IV ANALYSIS OF THE TWO RECEIVER RADIOMETER  62  APPENDIX V ANALYSIS OF THE TWO CHANNEL SUBTRACTION RADIOMETER WITH TWO NOISE SOURCES ' v  64  Page APPENDIX VI GAIN REQUIRED FROM THE BAND-PASS AMPLIFIER  70  APPENDIX VII DISCHARGE APPARATUS  72  REFERENCES  74  vi  L i s t of Symbols A,B  = constants  b.,b  = susceptances  b.  = b. + c  i s  b B  Wi  o  = b  so  s  i n the nonlinear-admittance mixer  o  + to C  s o  = output bandwidth  Q  C(t)  = capacitance i n the nonlinear-admittance mixer = C! + 2 C , cos out 0 1 2  C .0, o 1  = constants  f  = frequency  f^  = radiometer  ±2  = local oscillator  f^  = f i r s t intermediate frequency  f^  = idler  frequency frequency  frequency  t  f ,f g  = s i g n a l frequencies  g  Af  = a bandwidth i n the power  F  = radiometer n o i s e f i g u r e  F^  = n o i s e f i g u r e of the i ^ *  F^  = n o i s e f i g u r e of the system f o l l o w i n g the balanced mixer  F  = n o i s e f i g u r e of the parametric  1  spectrum  stage  amplifier  P  F g  i  , g  o  =  = noise f i g u r e of the second IF a m p l i f i e r ' ^ honlinear-admittance mixer c o n d u c  g  io  =  g  so  = s  g  g  t a n c e s  +  G  o  +  G  o  i  1 1 1  e  G(t)  = conductance i n the nonlinear-admittance mixer  G .G-,  = G; + 2 G cos w t 0 I d = constants n  0  1  0  Tii  = g a i n o f the hand-pass a m p l i f i e r = g a i n of the ( j - l ) ^ *  1  stage.  = g a i n of the parametric G-  amplifier  = t o t a l g a i n o f the a m p l i f i e r s  i n the  radiometer  S  G(9,0) = i s o t r o p i c g a i n o f the horn k  = Boltzmann's constant, d e t e c t o r constant  K K,  = constant = v o l t a g e gain-bandwidth product amplifier  L  = conversion l o s s o f the balanced  o f the parametric mixer  L ^ j L g , ! ^ = conversion l o s s o f c r y s t a l s L  = i n s e r t i o n l o s s o f the c i r c u l a t o r (between p o r t s )  1,  = l o s s between the balanced mixer and the parametric amplifier  I  = l o s s i n the c a l i b r a t i o n c i r c u i t , sum o f l o s s e s i n the radiometer  1  = l o s s i n the s i g n a l  Lw  = l o s s i n the waveguide r u n  n  = number o f stages  circuit  n ( t ) , n ( t ) ,n-^(t) ,n (t) = v o l t a g e s of noise Q  ^n'^n  2  sources  '^no•^nl*^n2 ~ average powers from noise  p  = output noise power from low-pass  out ^out  sources  filter  n  p  s  Q  o s  0U  ^P "' U  ;  Power from low-pass  filter  = average power from s i g n a l  s  p p  =  = minimum d e t e c t a b l e s i g n a l power  min  = output s i g n a l power from low-pass f i l t e r  out  = modulation = unloaded  u  frequency  Q f a c t o r of a cavity  R^,R,, e t c . = a u t o - c o r r e l a t i o n r  functions viii  s(t)  = signal voltage  (s/n)^  = input signal-to-noise r a t i o  (s/n)  = output signal-to-noise r a t i o  Q  t S,S  = suppression factors  t t ,t , c cp  = time = noise temperature ratios  T  &  = antenna -temperature  T  G  = electron temperature  T  N  = noise temperature  T  Q  = 290°K  = radiation temperature T  = minimum detectable temperature change  min  T(9$0) w w,, y  = temperature of the plasma at coordinates 0 and 0. etc. = power spectral densities = load admittance i n nonlinear-admittance mixer  i  g + jb = signal c i r c u i t admittance i n nonlinear-admittance mixer  =  y  s  ±  ±  s *\ = attenuation of the calibrated attenuator  =  a  g  +  t  oc^,a-^ , a (3 8^,P  2  = certain values of a  = bandwidth of the band-pass amplifier 2  = coupling factors = emissivity of the plasma  9,0 T  = spherical coordinates = variable associated with time = s o l i d angle  ix  LIST OP ILLUSTRATIONS Page F i g . 1-1  Types of Radiometers ........................  3  F i g . 2-1  Superheterodyne Radiometer Configurations ...  8  F i g . 2—2  B.C. Configuration  F i g , 3-1  Radiometer C i r c u i t .................  F i g . 3-2  Nonlinear-admittance Mixer  27  F i g . 3-3  Parametric Amplifier  30  F i g . 3-4  Equivalent C i r c u i t f o r the Parametric Amplifier with a Double-tuned Idler C i r c u i t  31  F i g . 3-5  ............so........»•.»  10  17,18,19  Voltage Gain-bandwidth Product vs Gain f o r Constant Pump Power .......  33  F i g . 3-6  Response Curve f o r the Parametric Amplifier .  33  F i g . 3-7  Frequency Response of the Second IF Amplifier  35  F i g . 3-8  Band-pass Amplifier Response f o r Measurements  F i g . 3-9  Band-pass Amplifier Response f o r Measurements  F i g . 4—1  during the Afterglow  37  Test Layout .................................  39  F i g . 4-2  Comparison between Observed and Calculated Values of T min F i g . 4-3 Traces of Output from Low-pass F i l t e r ....... F i g . I I - l The Dicke Radiometer with Two Sources of Noise ll ~~2 1 F i g . II-2 Function f = | 1 - {' / ) ~ ^ ^ 2  44 49  F i g . I I I - l The D.C. Configuration with Noise Source ...  59  F i g . V - l The Two Channel Subtraction Radiometer  64  s  40  1  s  F i g . V-2  Waveform of S  F i g . VII-1 Discharge Apparatus  n  %  ,.  58  66 72  F i g . VII-2 Voltage (upper trace) and Current (lower trace) 73 x  LIST OP TABLES Page 11  Table 2-1  Comparison of Radiometer S e n s i t i v i t i e s  Table 3-1  Radiometer Design Data  15  Table 4-1  Operating Minimum Detectable Temperature Changes  42  Table VI-1 Evaluation of System Loss and Gain  xi  71  Acknowledgement s The writer would l i k e to thank the National Research Council f o r supporting t h i s work through Block Term Grant A-68. The writer wishes to thank Dr. M.M.Z, Kharadly, the supervisor of t h i s project, f o r h i s help and h i s invaluable suggestions throughout the course of t h i s work. The writer would l i k e to thank Dr. D. A k i t t , Mr. A. Shankowski and Mr. E. Lewis f o r proof-reading the thesis and for t h e i r h e l p f u l comments. The writer wants to thank Mr. A. MacKenzie f o r drawing several of the figures which appear i n the thesis and the s t a f f i n the shop f o r building equipment used i n the project. F i n a l l y , the writer wants to thank Miss B. Rydberg f o r c a r e f u l l y typing the m u l t i l i t h sheets, especially the Appendices.  xii  INTRODUCTION A microwave radiometer i s a sensitive receiver which, can detect weak microwave signals.  It i s usually designed to  detect radiation such as that emitted from hot bodies.  This  type of signal can he related to a radiation temperature of the radiating body.  This radiation temperature, as measured by the  radiometer, may be equal to or lower than the physical temperature of the radiating body depending on the emissivity of the body at the radiometer frequency. In designing a radiometer, consideration should be . given to four parameters which can vary widely depending on the p a r t i c u l a r application of the r a d i o m e t e r ^ ) .  These are the  radiometer frequency, the bandwidth over which the radiation i s measured, the length of time taken i n making the measurement and the -radiation temperature. range from 400 M H z ^  Radiometer frequencies used  to several hundred G H z ^ .  Radiometers  having broad bandwidths are possible at the higher frequencies since t r a v e l l i n g wave tubes amplify over bandwidths of several GHz.  Also radiometers having narrow bandwidths have been used  where low noise amplifiers such as Adler tubes or varactor diode parametric amplifiers are available*  The integration  time constant of the radiometer depends on the length of time available f o r making the measurements.  In astronomic measure-  m e n t s ^ the source of radiation i s available f o r many minutes and the radiometer may Integrate the signal power over intervals (3)  of several seconds, but i n the case of a transient plasma  2 the signal power i s available f o r only a few hundred  microseconds  and the radiometer may he required to integrate the signal over periods of time i n the microsecond range.  The radiation tempera-  ture of the signal varies from a few degrees Kelvin f o r radia(5)  t i o n from other planets  w  y  to thousands of degrees Kelvin f o r  (6)  radiation from the sun  v  At microwave frequencies there are four basic types of radiometers.  These are the straight radiometer, the two  receiver radiometer ,• the two channel subtraction radiometer and the Dicke radiometer.  Their block diagrams are shown i n  Pig. 1-1. The straight radiometer, Pig. 1-la, i s the simplest i n construction but the least sensitive.  It has been used to (15)  advantage where long integration times are possible^  '• A  (16)  certain radiometer  ;  of t h i s type having a radiometer frequency  of 40 GHz, a bandwidth of 4 GHz and an integration time of 1 s has a minimum detectable temperature ohange of 80 deg K.  Better  performance can be obtained with the other three radiometers and the straight radiometer w i l l not be considered further. ; (17) The two receiver radiometer , Pig. 1—lb> cross correlates the outputs from two independent amplifiers i n a v  m u l t i p l i e r stage.  The signal voltages from the two amplifiers  are strongly correlated while the noise voltages produced by the amplifiers are uncorrelated* Thus,the signal may be separated from the amplifier noise. A comparison i s presented i n Table 2-1, Section 2.4, which shows that the two receiver, radiometer i s 2,22 times more  3  Signal a)  Detector  Low-pass Filter  D.C. Amplifier  Recorder  Straight Radiometer Amplifier No. 1  1  Multiplier  Low -pass Filter  H  Recorder  Amplifier No. 2 h)  Two Receiver Radiometer Amplifier No. 1  Signal  I  Detector No. 2  Two Channel Subtraction Radiometer  Signal  d)  Band- pass Filter  Switch  Amplifier No. 2  c)  Detector No. 1  Switch  Amplifier  Ref. Source  s i n 2itqt  sin  2jiqt  Low-pass Filter  Recorder  Band-pass Filter  L—Detector  W  Dicke Radiometer Recorder F i g . 1-1.  H  Types of Radiometers  Multiplier  Multiplier  Low-pass Filter  4  sensitive than the Dicke radiometer.  This r e s u l t , however, does  not take into account several p r a c t i c a l problems which should be considered i n the design and construction of a microwave radiometer.  F i r s t l y , the two receiver radiometer r e l i e s on the  signal voltages from the amplifiers being correlated, but correlation may be d i f f i c u l t to achieve especially i f mixers are used i n the amplifying stages.  Secondly,- i f the signal i s to  be detected over several d i f f e r e n t bandwidths i t would be desirable to use a superheterodyne receiver, which i n t h i s case could become d i f f i c u l t because some form of frequency control would be required between the two l o c a l o s c i l l a t o r s *  This l i n k  could introduce noise to the system that would be correlated i n the m u l t i p l i e r stage* (18) In the two channel subtraction radiometer  , Fig.  l-lc> the signal i s switched between two i d e n t i c a l channels at a certain switching frequency.'  The signal passes through one  channel while the input to the second channel i s terminated. The signal i s then switched to the second channel and the input to the f i r s t channel i s terminated.  The signal output from the  subtraction amplifier i s modulated while the noise produced i h the amplifiers i s not.  As a r e s u l t , the signal can be separated  from the noise. Theoretically,- the two channel subtraction radiometer i s twice as sensitive as the Dicke radiometer*  However,- from a  p r a c t i c a l standpoint two other factors should be considereds a) vthe d i f f i c u l t y i n achieving two i d e n t i c a l channels and b) the problem involved i n superheterodyningv  5  (19)  The l a s t type of radiometer,- the Dicke type^ Pig* 1^-ld, also uses signal modulation.  The input to the radios  meter i s switched between the signal source and a reference source at a certain switching frequency.  The signal i s thus  modulated and i t can be separated from the amplifier noise. Unlike the other radiometers* the Dicke radiometer i s well suited to superheterodyne operation. Also, i t requires approximately half as much equipment as either of the l a s t two radiometers since a large part df a microwave radiometer consists of the amplifying stage.  Thus, although the Dicke  radiometer may appear to have comparable s e n s i t i v i t y to the other two radiometers^it i s , by f a r , superior from a p r a c t i c a l point of view. This thesis i s conoerned with the design*- construct i o n and t e s t i n g of a Dicke type microwave radiometer operating i n the 35 GHz range which i s suitable f o r measuring i n a transient hot plasma.  temperatures  In Chapter II an analysis of the  radiometer i s presented and i t s s e n s i t i v i t y i s compared with that of other types of radiometers. design and construction.  Chapter III deals with i t s  Radiometer performance  i s discussed  i n Chapter IY and the conclusions drawn from this work are given i n Chapter V.  6  CHAPTER I I THEORY OP THE DICKE RADIOMETER 2*1  Introduction The main f e a t u r e o f the Dicke radiometer i s the  technique used to reduce f l u c t u a t i o n s i n the s i g n a l at i t s output*-  These f l u c t u a t i o n s are caused mainly by n o i s e i n the  a m p l i f i e r and v a r i a t i o n s i n i t s gain*  However, n o i s e may a l s o  enter the radiometer through the l o c a l o s c i l l a t o r , i f a superheterodyne  r e c e i v e r i s used, o r through the antenna from  sources  o t h e r than the s i g n a l source* An a n a l y s i s of the Dicke radiometer which c o n s i d e r s n o i s e e n t e r i n g the system a f t e r the s w i t c h * P i g . 1 - l d , i s presented i n Appendix I . d e t e c t a b l e s i g n a l power  The r e s u l t s show t h a t the minimum p  i s g i v e n by min  (2.1)  where  B  q  = output bandwidth of the radiometer  B. = radiometer bandwidth i P  N  = average power from the source of n o i s e .  T h i s a n a l y s i s i s v a l i d i n cases where there are no stages p r e ceding the switch and when the s i g n a l source i s not i n n o i s y surroundings-.  In cases where these c o n d i t i o n s are not met, i t  becomes necessary t o i n t r o d u c e source placed before the s w i t c h . a superheterodyne  i n the a n a l y s i s  a second n o i s e  As an example of t h i s c o n s i d e r  radiometer i n which the s i g n a l i s modulated  7  after the mixer, F i g . 2-lh.  Noise could enter the system before  the switch through the mixer and after the switch through the amplifier. An analysis of the Dicke radiometer with the two noise sources i s carried out i n Appendix I I . that p  The results show  i s given by min  ipg~i 4  -  4 4  _ S  f BT '  1  min " | l - 2/(s/n)  where p n  2  i  % (22)  £  - l/(s/n).*  1  = noise power from source after the switch  (s/n)^ = input signal-to-noise r a t i o . Eq. (2.2) predicts that i f the input signal-to-noise r a t i o (SNR)  i s less than or equal to 1 + ^jT, a cutoff condition can 7  arise since the quantity inside the square root bracket i n the denominator i s negative or zero.  This condition w i l l make i t  impossible to detect any signal and cannot be predicted from previous analysis.  Thus, antenna background noise entering the  radiometer could produce the cutoff condition.  Hitherto, the  introduction of antenna noise was thought to have only the effect of reducing s e n s i t i v i t y ^ ^ . 2.2  Superheterodyne Dicke Radiometer There are three possible configurations f o r the Dicke  superheterodyne radiometer.  These are shown i n F i g . 2-1. The  f i r s t , F i g . 2-la, i s used i f suitable switches are available. In certain cases, where the modulating frequency i s low, a (19) mechanical modulator may be useful^  . This configuration  does not, however, make f u l l use of the v e r s a t i l i t y of the  8  Signal  Switch  I  Ref. Source a)  Ref. Source  Amplifier  Recorder  Mixer  I  Switch  local Oscillator  Amplifier  Recorder  Modulator Switch After the Mixer  Signal  Mixer  I  Amplifier c)  I  Local Oscillator  Modulator Switch Before the Mixer  Signal  b)  Mixer  Local Oscillator  Modulator  Recorder  Local O s c i l l a t o r Modulation Fig. 2 - 1 .  Superheterodyne Radiometer Configurations  9  superheterodyne arrangement because a different switch i s needed f o r each new signal frequency. The second radiometer configuration, Fig* 2-lb, eliminates the problem of changing switches f o r signals i n d i f f e r e n t frequency ranges, hut i t introduces the problem of noise entering the system from the mixer stage.  Assuming that  no noise enters the radiometer with the s i g n a l , the input  SM  to the switch i s given by  (s/n), = -4 — p L n s  (2.3)  v  where,, P  s  = signal power entering the radiometer  t  p  n  = converted noise power from the l o c a l o s c i l l a t o r  1 = conversion loss of the mixer* t  If p  i s only one f i f t h of p_, the cutoff condition predicted s  II  by Eq. (2*2) can occur since L i s invariably greater than (21)(22) 5 dB  v  ,  In any case the insertion loss of the switch  reduces radiometer s e n s i t i v i t y * The third radiometer configuration,; using l o c a l o s c i l l a t o r modulation, F i g . 2-lc, eliminates the problem of changing switches and the loss i n s e n s i t i v i t y due to the i n s e r t i o n l o s s of a switch but cutoff can s t i l l result from noise entering the system from the l o c a l o s c i l l a t o r .  Modulation  of the l o c a l o s c i l l a t o r may be p a r t i c u l a r l y simple i f a klystron with r e f l e c t o r modulation i s used.  10  2.3  P.O. Configuration For large signal levels l a s t i n g short lengths of time,  the Dioke radiometer of F i g , 1-ld may he modified as shown i n (1)  the block diagram of F i g . 2-2,- called the d*c» c o n f i g u r a t i o n * w  The switch f i r s t connects the signal source to the system and the output i s recorded* of known power output.  Then i t switches to a reference source By" adjusting the calibrated attenuator  to obtain the same output i n both cases,- the signal power may be measured. Amplifier  Calibrated Attenuator  7\ Ref. Source  F i g . 2-2.  D.C. Configuration,  Note that the switch does not modulate the s i g n a l ,  i t merely  switches to the reference source after the transient signal has decayed. Since there i s no modulation-, the d.c. configuration i s a simple low noise receiver. I f the time duration of the signal i s short compared with the time taken f o r gain variations to occur, the minimum detectable signal power w i l l be by the noise figure of the receiver. This i s shown i n  determined  11 Appendix I I I *  Assuming the l i m i t of detection to he an output  SNR of unity*, the minimum detectable signal power i s over 2*4 times the average noise power of the receiver. 2.4  Comparison of Radiometers It may he interesting at this point to compare the  different types of radiometers.  Table 2-1 gives a comparison  of the minimum detectable signal powers. except f o r the d.c. configuration, p  It i s noticed that, varies l i n e a r l y with  min the noise power and as the square root of the r a t i o of the bandwidths'.  As a r e s u l t , p  can be lowered much more s  min  e f f e c t i v e l y by redv.cing the radiometer noise power than by Changing either of the bandwidths, B.^ or B . Q  Radiometer type  Minimum det* signal power  Dicke  5,66  |^'p  n  Remarks  sine wave modulation and (s/n)  4-44 | ^  P  n  ±  = o o  square wave modulation and (s/n) = © 0 1  D.c. configuration Two receiver*  Two channel** subtraction Table 2 - 1 .  2»41 P  n  (|*n  2  - f l J *n  2  2 2  (s/n). = 0 0  Comparison of Radiometer S e n s i t i v i t i e s  * See Appendix IV ** See Appendix V  12 2#5  Noise. Temperature. Minimum Detectable Temperature Change and Radiometer Noise Pigure The noise power  temperature  T  n  n  = k T  n  can be related to a noise  by p  where  p  n  Af  (2,4)  k = Boltzmann's constant Af = a bandwidth i n the power spectrum. Similarly, the minimum detectable signal power  p s  T  , can be related to a*' minimum detectable temperature change  min  s  >• * y min  1  p  min  = k I  • Af min  (2.5)  The noise temperature i s related to the radiometer noise figure P through (23) T , = (P - 1) T n  where  T  Q  (2.6)  Q  = 290°K.  Combining Eq. (2.4), (2,5) and (2,6) with formula (2,2) f o r the minimum detectable signal power of the Dicke radiometer yields  T  min  = 4.44 (P - 1) T M ^ V i 0  (2,7)  This expression i s useful since i t relates temperatures d i r e c t l y . The radiometer noise figure i s related to the noise figures and power gains of the i n d i v i d u a l stages  by^4).  13  (2,8)  L  where  F  1  j=2 noise figure of the f i r s t stage noise figure of the i  stage  power gain of the ( j - l ) stage n  number of stages i n cascade*  It i s seen from Eq. (2,8) that the f i r s t few stages of the radiometer are the most important i n determining the radiometer noise figure.  Ideally the f i r s t stage should have a low noise  figure and a high gain.  In the superheterodyne radiometer t h i s  i s not possible due to the conversion loss i n the mixer. ever, i t w i l l be shown, Section  3.7,  How-  that by using a high  intermediate frequency (IP) and a low noise f i r s t IP amplifier, the radiometer noise figure can he kept below 10 dB.  14 CHAPTER III DESIGN OP A SUPERHETERODYNE DICKE. RADIOMETER 3»1  Design Data The main object of t h i s work vv?s the development of a  Dicke type radiometer operating i n the 35 GHz range which would be suitable f o r measuring radiation from  high;., temperature  plasma such as that produced i n a pinched l i n e a r discharge. (25) Measurements have shown  v  J l  that such plasmas radiate at micro-  wave frequencies during the pinch and during the afterglow. The amount of power radiated i n a certain frequency band i s dependent on the electron temperature as well as on the electron density of the plasma.  Black body radiation can be detected  by the radiometer when the radiometer frequency i s approximately equal to the plasma frequency. In the discharge machine of the type available here the electron temperature during the pinch may reach 10^ °K^6)(27)^ During the afterglow the radiation temperatures can vary considerably depending on the electron density d i s t r i b u t i o n and (28) the pressure.  Using Saha's formula  v  1  f o r a homogeneous plasma,  the temperature during the afterglow i s of the order of 5000°K when the argon pressure i s 10  (im Hg.  For the design of this  radiometer, minimum detectable temperature changes of one-tenth of the above values were assumed r e s u l t i n g i n T = 10^ deg K min and T = 500 deg K f o r measurements during the pinch and. the min afterglow respectively. The output bandwidth of the radiometer should be v  s  15 s u f f i c i e n t l y wide to permit the measurement of the time v a r i a t i o n of the signal.  The pinch effect l a s t s f o r approximately  15 p.s^ ^ and accordingly a 3 dB output bandwidth of 160  KHz  was chosen*  radiate  2  During the afterglow period, the plasma may  for more than 1 ms^5)(29) was  a n d  a  n  0U  ^.p ^. -bandwidth of 6.4 U  KHz  selected. The radiometer bandwidth was chosen from considera-  tions given i n Section 3.10;  It was shown that a bandwidth of  approximately 38 MHz would give the lowest value of T  for min  the radiometer. The maximum permissible radiometer noise figure  may  now be calculated from Eq. ( 3 . 3 ) which takes into account antenna losses.  For measurements during the pinch, E must be  less than 16.4 dB,' approximately, and f o r measurements during the afterglow, E must not exceed 12.5  dB.  The design data are summarized i n Table 3-1.  Symbol Radiometer frequency  f  Minimum det. temp, change  T  l s  Output bandwidth  B  Radiometer bandwidth  B  Radiometer noise figure Table 3-1.  o  i P  Measurements during the pinch  Measurements during the afterglow  38.5  38.5  GHz  GHz  10,000 deg K  500 deg K  160  6.4  min 38  KHz MHz  <16.4  38 dB  Radiometer Design Data.  KHz MHz  <"12*5 dB  !6  3.2  C i r c u i t Diagram The c i r c u i t diagram of the radiometer i s shown i n  F i g . 3-1•  Since a switch was not available at the radiometer  frequency, the input signal was modulated using l o c a l o s c i l l a t o r modulation f o r measurements during the afterglow.  This was not  practicable f o r measurements during the pinch,; however, as i t would have required the use of a much higher modulating frequency and t h i s was d i f f i c u l t to achieve.  Consequently, diode switch  modulation a f t e r the mixer was used f o r measurements during the pinch.' The input signal i s converted' to an Intermediate frequency of 3*44 GfHz i n a balanced mixer.  Next the signal i s  amplified by a low noise varactor diode parametric amplifier and converted to the second IF where i t i s amplified i n the second IF amplifier.  The radiometer bandwidth • B^ ?  i s assumed  to be the o v e r a l l 3 dB bandwidth of these amplifier stages. The output from the second IF amplifier i s detected with a point contact diode and amplified using a band-pass-.amplifier,. The signal i s multiplied by the modulating signal i n the commutator detector and f i l t e r e d i n a simple RC low-pass f i l t e r . 3.3  Power Input to, the Radiometer Power radiated from the plasma enters the radiometer  through an optimum gain horn.  Using spherical coordinates 9  and 0 as seen from the aperture of the horn,the temperature of the plasma;;, T(9, 0); i s a function of 9 and 0 and the maximum power input, to the radiometer i s given  by^^)  2 x 1N53  Horn  Highpass Filter  —  —  —  —  —  y£n—Q  Local Oscillator  Balance Mixer  Band-pass Amplif i e r - 10 V  TUT' KM?  Commutator Detector  Argon Noise Source  r -i  —V—Ex  1st and 2nd IF Amplifiers  100 pF  Diode Switch  *±r 2 x 2N1305  Calibration Circuit  2N2495 a)  Diode Switch Modulation  F i g . 3-1. Radiometer C i r c u i t  2N2495  2 x 1N53  Horn  \ :h High" pass Filter  N31 **«. ^SO\  Local Oscillator  Ljva Balanced „ /  "AIL  . - 10 v  n  - 10 V  1:1  Mixer  300/v  Argon Noise Source  2.2 K  —  ~  Calibration Circuit  c  .st and 2 n l TJ' \mplif iers  I T3iode Switch  >2.2 K  120 K  120 K  y°  1_ _  A  0.01 \i. 2N2495  2N2495  b) Local Oscillator Modulation Fig. 3-1. Radiometer C i r c u i t  0  CommutatorDetector  - 10 V Input  T  Second IF Amplifier R 1 - Rg ~ IK  T 1 - T 6 = 2N2495  C ? = 0.1 uJ  D 1 = 1N416E  C 1 - Cg = 100 pF  C Q = 0.1 \x?  D 2 = 1N497 c)  F i r s t IF Amplifier, Second Mixer and C i r c u i t Diagram of Second IF Amplifier. F i g . 3-1. Radiometer C i r c u i t  20  *3  max where,  •I  B  T(©  i  0) G(©, 0) d_ru  r  (3.1)  p; = maximum power input to the radiometer max s  &(©, 0) = i s t r o p i c gain of the horn d«r\*_ = d© d0 s i n © = s o l i d angle subtended at the i horn. The factor of one h a l f has been introduced because the waveguide system can only support radiation of a certain polarization while the radiation from the plasma i s of random p o l a r i z a t i o n . The power entering the radiometer may he related to an antenna temperature, T  &  which i s the temperature of a source  that would produce the same power input to the radiometer as the plasma.  I f T(©, 0) i s considered constant, an assumption  which i s true f o r a homogeneous plasma of i n f i n i t e extent and j u s t i f i e d f o r a high gain horn close to a plasma column, then (27) the antenna temperature i s given by ' v  T a " where.  2 ~  2  e  (3.2)  T^ = T(©* 0) = constant = radiation temperature of the plasma = emissivity of the plasma T  g  <  1  = electron temperature.  Thus, i n e f f e c t , the maximum input power to the radiometer i s one half of the power at the antenna aperture and the minimum detectable signal power, p  i s doubled• min  In the experimental  21 set up t h i s i s further increased by 40$  due to losses i n the  waveguide run from the horn to the balanced mixer. Eq. (2.7)  Thus*  i s now rewritten as —I T  3.4  =  min  12.4  (F -  1)  T  (3.3)  \\ ^  Oalibration of. the Radiometer An S-band argon noise source and a calibrated variable  attenuator are connected as shown i n Pig, 3-la or Pig. 3-lb for the purpose of radiometer c a l i b r a t i o n .  The output l e v e l  due to the signal i s time varying and the l e v e l at any instant of time may be related to a temperature by using T  - T_  T  - T„  0 n 0 s n L = conversion loss of the balanced mixer r.  where  r  ,  I  = power loss i n the waveguide plus any losses between the balanced mixer and the point Of connection with the c a l i b r a t i o n c i r c u i t  L  = power loss i n the diode switch used i n the c a l i b r a t i o n c i r c u i t plus cable losses between the noise source and the switch. a = attenuation of the calibrated attenuator  T^ = noise temperature of the argon noise source. Eq. (3.4)  can be rewritten as T  where  K =  2LL n  r  = T (T  Q  +  f  - T_) = constant.  (3.5)  22 The constant Z can he determined by connecting the input waveguide to a hot load at temperature T^ °Z, noting the output from the radiometer, then adjusting the attenuator to to produce the same radiometer output using the noise source. Thus, from Eq. ( 3 . 5 ) Z = (^  - T ) oc Q  (3.6)  ±  With K known, temperature measurements can be made without the need to determine L, L , L and T . s n n 1  The hot load used was constructed from U-band (0*14 in. x 0.28 i n  I.D.) waveguide which was p a r t i a l l y f i l l e d  with powdered carbon to produce a matched load at 38.5  GHz.  The temperature of the load was measured using a thermocouple and was approximately 300 deg Z above ambient room temperature. Eq. ( 3 . 5 ) and ( 3 . 6 ) may be applied to the two types of modulation with Z f o r diode switch modulation approximately 1 . 6 times that f o r l o c a l o s c i l l a t o r modulation (since I i s s 2 dB greater i n the former case due to loss i n the switch). Using l o c a l o s c i l l a t o r modulation a^, was found to be 24 dB and Eq* ( 3 * 5 ) becomes T  = T  A  + T«5 x 1 0 ^  0  sr  I P  T  = T r  3.5  A  0  +  * a  l  o  c  a  l  o s c  i i i t o r modulation a  (3*7a)  a  10^ u  diode switch modulation  (3.7b)  Balanced Mixer A balanced mixer i s used as i t has the advantage  of reducing l o c a l o s c i l l a t o r noise entering the system and  23 i s o l a t i n g the signal input from the l o c a l o s c i l l a t o r signal. I f two crystals of opposite p o l a r i t y are arranged as shown i n F i g . 3-la, the output l o c a l o s c i l l a t o r noise power i s proportional to ( 1  (1  1 ) while the signal power i s proportional to  1 ) + "izzz  2  t  two c r y s t a l s .  where L, and L  0  are the conversion losses of the  The r a t i o of these two quantities, called the  suppression. S, i s given by.(30)  2  + 1 S  (3.8)  To i l l u s t r a t e t h i s point l e t L^ and  d i f f e r by only 1 dB i n  which case the suppression i s approximately 25 dB. The suppression required depends on the amount of l o c a l o s c i l l a t o r noise.  I t w i l l be shown i n Section 3.6 that  the suppression should be P£ the order of 40 dB i f the noise contribution from the balanced mixer stage i s to be neglected. As i t i s unlikely that L^ and L^ w i l l d i f f e r by much less than 1 dB, i t i s apparent that the suppression from the balanced mixer alone w i l l not be s u f f i c i e n t and further measures w i l l be required to reduce l o c a l o s c i l l a t o r noise. 3.6  Reduction of. Local O s c i l l a t o r Noise The output noise power spectrum from a klystron l o c a l  o s c i l l a t o r v a r i e s as fj_~^f where f ^ i s the intermediate frequency.  Data on the noise power spectral density of the  24 klystron used (Philips 55,335) Was not  >• available hut i t  was necessary to make an estimate of the suppression required. The only data that was available was that on the 723A/B klystron. —18 This klystron has a noise power spectral density of 2 x 10" W/Hz (32)  at an IP of 30 M H z  w  ' which would correspond to a noise tempera5 o  ture contribution to the system of over 2.5 x 10  K,  If local  o s c i l l a t o r noise i s to have negligible effect on the radiometer performance, i t should be reduced to a few degrees Kelvin. reduction corresponds to over 40 dB suppression. 3.44  This  At an IP of  GHz the noise temperature contribution would be only 20°K. The above calculation shows the advantage of using  a high IP i n reducing noise entering the system.  The value of  40 dB i s considered to give only an order of magnitude to the suppression value required f o r the klystron used. The use of a high IP has other advantages. the noise figure of the radiometer  It reduces  (Section 3.7), i t permits  the use of a simple low noise f i r s t IP amplifier and i t makes feasible the f i l t e r i n g of the Ideal o s c i l l a t o r signal using a cavity. The amount of suppression of l o c a l o s c i l l a t o r noise which can he achieved by using a transmission cavity i s given 4 Q f. • 2  S« = 1 +  _  u  p f  where  2  2  (  1  +  h  +  h  (3.9)  ]  0^ = unloaded Q of the cavity f  2  = resonant frequency frequency)  of the cavity ( l o c a l o s c i l l a t o r  25 = input coupling factor §2 = output coupling factor. It i s apparent from Eq, (3.9) that the higher the Q the higher the suppression and that t h i s method can he used to advantage only i f the l o c a l o s c i l l a t o r has a high degree of s t a b i l i t y . By employing hoth the balanced mixer and the high IF, i t i s estimated that the noise contribution from the l o c a l o s c i l l a t o r to the radiometer would be only a few tenths of a degree Kelvin,  Thus, i t i s not considered necessary to use the  resonant cavity as i t s additional contribution to the suppression would he negligible while the tuning d i f f i c u l t i e s introduced would be considerable. 3.7  Radiometer Noise Figure The radiometer noise figure F i s given F = L (F  where,  ± f  + t  c  - 1)  by^^ (3.10)  F^  = noise figure of the system following the mixer  t  = noise temperature r a t i o of the mixer crystal.  At low intermediate frequencies, say 60 MHz, t i s t y p i c a l l y (22) 1.6 (2' dB) but at microwave intermediate frequencies, t V  1  (35)  approaches the minimum value of u n i t y a s y m t o t i c a l l y .  Thus,,  the radiometer noise figure may be reduced considerably through increasing the IF provided that the conversion loss remains constant over the IF range. The conversion loss of a nonlinear-admittanoe  mixer  c r y s t a l may he determined by analysing the c i r c u i t shown i n  26 F i g , 3-2 and, for a noninverting mixer, i t i s given by (36)  4 g  ±  g  s  [ & 2  +  M  2  0  2 J  (3.11) where  G(t) = G  Q  + 2G  1  oos tOgt  0(t) = C  Q  + 2C  1  cos u t 2  2 f 2 = ^ = local oscillator w  frequency  to  f  = 2 ^ = signal frequency w  f ^ = 2 ^ = intermediate frequency = i + g  y g  s  *i0 e  s0  g  *S0  F y F. and F  0  ±  +  w  +  G  I  g  s  = b  =  %  = b. + =  =  + ^s  = s  i0 = g  1\  i 0 C  o  + s  are selective f i l t e r s having zero admittance  the frequencies f ,• f . and f_ respectively. S  1  at  In the derivation  c.  of expression (3*11) the signal i s assumed to be much smaller than that of the l o c a l o s c i l l a t o r . of the nonlinear-admittance admittance  This permits representation  of the diode by a time varying  which i s dependent on f g , Prom Eq. (3,11) i t can be shown that with proper  tuning the conversion loss can be made r e l a t i v e l y independent  27  G(t)  —wV-  Input Signal  Output Signal  NohtLinear Admittance  v  F  c(t  s  Or  +  F i g , 3-^2.  Nonlinear-Admittance Mixer.  of the IF. This result has been v e r i f i e d experimentally f o r 1N53 crystals up to an IP of 2,42 G H z ^ ^  and i t i s assumed that  the conversion loss remains r e l a t i v e l y constant up to frequencies i n the 3«5 GHz range.  Thus .•• P = L P  where.  L P. - = L. I P_ + — i f " cl L p 1^  (3.12)  ± f  (P  - 1 + t  2  G  ) - 1 ^-  p  = loss between the balanced mixer and the parametric amplifier = 2.5 dB f o r diode switch modulation = 0,5 dB f o r l o c a l o s c i l l a t o r modulation  P  = noise figure of the parametria amplifier  P F^ ~L_  3  = noise figure of the second IP amplifier = conversion loss of the second mixer  28 = noise temperature r a t i o of the c r y s t a l i n the second mixer = power gain of the parametric amplifier. From Eq. (3.12) i t i s seen that with a value of 1 of 8.5 dB, E would he under 10 dB with l o c a l o s c i l l a t o r modulation,?:. i f a very low noise amplifier were used having high gain and a noise figure under 1 dB. To achieve low noise operation of a mixer c r y s t a l , (38) the proper bias current must be used. that the noise figure of 1N53  I t has been shown  crystals has a broad minimum whioh  occurs at a bias current of approximately 3.8  K?  50 pA»  Modulation Erequenoy Due to square wave modulation the signal i s sampled  during h a l f of the time only.  The modulating frequency  should  he considerably higher than the reciprocal of the signal duration time, especially i f i t i s required to measure variations i n signal  amplitude. It was stated i n Section 3.1 that the plasma caa/d  radiate f o r durations of the order of 1 ms i n the afterglow period and 15 [is during the current flow period.  Consequently,  for measurements during the afterglow and the pinch periods the modulation frequencies were chosen to be 30 KHz and 1  MHz  respectively. 3.9  Choice of the F i r s t IE Amplifier low noise amplification at the f i r s t IF, 3 * 4 4  may be achieved by using  i)  a  GHz,  t r a v e l l i n g wave tube, 2) an  29 Adler t u b e ^ ^ , 3) a diode parametric amplifier, 4) a diode upconverter and 5) a microwave maser amplifier.  The up-converter  and the microwave maser amplifier are impractical i n t h i s case, because the former has an output at an increased signal frequency and the l a t t e r requires a l i q u i d helium bath.  Both the t r a v e l -  l i n g wave tube and the Adler tube are suitable but could not be considered as they were p r o h i b i t i v e l y expensive.  A diode  parametric amplifier i s also expensive but i t was possible to construct one within a reasonable time f o r a f r a c t i o n of the price of a commercially available u n i t . 3*10  Varaotor Diode Parametric Amplifier The required design features of an amplifier f o r the  present application are l ) s i m p l i c i t y i n construction, 2) ease i n tuning, 3) wide bandwidth and 4) low cost.  These have been  achieved on the basis of a d e s i g n u s i n g a double-tuned  idler  c i r c u i t composed of two coupled resonant c a v i t i e s as shown i n Pig. 3-3a.  The assembly i s shown i n the photo of Pig. 3-3b.  The signal power i s fed into one port of a c i r c u l a t o r (0.3 dB i n s e r t i o n loss and over 20 dB i s o l a t i o n between ports). The Tee-section, which forms the c a v i t i e s and the 1  pump power input, and the taper connecting the Tee-section to standard X-band waveguide, shown i n Pig. 3-3c, were electroformed. The varactor diode used, an XD-502, i s held at one end by a pin i n contact with the body of the Tee-section and at the other end by the pin i n an N-type connector. The amplifier bandwidth i s broadened by increasing the i d l e r c i r c u i t bandwidth through tuning the cavities to  30  Signal Line  0.20"  Varactor Diode  Adjustable Short  I  ±  a)  Adjustable Short  -3.85"-  i  ^  ^  •Lossy Screws  y]\ o  Cavity-  0.90"  -Cavity  "^3  f~  1  r  0 . 5 1 "  Pump Guide (X-band)  h) F i g . 3-3.  c) Parametric Amplifier a) Cross-sectional View b) Assembled View c) Tee-section Showing the Varactor Diode i n Place, the Plungers and the Lossy Screws.  31 s l i g h t l y different i d l e r frequencies with adjustable plungers and loading the c a v i t i e s with lossy screws.  The plungers are  made of brass with shimstock fingers at the ends which give good contact with the walls of the Tee-section.  The lossy  1  screws are made from red f i b e r block. The equivalent c i r c u i t of the parametric amplifier i s shown i n F i g . 3-4. Near resonance the i d l e r c i r c u i t s are represented by two resistances i n p a r a l l e l .  The noise figure  of the parametric amplifier F^ may be calculated at resonance from  (42  > P &  where  (1 + -S)  1 = 1.7 dB  (3.13)  f  = signal, frequency = 3.44 GHz s fj_' = i d l e r frequency =8.96 GHz I c = insertion loss of the circulator, Generator Resistance  Circulator  Signal Generator  load Resistance Double Stub Tuner  R.  2  'Idler C i r c u i t s F i g . 3-4. Equivalent C i r c u i t f o r the Parametric Amplifier with a Double-Tuned I d l e r / C i r c u i t  32 The optimum parametric amplifier gain i s that which gives the lowest minimum detectable temperature change f o r the radiometer.  It was found experimentally that f o r a constant  pump power the voltage gain-bandwidth product of the parametric amplifier i s almost constant, as shown i n Pig. 3-5. y^T  B  1  =  ±  = constant  Thus, (3.14)  Combining Eq. (3.14), (3.3) and (3.12) y i e l d s  T  12.4 T UB  _  0  =  ' min s  fK^  V  0  n  i  GJ"  T  P  LL„ (F_ +  |  P  d  L,(F. i  -  1 + t ,) - 1 fs- 22— ) - 1 p G  (3.15) Minimizing T s  min  with respect to G  results i n p  3 |~L, (F. - 1 + t _) - l ] G = ? • 22 1. P F - —=— P d 1  t  (3.16)  L L  According to manufacturer's specifications t y p i c a l values of 1, and t ~ f o r the mixer c r y s t a l used (lN4l6E.) 'are 3 c3 ;  ,i  5 dB and 1.4 respectively.  It i s shown i n Section 3.12  that  the second IF amplifier noise figure i s approximately 7.4  dB.  Thus, the optimum gain of the parametric amplifier, according to Eq. (3*16), i s approximately 16 dB,  However, i t was found  that a v a r i a t i o n i n G^ of ±3 dB from the optimum gain increases T by less than 6$. min The measured frequency response curve of the parametric amplifier i s shown i n F i g , 3-6,  The 3 dB bandwidth i s  33  Voltage gainbandwidth Product i n MHz 200  , 100  0 J  1  1  10  20  1 30  1  Gain i n dB, Pig. 3-5.  Voltage Gain-bandwidth Product vs Gain f o r Constant Pump Power.  20 Gain i n dB  10  0  3400  3420  3440  3460  3480  Frequency i n MHz Pig. 3-6.  Response Curve f o r the Parametric Amplifier.  34 38 MHz and the mid-hand gain i s 14 dB. The gain was measured by a substitution method tb an estimated accurapy of•+ ^ dB using a calibrated variable attenuator and a matched detector. The frequency was measured using a spectrum analyser and the estimated accuracy of the bandwidth was + 2MHz.  With 14 dB  given by Eq. (3.15) are  gain, the values of T min T s  T  min  = 6.2'x 10 p  min  = 7.8 x 10  deg K diode switch modulation ;  deg K  l o c a l o s c i l l a t o r modulation'  The l i n e between the parametric amplifier and the second mixer was tuned using a, single stub tuner.  It was  found that parametric o s c i l l a t i o n could occur f o r certain stub positions. 3.11  Second Mixer A broadband coaxial c r y s t a l mixer i s used to convert  the f i r s t IP of 3.44 GHz to the second IP of 70 MHz.  The c r y s t a l  i s i n series with the center conductor of the high frequency l i n e and a fine wire choke connects the 70 MHz conductor as shown i n P i g . 3-lc.  I t was found that the lowest conversion  loss of the mixer was achieved with the maximum output l o c a l o s c i l l a t o r power available of approximately 1 mW. The effect of noise from the l o c a l o s c i l l a t o r on T  min  i s negligible.  This was ascertained by placing a resonant  cavity with 6 dB of suppression between the l o c a l o s c i l l a t o r and the second  mixer.  35  3.12  Second IF Amplifier The second IF amplifier i s a six stage t r a n s i s t o r  amplifier, the c i r c u i t diagram of which i s shown i n F i g . 3 - l c . Coupling between stages i s achieved through f e r r i t e toroid." transformers.  The turns r a t i o s of the transformers were  optimized f o r maximum gain. The frequency response curve of the amplifier shown ?  i n F i g . 3-7, i s f l a t to within + \ dB over the 40 MHz  bandwidth.  A gain of 70 dB was measured by using a substitution method. The noise figures at 60 MHz and 70 MHz, as measured by a noise figure meter, were found to be 7 dB and 7.4 dB, respectively.  Fig. 3 - 7 .  Frequency Response of the Second IF Amplifier.  The output from the second IF amplifier i s fed d i r e c t l y into a 1N497 point contact type diode detector.  With  an input signal of constant amplitude, the output voltage was found to be approximately constant over the frequency range between 40 MHz and 100  MHz.  36 3.13  .Baxtd-joasg Amplifier A ba'ncV-pass amplifier i s used instead of a band-pass  f i l t e r as additional gain i s required.  It i s shown i n Appendix  VI that i n order to produce a.power of 1 mW at the input of the lowpass f i l t e r i t i s necessary f o r the band-pass amplifier to have a minimum gain of 30 dB f o r measurements during the pinch and 37 dB f o r measurements during the afterglow.  The bandwidth, p  of the amplifier should s a t i s f y the r e l a t i o n 2q > where  q = modulating  P>  2B  (3.17)  Q  frequency.  This results from assumption 3)and the analysis i n Appendix I I . Eq. (3.17) y i e l d s a range f o r p of 2 MHz^ measurements during the pinch and 60 KHz ^ p measurements during the afterglow.  P>  320 KHz -for  ^12.8  KHz f o r  For measurements i n these  ranges two amplifiers were constructed and t h e i r c i r c u i t diagrams are shown i n F i g . 3-la and F i g . 3-lb.  The amplifier of Fig,/ ) j  3-la has a mid-band gain of 30.5 dB and a 3 dB bandwidth of 1 MHz  (Fig. 3-8).  The amplifier of Fig,j 3-lb has a mid-band gain  of 39 dB and a 3 dB bandwidth of 40 KHz 3.14  (Fig. 3-9).  Coherent Detector When the input ^NB. to the detector i s less than unity,  as i n this case, a coherent detector has to be used to extract the signal from the n o i s e ^ ^ . detector i s shown i n F i g . 3-la.  The c i r c u i t diagram  of the  The detector i s driven by a  square wave which has an amplitude of approximately 1 V peak-topeak.  37 30 i ME:Z  Gain i n dB.  20  1 0  o.oi  o.io  1.0  10  Frequency i n MHz F i g . 3-8.  Band^pass Amplifier Response f o r Measurements During the Pinch. 40 -  Gain i n dB.  40 KHz  30  20  10  1  10  100  Frequency i n KHzF i g . 3-9.  Bandj-pass Amplifier Response f o r Measurements During the Afterglow  38  The output from the detector i s fed d i r e c t l y into a low-pass f i l t e r which has an output bandwidth of 160 KHz for measurements during the pinch and 6.4 KHz for measurements during the afterglow.  The f i l t e r reduces the bandwidth of the  noise power spectrum without changing the signal bandwidth thus increasing the output SKR.  39  CHAPTER IV RADIOMETER PERFORMANCE 4.1  Radiometer Tests 4.1.1  Preliminary Tests The procedure followed i n t e s t i n g the radiometer  performance w<?s as follows;  The system was divided into two  parts, one consisting of the balanced mixer with the input waveguide and the other consisting of the remainder of the system. Using a klystron as a signal source the f i r s t part was simply tuned f o r a maximum power output at the f i r s t IP. The second part was optimized f o r minimum detectable temperature  change  T  using the S-band noise source*' The  min , test layout i s shown i n Fig.' 4-1. s  Curves of T  s  min  versus B  n  u  are plotted i n F i g . 4-2 f o r both l o c a l o s c i l l a t o r modulation and diode switch modulation. The conversion loss i n the b a l was calculated from anced mixer was taken into account. T s.min Eqw (3.15) and the measured value of T was obtained min Modulating Signal Calibrated Attenuator  Diode ~7[ Switch  / ^ \ $((^ J  To the remainder of the of th< system sister ^  Parametric Amplifier  Argon Noise Source  F i g . 4-1.  Test layout.  40  10,000 T min in deg K s  1,000 * ^ +- Diode Switch Modulation • •- Local O s c i l l a t o r Modulation - — Theoretical curve for diode switch mod, - Theoretical curve for l o c a l osc. mod.  100  10,000 1000 Output Bandwidth B i n Hz  100,000  q  Pig. 4-2.  Comparison Between Observed and Calculated Values o f  s .  T  '  mm from the r e l a t i o n  <*g -  T  T a  n  l  Vl w L  a,  mm where  1 }  (4.D  = 11,000 K U  =  8 . 5 dB with diode switch modulation 6 . 5 dB with l o c a l o s c i l l a t o r modulation  L •= loss i n the waveguide run w 1.5 dB  c<2 = attenuation of the calibrated attenuator.  41 ct^ was determined by introducing large attenuation, noting the trace position and then reducing the attenuation to the point where the trace began to move.  The value of the attenuation  at t h i s point gave' a^. 4.1.2  Hot Load Test The radiometer was tested by connecting the hot load  described i n Section 3.4  to i t s input.  With l o c a l o s c i l l a t o r  modulation and an output bandwidth of 0.32  Hz, T  was min  determined  experimentally to be 11 deg K, approximately, as oppos  to a value of 5.6  deg K as determined  from Eq. (3.15).  The  discrepancy between the two values i s thought to be due to the lack of tuning i n the l i n e between the balanced mixer and the parametric amplifier.  Considerable d i f f i c u l t y was  experienced  i n the attempt to tune this l i n e as the parametric amplifier tended to o s c i l l a t e .  Also the small amount of signal power  from the hot load made i t d i f f i c u l t to tune the radiometer. The ideal arrangement would have been to use a modulated noise source i n the 35 GHz range to provide about 13 dB more power than the hot load.-  A small capacitor i n the low pass f i l t e r  would be used i n this case to reproduce the modulated signal. <  The operating minimum detectable temperature change  may now be found f o r the radiometer. Eq. (3.3)  It can be seen from  /\f^n i constant and Table 4-1 shows min corresponding values of T f o r different values of B , min that T  sa  s  v  u  u  42 for local min o s c i l l a t o r modulation  T  17 deg K  T  0.-32  Hz  11 deg K  6.4  KHz  1.6 x 10  160  KHz  5  f o r diode min switch modulation s  deg K 12 x 10  Tahle 4-1. 4.2  s  5  deg K  Operating Minimum Detectable Temperature Changes  Radiometer Improvements  It i s seen from Table 4-1 that the mJLn';Lmum detectable 3 temperature change f o r the pinch measurements i s 12 x 10 deg K, which i s close to the design value, while T f o r afterglow _ min measurements i s 1.6 x 10 deg K, which i s considerably above the design value.  With certain modifications this performance  can be s i g n i f i c a n t l y improved. F i r s t l y , the conversion loss of the balanced mixer can be reduced 2 dB by using a superior c r y s t a l type, the 1N$3D,I instead of the 1N53.  This gain corresponds to a reduc-  tion i n T  1.6. - -  by a factor of s  min  Secondly,- the gain of the parametric amplifier can be increased by using higher pump power /than i s available from the VA-237D klystron.  The gain, however, i s limited by a maximum  voltage of 6 v o l t s which can be applied across the varactor diode. An expected increase i n gain of 6 dB would further reduct T by a factor of 1.4. min s  Thirdly, a coaxial i s o l a t o r can be used to advantage between the parametric amplifier and the second mixer.  Tuning  the l i n e between the balanced mixer and the parametric amplifier  43  was quite d i f f i c u l t as i t made the parametric amplifier unstable. F i n a l l y , an argon noise source at the radiometer frequency would permit better tuning;of the system as a whole. It i s not possible to make even a crude estimate of how this .. would affect T  ,' but i f T  mm  were reduced ..by. a. factor of  ; mm  ••  •'  2, approximately, i t would be i n agreement with the t h e o r e t i c a l values of Section 3.10.  Such a noise source was not available  during the course of t h i s investigation. 4.'3  Plasma Measurements Attempts were made to measure temperatures during the  pinch and during the afterglow i n an existing pinched l i n e a r discharge machine . (Appendix VII).  These attempts were not  successful which indicates that the radiation temperature at 35 GHz was not high enough to be detected by the radiometer. From a b r i e f review of the l i t e r a t u r e on such measurements(45)(46)^  ^  k  e c a m e  apparent that these measurements  could be possible only i f the discharge took place at much  f  lower pressure (0.5M-m.iHg) than has been used (20';UmrJ3g). the present plasma machine, which was'designed  With  primarily f o r  electron density measurements, breakdown at low pressure would require modifications which are beyond the scope of t h i s work.  i  .  Also pickupy although'small,, obscured a possible signal during the pinch.  The screened room, which i s quite adequate f o r elec^ ;  tron density measurements, has not proven suitable,in t h i s application because of the very high gain of the^radiometer. I t i s f e l t that the screened room could be greatly improved by using double shielding.  Traces of the output from the low-pass  44  f i l t e r are shown i n F i g . 4-3.  The f i r s t two are with no  attenuation i n the waveguide run between the horn and  the  radiometer input and the last two with 20 dB attenuation.  It  i s seen that the magnitude of the output from the low-pass f i l ter  i s not affected by attenuation, which indicates that the  traces show pickup only. A great deal of pickup was  eliminated by shielding  the interconnecting coaxial cables with aluminum f o i l .  Also,  batteries i n metal containers were used as power supplies f o r the second IF amplifier and the commutator detector.  (a)  (b)  Fig.: 4-3.. Traces of the Output from the low-pass F i l t e r . a) No Attenuation and b) with 20 dB Attenuation.  45 CHAPTER V CONCLUSIONS A superheterodyne  Dicke type radiometer s u i t a b l e f o r  the measurement of r a d i a t i o n from a h i g h temperature i n the 35 GHz range has been developed. t h i s radiometer i s a h i g h f i r s t advantages:  a)  fier.  The s p e c i a l f e a t u r e of  IE which g i v e s the f o l l o w i n g  i t reduces the n o i s e e n t e r i n g the system  the l o c a l o s c i l l a t o r , b) and c)  plasma  i t reduces the radiometer n o i s e f i g u r e  i t permits the use of a simple low n o i s e f i r s t The f i r s t  IF ampli-  IF a m p l i f i e r i s a v a r a c t o r diode parametrio-  a m p l i f i e r which has a v o l t a g e gain^bandwidth mately 200 MHz.  from  product of a p p r o x i -  The gain of the a m p l i f i e r was chosen f o r the  lowest minimum d e t e c t a b l e temperature  change o f the radiometer.  The minimum d e t e c t a b l e temperature  change found  from  the hot load i s 11 deg Z f o r an output bandwidth of 0.32 Hz as compared t o a c a l c u l a t e d value of 5.6 deg K.  The d i s c r e p a n c y  i s thought t o be due to l a c k of t u n i n g between the balanced mixer and the parametric a m p l i f i e r .  Based' on t h i s  v a l u e the minimum d e t e c t a b l e temperature  experimental  changes f o r measure-  ments d u r i n g the p i n c h and the a f t e r g l o w are c a l c u l a t e d . These 3 are 12 x 10 deg Z w i t h an output bandwidth of 160 ZHz and 1.6 x  deg Z w i t h an output bandwidth of 6.4 ZHz r e s p e c t i v e l y .  However, w i t h the same bandwidths, argon n o i s e source measure3  ments gave a minimum d e t e c t a b l e temperature  change of 9«5 x 10 3  deg Z f o r measurements d u r i n g the p i n c h and 1.4 x 10  deg Z f o r  measurements d u r i n g the a f t e r g l o w . The equations f o r the minimum d e t e c t a b l e s i g n a l power  46  of the Dicke radiometer, the two receiver radiometer and the two, channel subtraction radiometer have been deduced using conventional analysis.  They are found to be similar i n form  to those already determined from other sources;  However, the  steps of the derivations are not altogether similar to those presented i n the l i t e r a t u r e . mum  The measured values f o r the mini-  detectable signal power check reasonably well with those •  calculated.  been  Also i t has shown that, unlike the other radioA  meters considered, the d.c. configuration has a minimum detectable signal power which i s independent  of the choice of  bandwidths. It has also been shown that f o r the Dicke radiometer and the two channel subtraction radiometer cutoff can occur i f the Sffi just before the modulating switch i s less than or equal to 1 +^~?  .  As a r e s u l t , i t i s seen that cutoff can  occur with modulation after the mixer i n a radiometer.  superheterodyne  In addition, i t i s found that l o c a l o s c i l l a t o r  modulation eliminates the problems associated with modulation using a switch and can be p a r t i c u l a r l y simple i f a klystron with r e f l e c t o r modulation i s used. It has not been possible to measure radiation from a plasma produced by an existing discharge apparatus.  This i s  thought to be due to the use of pressures higher than those suitable f o r t h i s type of experiment; breakdown could not be achieved with t h i s apparatus at lower pressures.  This i s i n  agreement with experimental results obtained by previous workers which indicate that measurements i n the 35 GHz range would be possible only at pressures c&. the order of O.^  ^m  Hg^.,  47  APPENDIX I ANALYSIS OP THE DICKE RADIOMETER WITH ONE NOISE SOURCE "I  An analysis of the Dicke radiometer has been presented (17) by S.J. Goldstein  v  which considers noise entering the  radiometer from a source placed just a f t e r the switch (See Pig. 1-ld).  The results of this analysis showed that the out-  put,- u ( t ) , from the m u l t i p l i e r i s given by u(t) = (A + B m(t)) s i n  2  2*qt  2 k 2 A = -r~ P„ 4 s 2  where  k = constant p P  s N  of the square law detector  = average power from the signal = average power from the source of noise  B^ = radiometer bandwidth. »(t) m(t + T ) „  > ? * ^  The auto-correlation function of u ( t ) , neglecting terms that are removed by the low-pass f i l t e r , i s *  * D.H. R i n g ^ ^ ) has reported that the second term i n the equation f o r R,(tr) should contain an additional factor of 1/2. 5  48 The spectral density at the output from the low-pass f i l t e r i s given by  w'  = 4  -2  W  /  R (f)  = ^  [%  cos  3  s  p  2  2ieft*df  (f) + Wg  = w^  (f)  o <f  * f >s Pn +  <|  The signal power i s given by  °U\t where,  B  n  ft  = output bandwidth of the  radiometer.  The noise power i s given by  Pr, n  out  =  B  Tt  P  i l?  2  3  +  2 0  i 2  P s  a  P n  2  1  + 2p *n J  B. 0  Thus, f o r an output signal-to-noise r a t i o (SNR) of unity, the minimum detectable signal power, p  , i s given by min  p s  min  = 4 v 2 1/ F i V  B  p„ (sine wave modulation) .  (1.1)  n  With square wave modulation (47)  **  =V^  . "VBT Pn mm » i S.J. G o l d s t e i n ^ ^ gave a value f o r w-^(f) of h a l f t h i s value, p  8  1  49  APPENDIX II ANALYSIS OF THE DICKE RADIOMETER WITH WO  NOISE, SPURGES  An analysis of the Dicke radiometer with two noise sources i s presented.  The f i r s t noise source i s before the  modulating switch and the second i s between the switch and the amplifier as shown i n F i g . I I - l . n (t  i (t)  x  2  x(t)  y(t) Signal  Switch  Bit)  1  -J^JI ^Jt Amplifier  etector  Band-jJass Filter  x|/ Ref. Source  sin 2itqt  v(t)  Multiplier \ l / u(t )  Low -pass Filter Fig. I I - l . The Dicke Radiometer with Two Sources of Noise. Assumptions 1)  The signal voltage s ( t ) and the noise voltages  n^(t) and ng(t) have independent stationary Gaussian amplitude distributions with zero means and average powers p 2)  g t  p ^ and p g n  respectively.  Signal and noise voltages have uniform spectral  densities over the bandwidth of the radiometer B^ centered at frequency f ^ . 3)  The band-pass f i l t e r has uniform response and only  passes frequencies i n the range q - | to q + |,  50 where  q i s the m o d u l a t i n g f r e q u e n c y .  filter 4) -  does not pass harmonics o f q .  The l o w ^ p a s s f i l t e r  from zero  has uniform frequency  t o BQ a n d z e r o  response  5)  The s w i t c h p r o d u c e s  the  signal voltage  6)  The a m p l i f i e r i s l i n e a r >  over the s i g n a l 7)  The b a n d - p a s s  The o u t p u t  response  elsewhere.  100$ a m p l i t u d e m o d u l a t i o n o f  and n o i s e v o l t a g e having  n^(t)  at q Hz;  constant  gain  spectrum. of the detector  z(t)  i s related  to  o  the  input..  8)  The o u t p u t  u(t)  y(t)  = v(t)  band-pass  ;  by the equations x ( t )  = ky  (t).  of the m u l t i p l i e r u ( t ) , i s given  s i n 2«qt where v ( t )  i s the output  of the  filter.  Analysis The  input  to the square  law detector  i s given by  y ( t ) = \ j s ( t ) + n ^ t ) ^ j l + s i n 2*qtJ + n ( t ) 2  The  x(t)  output  = k  (s(t)  The  is  j|(s(t)  + n-Jt))  + n^t))  2  n (t) 2  (1 + s i n 2 * q t )  2  (1 + s i n 2 « q t )  auto-correlation function  of x ( t )  +  + n  is  2  2  by  (t)]  R-^CC).  51  R ('Tr)  = time average (x(t) x(t+ T)) r  1  = x(t) x ( t + T ) s (t) s (t+T) + s ( t ) n^Ct+T) + n^Ct) s ( t + T ) + 2  2  2  2  n ( t ) n ^ C t + f ) + 4 s(t) s ( t + t r ) ^ ( t ) n ^ t + T r )  ]  2  x  ^64'  +  8  c  o  s  2  ^ '  r  lfe  +  c  o  s  4 5 t  ^ t r ) + | [ s ( t ) n (t+Tr) + 2  2  2  n ^ C t ) n (t+Tr)j+[s(t) s(t+Tr) ( n ( t ) n t + f ) + 2  2  2  2  n ( t ) n ^ t + T ) n ( t ) n (t+-r)J (1 + o o B ^ q - T ) x  |J^n (t) 2  2  +  2  2  s (t+T-) + n ( t ) n ( t + T ) ] + n ( t ) 2  2  2  2  2  1  2  n (t+T)j 2  2  It has been shown t h a t ^ ^ s (t) s ( t + T ) = p 2  2  + 2[RT(T")J  2 s  where R (IT) i s the auto-correlation function of s ( t ) . Similar relationships hold f o r n ( t ) n - ^ t + i r ) and n ( t ) n 2  2  x  2  2 2  (t+f).  The auto-correlation functions f o r s ( t ) , n^(t) and n ( t ) are 2  • • ^tT^^F)  •  cos 2% f,T: s i n JtB/tT = p  ffB  a  ^r  '  ~  cos 2% f £ f s i n utB£TT n (t) n^t+T) x  =  p  nl  *BsX'  >  52 cos 2Jtf.|T sirutB.jT n (t; n^t+T-y = p 2  JTB^T  n 2  Thus, neglecting terms which are periodic with frequency 2f^» R ^ ( f ) hecomes p 2  p  ^  P  ^ 64  8  +  [I:  0  0  8  UB/T)  2  *  2  128  +  c  o  p  8 s  P  "  s  '  n  P  («B T)  l  ±  + *n2 P.  s  s  p  2  p  +  n l  +  2 +  ! s nl p  p  p  p  64 n l  +  P  4 n l n2 P  8 nl >  +  J  2  [ s n2 p  P  +  p  n l n2] p  sin 3tB.T • 2  .(ttB/T)  n 2  2  •]•  ( 1  +  cos^q-T)  • N2  6? s n l  +  P n l  sia  2  p  2  +  I nl >  +  p  lis  +  2  p  nl  4 s n2  +  P  p  4 s nl P  P  g cos2jtqf s i n «B/f P  P i a  4*q/t:) + |  s  2  32 s n l  2_  T +  2 P s  sin^B^T  2  1  [ (l  P  q  +  wB£f  2  n 2  p  (  *  p  J  8  = k<  +  2  s i n jtB/f Pv,o ~ • -T5- + Pv,i P. " (*B,TT) * "  Pa  P^o h2  *  sin  2  sin JIB.T  2  UB.T)'  +  +  0  2 )  0  8  0  0  2  *4-C +  8  4 n l n2 P  p  4 s n2 P  P  ^ *s 64  +  +  +  p  n2  2  +  +  53  p 1  2  ? 128 s p  (  64 V  1  1  64 s n l  +  P  P  32 s n l  +  P  p  0  0  p  p  p S  s i n  n2 2  4«q.^sin JtB/Tr  3  '(«B T )  128 n l  +  2  +  2 )  I nl n2  +  p  p  2  +  64 n l  +  P  2  +  p  n2  '  2 )  ^ ^  (tfB^)  2  The power spectrum can now he found from  R-L(T) COS 2 * f r d T  w(f) = 4 ^  0 =  ( f ) + w ( f ) + w ( f ) + w (f) + w ( f ) + Wg(f)  W l  2  5  4  5  where. (f) = k  2  w (f) = k  2  W l  (| p  V  f)  =  * 64 s (  k  p V  f}  =  2  k  +  (jfg. p  2  P  2 n 2  2  w (f) = 2k  n l  ^  2 s  p  P s  +  P p s  32 s n l  2+  p  | p  +  p  2 nl  > P  n l +  4 s n2  +  £ (f - o  P  p  2 n l  )  £ ( f - 2q)  4 nl n2  +  P  p  64 n l  +  P  2  )  (  2  |  2 s  64 s P  (| p  2+  2 s  32 s n l p  p  + \ p p s  +  n l  \ s n2 p  p  +  + \ p p s  2 nl n2 p  n 2  p  + | P  0 < f <q  64 n l  +  n l  P  P  n 2  2  +\ P  2 n i  )  5 4  w ( f ) = 2k  (§ p  2  5  + J p p  2 s  s  + J p p  n l  s  "4-2— i  + i p  n 2  q < f < B  ±  n l  p  + | p  n 2  2 n l  ) .  - q  B  =  k 2  (  l  »B2  4 s nl P  +  P  \ s n2  +  p  (B. + q - f ) * 2 i  p  B  i  \ nO| n2  +  p  p  8 O  +  - q < f < B  i  •  q  +  B  W ( f ) = 2k  2 P  +  s  P  ^  2  6  ^  P ^ )  jjg  +  2  ^  <  0  f  < * 2  i  =  2 =  'lis * 3  2 k 2  k  (  1 2 128 s P  6? » A l  2+  1 64 s n l  +  P  p  +  ife n l > ^ T ^  +  2  P  2  i  1 128 V B  ±  2N 1 ^2 B  }  * < < i " * f  B  2  2q - f  +  i -> 2q < f < B  i  + 2q  The hand-pass f i l t e r i s assumed to remove contributions of w ( f ) and w^(f) from the system. 2  The auto-correlation function of the input to the m u l t i p l i e r i s given by <1 +  R (T) = 2  J * - |  |  [ i w  ( f )  +  V  f )  +  w  5  ( f )  +  w (f)^jcos 6  2*fTdf  55 E2(T)  - *  [t|  2  2 P  »A2  I  +  a  I  +  1 p p + §Pnl2;) + s  Pnl n  (|f  nl  p  Pm*  2f  + 2  +  S  2  Prf'  2  cos 2 « q T  P  • If  P s  p  Hl^ ]  n l  +  •  2  q  A correlation function of the same form would result i f v ( t ) were represented by  v(t) =^T  = y(t) v(t  R (T) 3  = k where.  k (A + B m(t)) s i n 2*qt  I  A  |^A + B 2  2  = | p  2  B 2  P  2  p  m(t) m(t +V)  2  m(t) m(t  + i p P  2 g  64 s  =  +T)  s  n2  p  p  + § p  n l  fl s n l  2 +  cos 2 n l  2 s n2  +  P  p  2itqT.  2 nl n2  +  p  p  +  If  2  = y *PJt B  m p j ; = m(t +Tr ) = 0 Now u(t) = v ( t ) s i n 2jtqt = fP  k JA + B m(t)J s i n  2  2rtqt  The auto-correlation function of u(t) i s  R  4  ( T )  =k  2  [A  2  + B  2  m(t) m(t T T +  )]  (f  +  ^J*^)  P  nl  2  +  =  [(i  k 2  p  2 s n2 p  p  (1  s  J  2 +  s nl  p  p  2 nl n2  +  p  p  +  I nl ) p  2  64 n l  +  P  +  ^64  +  2  p  n2  P  2  64  +  S  }  P  s nl p  « B Tr  (  }  ±  J  *  cos 4ffq"F)  +  Now find the power spectrum w'(f) w'(f) = w '(f) + w '(f) + w '(f) + w '(f) 1  2  3  4  where w '(f) = k  (g  2  x  p  2  +  s  w '(f) = «-f- ( f f p  p  nl  = 0  +  2  s  2  n l  | p  +  + f§ P P  s  s  p  | <  = 0  s  n2 )  p  64 s  nl  P  2  +  2  + f P  n 2  ° <  2  2q.+ f (  cT(f)  )  + | p p  n l  0 < f <2q  = W±  2 n l  f  n l  P  n 2  +  < f  f  w'(f) = 0  f  p p  2  5  g  J  2 +  p  52 s n l p  p  n2 ) 2  - |  <f +  2 s n2 P  P  +  2 nl n2 P  p  2q - f < f <2q  +  §  +  For a low-pass f i l t e r of bandwidth B , the output Q  power i s given by p  out =  0  ^'(f) +¥ '(f)) 3  0  df  B ^§ 0  57 = I"  (  l  p  s  4 V n l  2+  2 s n2 2 nl n2 p  p  +  p  p  8 nl p  +  64 n l  +  P  2  2 )  +  ^  +  2  p  (  n2  64  P  S  2  +  ft  p  s nl p  +  2 )  The SUR at the output i s given by 1 2 ? 0 2 16* s 12TB7 s 5 B  P  ( s  =r-r——, ,  / o n )  2 | s nl  +  2 nl n2  2  (  p  p  p  p  +  3 nl  n  p  "V  p  p  +  2 )  +  B„ 4:  (  ./  64 n l P  2  32 V n l  +  +  2 s nl p  p  +  2 ) 2  s = (s/n). = Sffi of power entering nl the radiometer just before the switch. p  Now substitute  p  1  _1 ^ 0 „2 16 s 128 B, s 2  3  n p  (s/n)  _  Q  5  B  +  p  2  1. ,.a.. , p  . __1 . s 16 2  , _f0/25_ B <64  p  ( B / n ) i  3 s n2 2 T77n77 p  3  2 s n2 p  p  +  ±  p  +  2  P  n2  p  s  ( B / n ) ±  „ 2 ' . 15. s . 32 T s T ^ P  2  2\ }  Assume that the l i m i t of detection i s ( s / n )  n  = 1 and  that '0 J  Then 5  P  s  =  fl  |j  n2  1  ,  (H.D  (sine wave modulation)  58 For square wave modulation;  'n2 9.m i n  1 -  TifnT  (II.2)  (s/n). ...  F i g . II-2 shows the graph of W 1 - / / \ I ^ / ^i s  versus (a/n)^.  n  X i  .  ' —5: (s/n)^  It i s seen that i f (s/rO^ i s not greater than  1 + ^~2~ a cutoff condition results and no signal can he detected. l  If no noise i s present at the input, ( s / n ) j — ^  and Eq, ( I I . l )  and (II.2) are i d e n t i c a l to Eq. ( I . l ) and (1.2) respectively.  (s/n).  8  10  59  APPENDIX I I I ANALYSIS OF THE DwC. CONFIGURATION An analysis of the d.o. configuration i s presented with one noise source i n the system asvshown i n Pig. I I I - l .  n(t) x(t)  y Signal sit)  Ref. s^(t)  \  Sun r*Vi U W X u UX1  1  Amplifier  Sq. Law Detector  ^Recorder  Calibrated attenuator  Fig.  III-l.  The D.C, Configuration With Noise Source  Assumptions Assumptions 2\ 6) and 7) of Appendix I I are considered to hold-.  In addition i t i s assumed that the signal voltage  s ( t ) , the noise voltage n(t) and the reference voltage s ( t ) r  have independent stationary Gaussian amplitude  distributions  with zero means and average powers p , p„ and p respectively. Analysis  *>y  The input voltage to the square law detector i s given  y(t) = s(t) + n(t) The output. x ( t ) . i s given by  60  + n(t)]2  s(t)  x(t) = k  = k V(t)  + 2s(t) n(t)  + n2(t)]  The auto-correlation function of x(t) i s R ( T ) which i s given by R ( f ) = x(t) x(t +tr ) = k  (p  2  o  2 s  o  k (p  +  2p p s  + 2p p  P s  + p ) 2  n  n  .  P s P n  + p  o  P n  +  p  *R>SX hr(itBJTT)  s i n  )  ^  The power spectrum i s given by  r  w(f): = 4j R ( T ) cos 2 * f T d T 0 = k k  (p  2  '  ( p  + 2p p  2 s  s  2  g  +  2 p  sPn  +  n  + p/)  Pn')  g  (f) +  "TT"~ B  i  From t h i s expression i t appears that no improvement i n the output SER can be achieved by use of frequency selective c i r c u i t s as i n the case of the Dicke radiometer.*  Thus, the  output SKR i s p  (s/n)  u  =  n  2  ^ p 2p•^s^n p + p *n  (III.l)  Assuming the l i m i t of detection to be an output of unity, the minimum detectable signal power,, p  SWR  i s given s  min  * F. Warner, et. a l .(3) ' reported that the output SWR from the d.cv radiometer could be improved i n exactly the same way as i n the Dicke radiometer. J  61  P  _ = (1 min s  +lf7 ) 1  1  (111.2)  P n  It i s shown i n Section 2.5 that the noise power may he related to the noise figure of the receiver* p  Thus,' from Eq. ( I I I . 2 ) ,  i s seen to he dependent only on the noise figure of the min system.  62 APPENDIX IV ANALYSIS OP THE TWO RECEIVER RADIOMETER (17) An analysis of the two receiver radiometer  '  v  (Pig, l - l h ) has shown that the auto-correlation function of the output from the m u l t i p l i e r i s given by R(T)  =  p  where  s  +  s  p  ( p  nl  +  p  n2  }  +  p  nl n2J p  (  ^  r  )  2  k = constant of the m u l t i p l i e r c i r c u i t p_s = average power from the signal entering each amplifier P  = average noise power entering amplifier no. 1  n X  P 2 = average noise power entering amplifier no. 2 . n  The power spectrum i s given by  w(f) = k < 2  2 p  s  +  s  p  ( p  nl  +  p  n2  }  +  p  nl n2 p  The output power i s given by  0 <f  3 ,  / <j"2p ^(f)  = k'  out  2  0  s  +  2  p (  2 s  +  s  P n l  +  p ) n 2  +  ;  L  0  B ' f Pnl n2 - * — J o p  [ p  1  9  4  f  B  = where  fc2  {s p  B  2  n  +  [  2 p  s  2 +  p  ( p s  nl  +  p  n2»  +  Pnl^na] \  J"  = output bandwidth of the radiometer.  <B.  63  where ,  B^ = radiometer bandwidth. For an output SNR of unity, the minimum detectable  signal power, p s  P  s  . = mm  min  , i s given by  V i171 P  ( p n  n l = n2 = n p  p  }  Since two receiving antennas are required f o r t h i s radiometer the minimum detectable signal power should be doubled when comparison i s made with a single antenna r a d i o m e t e r ^ 7 ) . I  Thus,  p  s  min. single  =  2  11 1^ i i  p  n  64  APPENDIX V ANALYSIS OP THE TWO  CHANNEL SUBTRACTION RADIOMETER WITH TWO NOISE SOURCES  The block diagram of the two channel subtraction radiometer i s shown below*  In the analysis of t h i s radiometer  three noise sources are considered to be present, one at the input to the switch and the other two at the Inputs of the amplifiers.-  n-^t n (t Q  Amplifier No. 1  Signal  Defector No. 1  v(t) 1 Subtracter  Switch r (t)~~^  Channel 1  Amplifier No. 2  2  Detector No. 2 Channel 2  |n (t{ p  Recorder  Band-pass g Filter I Multiplier Low-:pass Filter  F i g . V - l . The Two Channel Subtraction Radiometer. Assumptions. Assumptions 2), 3), 4) and 8) of Appendix II are considered to hold.  In addition the following assumptions are  made: 1 ) The signal -voltage s ( t ) and the noise voltages n ( t ) , n, (t) and n ( t ) have independent stationary n  9  I  .65 Gaussian amplitude distributions with zero means and average powers p , P n* P i  a  g  n  n  P 2 respectively-.  d  n  n  2) The switch alternates from position one to position two to position one at a frequency of q times per second.  In p a r t i c u l a r ,  r ( t ) = s(t) + n ( t ) x  <  0  Q  t  1  r (t) 2  < 2q 1  = 0  2 i < * < f  =0  0 <t  = s ( t )  +  n  0  ( t )  < ^  ^ < * < |  3) Both amplifiers are i d e n t i c a l and l i n e a r having constant gain over the pass" ha&d» 4) Both detectors are square law with a detector constant k. 5 ) The output from the subtracter i s the input from channel one minus the input from channel two. Analysis. The output from the subtracter f o r one complete cycle i s given by v(t) = k  [(s(t) + n ^ t ) + n ( t ) )  2  - n  2  Q  = - k [ ( s ( t ) + n (t) + n ( t ) ) 2  2  Q  2  2 2  (t)] 0 <t  < ^  - XL, ^)] ^ < t < | 2  Let S be a unit square wave as shown i n F i g . Vfcjfc.  66  s 1  1  1  '  1  0  ' 1 <1  F i g . V-2-. Waveform of S* Then v ( t ) i s given by  v(t) =  k <T(s (t) 2  2  n (t)])S + Q  where.  + 2s(t) n ( t ) + n ( t ) + 2n(t) [ ( s ( t ) + 2  Q  2 n i  (i)  - n  Q  2 2  ;  (t)|  n(t) = n ^ t ) n (t)  2 i < ^ < |  2  The auto-correlation function, B.^irv)t \(^)  i s given by  = v(t) y(t+T) (t) s (t+1T) + 4 s(t) s ( t + T ) n ( t ) n ( t + t r ) + 2  ft  Q  n ^ ( t ) n ^(tH-TT) + 4 n ( * ) ' n ( t + T ) 0  0  s (t) n^t+'O 2  + s (t+T") n 2  2 Q  (s(t )+n (t)) (s(t+f)+n (t+r)) Q  2  2  0  ( t ) ] S(t) S ( t + t ) +  (n ( t ) - n ( t ) ) ( n ( t + T ) - n ( t + T ) ) 2  0  2  }  +  Now,- S(t) i s given by -1 sin 2tfhqt nrt  S(t) = n—1,3,5ti,•*• Thus,  cos n 2KQH^ n  S(t) S ( t + T n=l,3,5,7,..  Substituting the auto-correlation functions and assuming p  n l  = k'  = p  = p  n 2  L  yields  n  n=l,3,5,7,. • •  L  1  2 p  s  2 p  n0  i  5  ItB^r  (  20 +  2 p  n0  (  cos artf/t s i n itB.1T  d  '^2 c'§.s 2wf T^sin « B f  0  5  2rt  ~  +  4 p  s nO  f £ C s i n xB.*Xf ^~?P ~ )  p  • itB.nr  (  —  2  +  3tBTr ±  4 P  ta s ( p  2  +  p  n0  ) (  cos 2tff,T s i n J t B . f i \ i t1B T r }  c  o  s  2%t  + 2p < (  {^  s  i  n  $&£C  a  2 p  s nO ] p  +  2, )  - 2p.  n  terms periodic with frequency 2f^ and  finding the power spectrum w(f), y i e l d s w(f) = w (f)'+ w ( f ) + w„(f) 1  +  ±  2  Neglecting  2  2  ]  68 where w f) l (  = %  k  (p  2  p  s+  n Q  )  X]  2  /-N 16 , 2 / . , s2 w (f)=- k (p + p ) * 5  2  s  16 ,2 , 2 " (P * k  • J  5  <f  n=l, 3,4/7,.. .  51  8 k  2/ ' <*»  > (B. - nq) / , i n=l,3,4,7,... B/  n 0  .  + B  N2  _  W  'no''  +  >• < " ^ • '2 n=l,3,5/7,... i 1  N2  \  (B  *  -r  VJJ,  5_!  + B  n=l,3,5,7,......  »,(f) = 4k p  f }  nq<f <B .- nq ±  nq - f ) 2 B -nq<f<B nq 1  n  1+  1  0 < £ <B.  2  2  0<f<nq  .  i The auto-correlation function of the signal from the hand-pass f i l t e r , R ^ T " ) , may now he found, noting that the f i l t e r does not pass harmonics of q.  R cr).  * jjf'(P3 2  2  +  v f  *  n0  (p + P > s  n 0  2 +  4  2 P  f  a  ]  s  "  B  y  cos 2jcqf The remaining steps are similar to those carried out i n Appendix II r e s u l t i n g i n the output power, P ^» being given QU  by Pout =  k  <4  2  2 p  n  + i  B"J 1  I ? ) Ps--  k  2  0 P PnO 2  S  +  PnO^H  +  ~2  B?> +  69  where B  n  i s the bandwidth of the low-pass f i l t e r .  -  B  For  0  an output Sffl of unity and 4  1 i  _£ 2 2 Ps  ~§ V n O IT (2  +  *W  ?  +  2 p  n 57 2  1 P  S  Noting that the input SNR to the radiometer i s - — p  n0  (s/n)^ the minimum detectable signal power i s given by* ^  IT P n  2 P S  min  lH  2  P  1  '  This result shows that the two channel subtraction radiometer cuts o f f the output signal i f the input SNR i s not greater than 1 + ^T  1  , as i n the case of the Dicke radiometer.  * M. G r a h a m h a s reported a value f o r p of -== of the value given here. min y2  70 APPENDIX VI GAIN REQUIRED FROM THE  BANDTPASS  AMPLIFIER  The gain required from the hand-pass amplifier can he found by r e l a t i n g the available power at the horn to the power input to the low pass f i l t e r of 1 mW. 1 mW  where  p  G = p jfmin s  = k T s  min  Thus,. (VI-1)  B. min  1  = 32.6 x l O * ^ mW -  for measurements during  the pinch(6.2 x 10^ deg = 40.7 x 10"""^" mW  K)  f o r measurements during  the afterglow (7.8 x 10 deg K) = t o t a l gain of the amplifiers 2  G L G  s  s s  and L  = sum of the losses i n the system. s  are given i n Table  Thus, f o r diode switch modulation G^ = 30 dB and for l o c a l o s c i l l a t o r modulation G^ = 37 dB, where G  fe  the band-pass amplifier.  i s the gain of  71 Diode Switch Modulation Gain  Loss  Local O s c i l l a t o r Modulation Gain  dB  Loss dB  loss due to random polarization  3  loss i n waveguide run  1,5 dB  1.5 dB  loss i n balanced mixer  8.5 dB  8.5 dB  loss i n cable between balanced mixer and parametric amplifier  0.5 dB  0.5 dB  Loss i n diode switch  2  dB  Loss due to modulation  3  dB  Gain of parametric amplifier  14  dB  Gain of 2nd IF amplifier  Gain i n bandpass amplifier  Table VI-1.  5  dB  5  dB  dB  dB  b  (84+G^)dB . 28.. 5&B  Totals  dB  70 dB 5  G  •  3  dB  70 dB  Loss i n detector (assumed)  —  14  5  Conversion loss of 2nd mixer  3  G  b  (84+G^)dB  Evaluation of System Loss and Gain  26.5dB  72 APPENDIX VII DISCHARGE APPARATUS The discharge apparatus shown i n Pig. VII-1 i s similar (ll)  to one described e l s e w h e r e . w  The high voltage power supply-  charges a capacitor hank of approximately 180 uP through a charging r e s i s t o r of 12.5 E - n _ to a maximum voltage of 10 kV.  Charging Resistor  Argon Input  Capacitor Bank  Trigger Circuit  One of Six Rod"s~ Brass Electrodes Glass Discharge Tube  Pig. VII-1,  Discharge Apparatus.  73 The discharge takes place i n argon i n a glass tube 6 in  i n diameter and 30 i n long.  The pulses which trigger the  ignitron and the oscilloscope are generated i n a control c i r c u i t which incorporates a multivibrator and a delay c i r c u i t .  The  pulse repetition rate can be varied from 1 pulse every 7 s . to 1 pulse ever 90 s. The maximum current through the discharge tube i s approximately 10^ A, when the discharge voltage is" 10 kV.  This  current i s determined by measuring the voltage drop across a stainless s t e e l s t r i p of known resistance. The voltage across the discharge tube i s measured by using a capacitor voltage divider connected between the transmission l i n e s .  Current and  voltage traces are shown i n F i g . VII-2 f o r a discharge at 40 , nm and an i n i t i a l voltage of 5 kV.  F i g . VII-2.  Voltage (upper trace) and Current (lower trace). Time Scale 10 us/major d i v i s i o n .  74 REFERENCES 1.  Seeger, C.L., Stumpers, F.L.H.M., and Van Hurck, N., "A 75 cm. Receiver f o r Radio Astronomy and Some Observational Results/ P h i l i p s Tech. Rev.. Vol. 52, p. 317, September 27, I 9 6 0 . 1  2.  Conn, M., Wentworth, F.L., and ¥iitse, J.C., "High-Sensit i v i t y 1 0 0 - to 300Gc Radiometers," Proc. I.E.E.E.. Vol. 51, p. 1227, September, 1963.  3.  Meredith, R., Warner, F.L., Davis, Q.V., and Clarke, J.L., "Superheterodyne Radiometers f o r Short Millimeter Wavelengths," Proc. I.E.E.. V o l . I l l , p. 241, February, 1964.  4.  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