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Frequency stabilization of a klystron in a paramagnetic resonance spectrometer Rundle, Howard Norton 1955

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FREQUENCY STABILIZATION OF A KLYSTRON IN A PARAMAGNETIC RESONANCE SPECTROMETER by HOWARD NORTON RUNDLE  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Physics  We accept this thesis as conforming to the standard required from candidates f o r the degree of MASTER OF ARTS  Members of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA September, 1955  ABSTRACT  A f i e l d modulation, paramagnetic  resonance  spectrometer i n use as a wide band Instrument employs a r e f l e x klystron.  The frequency of the klystron has been  s t a b i l i z e d to at least one part i n one quarter m i l l i o n , over a period of a few hours, to the resonant frequency of a microwave cavity.  A variation  of the A .C. Pound s t a b i l i z i n g T  c i r c u i t was employed. With f i e l d s t a b i l i z a t i o n , this frequency s t a b i l i z a t i o n makes i t possible to operate the spectrometer as a narrow band instrument, thereby increasing the o v e r a l l  sensitivity.  ACKNOWLEDGMENTS  I am indebted to Dr. H.E.D. S c o v i l f o r suggesting the topic of this thesis and f o r h i s guidance and interest* I am likewise indebted to Mr. H.A. Buckmaster f o r h i s assistance with many aspects of the work and many i l l u m i n a t ing discussions. I wish to thank Dr. J.M. Daniels f o r h i s help and interest i n this research. I should l i k e to express my gratitude to Mr. A. Frazer and Mr. W. Morrison for t h e i r h e l p f u l work and advice i n the machining work and to Mr. E. Price f o r advice about the electronic c i r c u i t s and to Mr. J . Lees f o r the necessary glass blowing. I also wish to express my gratitude to the members of the University of B r i t i s h Columbia Physics Department f o r t h e i r patience, guidance and i n s p i r a t i o n i n the f i e l d of physics. This work could not have been carried out without the research grants to Dr. H.E.D. S c o v i l and a bursary to the author granted by the National Research Council.  TABLE OF CONTENTS Page 1  General Introduction Chapter I  Frequency S t a b i l i z a t i o n i n a Paramagnetic Resonance S p e c t r o m e t e r  Introduction  .  •  2 2  . . . . . . . .  1.1  Paramagnetic Resonance  2  1.2  Wide Band and Narrow Band S p e c t r o m e t e r s . . . .  4  1.3  Wide Band S p e c t r o m e t e r s Employed i n t h e 5  Laboratory . . . . . . . . . . 1.4  F i x e d Frequency C o n s i d e r a t i o n s  1.5  Amplitude C o n s i d e r a t i o n s  Chapter I I  .  Methods o f S t a b i l i z a t i o n  6 . . . . .  8  .  10  Introduction  10  2.1  Resonant Frequency C o n s i d e r a t i o n s  10  2.2  E x i s t i n g Methods  11  2.3  B.C. Methods  13  2.4  A b s o r p t i o n Methods  2.5  A.C. Methods  2.6  C o m b i n a t i o n o f Methods  2.7  F e a s i b i l i t y o f V a r i o u s Methods  Chapter I I I  .  15 16  .  Frequency M o d u l a t i o n Method  18 19 23  Introduction  23  3.1  Operation  23  3.2  Circuitry  25  TABLE OF CONTENTS - C o n t i n u e d  Chapter IV  Performance o f S t a b i l i z a t i o n System . . .  28  Introduction  28  I4..I  Some C a l c u l a t i o n s  28  ij.,2  E x p e r i m e n t a l Performance  32  Appendix A . .  35  Appendix B  37  Appendix C  39  REFERENCES  i l l  TABLE OF FIGURES Facing Page 1.  Single Modulation Spectrometer  5  2.  Double Modulation Spectrometer  5  3.  Microwave Descriminator and D.C.Output . . . .  13  4.  Pound's D.C. C i r c u i t  Hi  5.  Hideout's D.C. C i r c u i t  Hj.  6.  Molecular Absorption Method  15  7.  Pound's A.C. Method  16  8.  Cavity Modulation Method  17  9.  Frequency Modulation Method  17  10.  Proposed Adaption for a D.C.Method  19  11.  Detailed Block Diagram of Frequency S t a b i l i z ation System using the Frequency Modulation Method  23  12.  Detected Signal from the Cavity  2k  13.  O s c i l l a t o r and Buffer C i r c u i t  26  14.  I.F. Amplifier and Phase Sensitive Detector Circuit  26  . . . . . . .  15.  C i r c u i t of the "Klystron Box"  16.  Klystron Power Supply  27 on Page 39  17.  300 V o l t Power Supply  ^°  18.  S t a b i l i z i n g Loop i n the Spectrometer  28  TABLE OF PLATES F a c i n g Page  1. 2. 3. 4.  General View of the Spectrometer i n the Laboratory  6  G e n e r a l V i e w o f the S p e c t r o m e t e r i n t h e Laboratory  6  Top View o f the Frequency S t a b i l i z i n g System  25  Bottom V i e w o f t h e Frequency S t a b i l i z i n g System  25  1  INTRODUCTION t  In an experimental study of paramagnetic  resonance,  the two quantities measured are the frequency o f the exciting radiation and the magnetic f i e l d .  To obtain reproducible  experimental results of a given accuracy, both of these quantities should be s t a b i l i z e d . A spectrometer can be operated i n a wide or a narrow band manner*  In wide band operation where measurements are  made i n a few minutes, only short term frequency and f i e l d s t a b i l i t y i s necessary, whereas i n narrow band operation, long term s t a b i l i t y i s required as measurements are made i n a few hours.  The high s e n s i t i v i t y , double modulation, wide band  spectrometer i n this laboratory possess the required short term s t a b i l i t y .  I f long term frequency and f i e l f l s t a b i l i t y  could be achieved, then narrow band operation can be executed, resulting i n an increase i n s e n s i t i v i t y of the spectrometer by a factor of about 1 0 0 , This thesis deals with the s t a b i l i z a t i o n of the f r e quency, the f i e l d s t a b i l i z a t i o n being l e f t as a separate problem.  2  CHAPTER I .  FREQUENCY STABILIZATION IN A PARAMAGNETIC SPECTROMETER  Introduction In this chapter an i n d i c a t i o n of the phenomena of paramagnetic resonance i s noted.  The two major types of  operation of a spectrometer are described, the narrow and wide band.  The two wide band spectrometers, i n operation i n t h i s  laboratory, are then described.  I t i s then shown that i n both  these spectrometers, i t i s important to s t a b i l i z e the frequency of the microwaves generated by a r e f l e x klystron. 1.1  Paramagnetic Resonance, The phenomena known as magnetic resonance results when  a p a r t i c l e with a magnetic moment i s placed i n a steady magnetic f i e l d .  The magnetic moment of the p a r t i c l e processes  about the d i r e c t i o n of the steady magnetic f i e l d such that the p a r t i c l e has the lowest energy possible.  I f a periodic magnetic  f i e l d i s applied at right angles to the steady magnetic  field  and i f the frequency of the periodic f i e l d i s equal to the frequency of the processing magnetic moment, then the p a r t i c l e ' s magnetic moment f l i p s over such that the p a r t i c l e has a higher energy; this energy being absorbed from the fluctuating f i e l d . This action, we can c a l l a t r a n s i t i o n .  Many such transitions  combine to produce a resonance which i s observed by the energy absorbed from the periodic magnetic  field.  3 Paramagnetic resonance arises by the above method from paramagnetic ions which have a partly f i l l e d electron s h e l l . Such ions have a resultant angular momentum due p a r t l y to o r b i t a l motion and p a r t l y to the i n t r i n s i c spin of the e l e c t rons.  The resultant angular momentum gives r i s e to a permanent  magnetic moment which w i l l have the same d i r e c t i o n as the angular momentum.  I t has been found that the quantum mechanical  explanation of this phenomena i s quite successful.  In a simple  case, where only two energy l e v e l s of the paramagnetic ion e x i s t , the energy absorbed i n the transitions occur i n quanta v = frequency of the periodic f i e l d ; y * spectro-  equal to  scopic s p l i t t i n g f a c t o r ; . fb - the Bohr magneton.  This r e l a t i o n *  ship known as Kramers doublet r e l a t i o n makes i t possible to observe resonances as a function o f v or H % tb-© other being kept constant. When paramagnetic resonance experiments are performed at microwave frequencies, i t i s found necessary to hold v fixed and vary H because of the type of o s c i l l a t o r used.  These experiments are usually carried out at a wave-  length of a few centimeters, the magnetic f i e l d being a few kilogauss; i . e . f o r ^ =• 2, v « 25 kilomega cycles per second, H  i s about  8,800  gauss.  I t i s desirable to use short wave-  lengths since the s e n s i t i v i t y i s inversely proportional to the wavelength.  The use of wavelengths shorter than one c e n t i -  meter has been r e s t r i c t e d by the lack of suitable sources and detectors of radiation i n t h i s region.  4  1.2  Wide and Narrow Band Spectrometer Operation The spectrometers employed to observe the phenomena of  paramagnetic resonance at short wavelengths employ d i s t r i b u t e d parameter c i r c u i t r y .  The sample under observation i s placed  i n a tuned cavity Instead of an extended waveguide f o r two reasons (a) The sample must be located i n a strong homogenous magnetic field (b) The samples are usually small single crystals and the highest s e n s i t i v i t y i s obtained by concentrating the microwave magnetic f i e l d on them. There are two types of operation of paramagnetic spectrometers, (a) the wide band, (b) the narrow band.  In  wide band operation, the steady magnetic f i e l d i s modulated at a low frequency with an amplitude greater than an absorption l i n e width at h a l f power expressed i n terms of the magnetic field.  When centered on a resonance l i n e , the magnetic  field  swings through the region of the resonance, thereby making i t f e a s i b l e to observe the resonance curve on some recording device.  The energy absorbed during a paramagnetic resonance,  amplitude modulates the microwave power l e v e l at the f i e l d modulation frequency.  This modulation i s detected, amplified  by a broad band amplifier to preserve l i n e shape, and displayed on an o s c i l l i s c o p e . ( r e f . 1 ) , In narrow band operation, the steady magnetic f i e l d i s modulated at a low frequency, the modulation having an amplitude  KLYSTRON  CAVITY  XTAL  AMPLIFIER  DETECTOR  60  CYCLE  SCOPE  MODULATION  COILS 60  SINGLE  MODULATION  FIG.  To be facing page 5  CYCLE  S P E C T R O M E T E R  I  PHASE SHIFTER  h  60  C Y C L E M O D U L A T I O N COILS  500  XTAL KLYSTRON  CAVITY  DETECTOR  K.C.  AMPLIFIER  PHASE  AUDIO  SHIFTER 500  DOUBLE  60  MODULATION  FIG.  To  be f a c i n g page 5  SCOPE  K.C.  TRANSMITTER  2  DETECTOR  CYCLE  SPECTROMETER  AMPLIFIER  1  less than the l i n e width.  As i n wide band operation, we obtain  an amplitude modulation on the microwave power l e v e l which i s detected, amplified i n a narrow band amplifier, converted to D.C.  and displayed on a pen recorded.  one point on the absorption curve.  This procedure gives  To obtain the entire curve,  the steady magnetic f i e l d Is slowly changed.  The recorder  then reproduces the f i r s t derivative of the absorption l i n e . Since the noise generated by an amplifier i s proportional to the band width, the narrow band operation greatly reduces the noise of the spectrometer, provided the noise generated by the detector i s not overwhelmingly large.  Because the noise i s  greatly reduced, the deciding factor f o r s e n s i t i v i t y of the spectrometer i s the s t a b i l i t y , rather than the noise as i n wide band operation. Thus frequency s t a b i l i z a t i o n i s an important problem f o r narrow band operation. 1.3  Wide Band Spectrometers Employed i n the Laboratory In t h i s laboratory there are two wide band, f i e l d  modulation spectrometers employing a frequency of megacycles per second i . e . a wave length of 1.25  kilo-  centimeters.  In both systems, a r e f l e x klystron generates the microwave radiation which i s transmitted by wave guides to a transmission cavity (as compared to a r e f l e c t i o n type c a v i t y ) .  The  difference between the two spectrometers i s i n the f i e l d modulation, one using a single modulation and the other a double modulation.  The single modulation spectrometer ( f i g .  1),  To be f a c i n g page 6  General view of the Spectrometer  6 employs a 60 cycle modulation.  The r e s u l t i n g modulated  waves are detected i n a c r y s t a l converter.  micro-  The resonance s i g n a l  i s then displayed on an o s c i l l i s c o p e a f t e r amplification. The second spectrometer ( f i g . 2) employs a double modulation of the magnetic f i e l d .  In addition to the 60 cycle  sweep covering at least the l i n e width, a 500 k i l o c y c l e per second sweep covering.at most the l i n e width i s also used.  The  500 k i l o c y c l e component of the modulation i s detected, amplif i e d i n a broad band amplifier.  The 60 cycle component i s then  detected, amplified and displayed on an oscilloscope. derivative or i t s modulus i s obtained.  The f i r s t  I t may be mentioned  that a high s e n s i t i v i t y has been obtained with t h i s spectrometer since the c r y s t a l detector detects a high frequency (ref.2).  A picture of the combined spectrometer i s shown i n  Plates I and I I . 1.4  Fixed Frequency Considerations Both spectrometers operate at fixed frequency, resonances  being observed as a function of the magnetic f i e l d .  As stated  before (1.1), the main reason i s due to the nature of the microwave generator or r e f l e x klystron.  A r e f l e x klystron o s c i l l -  ates i n d i f f e r e n t modes, a mode being several hundred per second wide.  Further, i t i s very d i f f i c u l t  frequency over a large range. a l l y on the mode of operation.  megacycles  to vary the  The output power depends d r a s t i c -  7 In practice the condition of a constant frequency i s d i f f i c u l t to obtain.  The factors a f f e c t i n g short term s t a b i l i t y  (over a period of a few minutes) are the following: (a)  Short term fluctuations i n the r e f l e x klystron power  supply w i l l cause short term frequency s h i f t s i n the klystron output. (b)  The output frequency of the r e f l e x klystron i s a function  of the impedance i t works i n t o .  This impedance i s p a r t i a l l y  determined by the standing wave r a t i o of the microwave system. This r a t i o depends on the r e f l e c t i o n c o e f f i c i e n t of the c a v i t y which i n turn Is a function of the energy absorbed i n i t .  This  change i n r e f l e c t e d energy, w i l l r e s u l t i n a p u l l i n g of the klystron's frequency.  The main factors a f f e c t i n g long term  s t a b i l i t y (over a period of a few hours) are the following: (a)  Long term fluctuations i n the r e f l e x klystron power supply  w i l l cause long term frequency s h i f t s i n the klystron output. (b)  Within the r e f l e x klystron there i s a resonator giving  r i s e to resonances by electrons passing through i t . the basis f o r the generation of microwaves.  This i s  The frequency of  the microwaves w i l l be affected by the resonant frequency of this resonator.  As the klystron continues operation,  i t becomes  warm, thereby, expanding the resonator i n the klystron and changing the frequency of i t s output.  This i s known as thermal  d r i f t of the klystron. (c)  The p u l l i n g effect of the klystron w i l l also  to the long term s t a b i l i t y .  contribute  8 1.5  Amplitude Considerations In both spectrometers, the amplitude of the resonance  observed i s proportional to the microwave energy i n the cavity, since i t i s the f i e l d of the microwaves which induce the transition.  The microwave power l e v e l i n the cavity i s deter-  mined by three factors. (a)  The operating conditions of the klystron must be c a r e f u l l y  selected because the microwave power depends upon the mode of operation and the position within the mode. (b)  The magnitude of the Q of the cavity indicates how much of  the microwave energy i s absorbed and how much can be considered useful energy. (c)  Most c a v i t i e s have a Q of about 10,600.  To take advantage of the high Q of the cavity, the frequency  of the microwaves should be at the resonant frequency of the cavity.  Since Q ..= 2Z. where  $v i s the width of the cavity  resonance curve at the half power pointy then f o r a Q of 10,000 and a frequency of 25 kilomegacycles per second, megacycles.  $ v i s 2.5  This shows that i f the frequency i s s t a b i l i z e d to  only one part i n 10 " there can be a f l u c t u a t i o n of 5<# l a the 4  microwave energy i n the c a v i t y .  However, i f the frequency i s  s t a b i l i z e d to one part i n say, 10^ and i s at the cavity's resonant frequency, then the energy of the microwaves i n the cavity w i l l remain e s s e n t i a l l y at the maximum value. Because of the necessity f o r a constant frequency during a set of measurements and of the d e s i r a b i l i t y of a  maximum amplitude of the resonance s i g n a l i t i s important to s t a b i l i z e the frequency of the klystron to the resonant f r e 6 quency of the cavity to approximately one part i n 1 0 time of recording a measurement.  f o r the  10  CHAPTER I I .  METHODS OF STABILIZATION  In this chapter, the various methods employed f o r s t a b i l i z i n g a r e f l e x klystron w i l l be described and discussed from the standpoint of f e a s i b i l i t y t o the present problem of s t a b i l i z i n g the frequency of the klystron to the resonant frequency of the cavity.  The chosen method must not i n t e r f e r e  with the observation of paramagnetic resonance. 2.1  Resonant frequency considerations It may be noticed that we are not interested i n  s t a b i l i z i n g the frequency to a fixed value but only to the resonant frequency of the cavity.  While the frequency stab-  i l i t y i s limited by the s t a b i l i t y of the resonant frequency, the  amplitude of the microwaves i n the cavity, and thus the  i n t e n s i t y of the paramagnetic resonance, i s held reasonably constant.  Any changes which are present i n the microwave  i n t e n s i t y w i l l arise from the shape of the power vs. frequency curve of the mode of operation of the klystron. The resonant frequency of the cavity i s subject to short term i n s t a b i l i t i e s and long term i n s t a b i l i t i e s .  The short term  i n s t a b i l i t i e s are caused by short term temperature fluctuations and mechanical vibrations of the cavity.  The long term instab-  i l i t i e s w i l l be caused by long term temperature fluctuations  and variations of the contact of the running plunger threads with the cavity.  The short term i n s t a b i l i t i e s i n the resonant  frequency are not serious f o r the high s e n s i t i v i t y , double f i e l d modulation spectrometer with wide band operation. However, with narrow band operation i t i s probable that the long term i n s t a b i l i t i e s would l i m i t the s e n s i t i v i t y .  These long  term i n s t a b i l i t i e s can be minimized by immersing  the cavity i n  a l i q u i d which i s preferably at i t s b o i l i n g  temperature.  Such changes i n the resonant frequency caused by the presence of d i e l e c t r i c materials, as helium, i n the cavity or by a large change i n temperature, as from room temperature to l i q u i d helium temperatures, can be corrected f o r by mechanical tuning of the klystron or detuning the klystron i n the correct d i r e c t i o n before the occurrence of the change i n the resonant frequency. 2.2  E x i s t i n g Methods As the klystron power supply i s e l e c t r o n i c a l l y regulated  the short and long term I n s t a b i l i t i e s due to t h i s cause are kept to a minimum.  The short term i n s t a b i l i t i e s present i n the  high sensitive) double f i e l d modulation spectrometer are mostly due to the p u l l i n g effect of the cavity.  The long term i n s t a b i l  i t i e s present, result mostly by the thermal d r i f t and the pulling effect.  Along with these e f f e c t s , the i n s t a b i l i t i e s i n  the resonant frequency of the cavity, described i n 2 . 1 , are present.  The chosen method must lock the frequency of the  klystron output to the resonant frequency of the cavity, r e gardless of the i n s t a b i l i t i e s present.  12  The thermal d r i f t of the klystron and temperature effects of the cavity can be minimized by allowing the spectrometer to warm up to an equilibrum temperature.  Further, the  klystron could be immersed i n an o i l bath to minimize thermal effects due to temperature fluctuations i n the laboratory. However, only an electronic method can deal with the thermal, p u l l i n g , and mechanical effects simultaneously.  Hence i t was  decided to use such a method. The various existing electronic methods have been designed  to s t a b i l i z e a r e f l e x klystron's frequency to a fixed  frequency, the fixed frequency usually being the resonant frequency of a cavity.  These methods of frequency control  s h a l l f i r s t be presented as they exist for this function, before discussing t h e i r a p p l i c a b i l i t y to the present problem. There exist three catagories of methods. a.  D.C. method  b.  Molecular or atomic absorption method  c.  The A.C. method.  The f i r s t and l a s t methods have several variations which w i l l be described. property.  These three methods have the following common  As the frequency of a klystron i s a l i n e a r function  of i t s r e f l e c t o r voltage over a small range of operation i n any p a r t i c u l a r mode, a D.C. correction voltage proportional to the frequency error i s created and applied to the klystron's reflector.  To obtain this correction voltage, use i s made of  a frequency discriminator containing a cavity i n the microwave  ATTENUATOR  XTAL  TO  B  LOAD  KLYSTRON  IS. C AVIT Y  XTAL  A  D.C.  (VI I C R O - W A V E  OUTPUT  DISCRIMINATOR  FIG.  3A  <  t  v- v  O  D.C.  Q  C) U T P U T FIG.  3B To be facing page 13  13 c i r c u i t , as i s done i n the D.C. method, or use i s made of an a u x i l i a r y o s c i l l a t o r whose s i g n a l acts as an information c o l l e c t o r on the difference between the frequency of the k l y stron and a reference, such as, a microwave cavity's resonant frequency as i s done i n the A.G. and absorption methods. 2.3.  D.C.Methods There are two main v a r i a t i o n s of this method one  developed by R.V. Pound ( r e f . 3>4>5>6) and the other developed by V.C. Hideout ( r e f . 7).  The microwave discriminators  employed by these two people are s i m i l a r , both employing two magic tees.  The discriminator due to R.V. Pound s h a l l now  be described  ( f i g . 3)*  figure 3A. ator.  Two magic tees are joined, as shown i n  An attenuator separates the klystron and d i s c r i m i n -  Two c r y s t a l detectors are present i n arms 4 and 7 and a  cavity i s joined to arm 6 .  The D.C. output of this discrimin-  ator i s shown i n figure 3 B as a function of v->J», v being the frequency of the klystron, cavity.  y  9  the resonant frequency of the  The operation can be explained q u a l i t a t i v e l y by the  following arguements. The klystron's output i s divided between the load and regulating c i r c u i t , the attenuator  causing the  majority of the microwave energy to go to the load.  The atten-  uator also serves as a matching device of the load to the klystron.  The energy which enters the regulator c i r c u i t a f t e r  passing through the attenuator  i s divided equally between arms  2 and 3.  Arm 2 i s terminated so that there i s no r e f l e c t i o n  from i t .  That i n arm 3 , enters arm 5 and i s divided equally  A T T E N U A T O R D I S C R I M I N A T O R T O L O A D  D.  C.  K L Y S T R O N  A M P L I F I E R  POUND'S  D . C .  CIRCUIT  Fl G. 4  K L Y S T R O N TO L O A D D I S C R I M I N A T O R G E A R B O X  6 0  C Y C L E  J~L  C O N V E R T E R  M O T O R  60  RIDEOUT'S  C Y C L E  D.C. FIG.  CIRCUIT  5 To "be f a c i n g page 14  14 between arm 8 which i s terminated to prevent reflection and arm 6 which leads to the cavity. *  r  The cavity reflects when  •>/. and doesn't reflect i f vs*  action is that when v*- v  W/  The result of this  there is more energy In arm 6  than in arm 8 thus some energy arrives at crystal A i n arm 7. A small amount of the reflected energy w i l l also find i t s way to crystal B in arm 4. The sign of the D.C. output depends whether  or v ? v . #  i n each of these two cases, the phase  of the reflected microwaves i s 180° different from the other case, resulting i n a cancellation or addition in arm 6 which causes the D.C. output to be negative or positive. The Pound circuit (fig.4) amplifies this D.C. correction voltage and applies i t to the klystron's reflector. The Rideout circuit ( f i g . 5) converts this D.C. correction voltage to 60 cycles A.C. which i s amplified and applied to the control phase of 2-phase, low inertia, induction motor. signal is applied to the other phase.  A reference 60 cycle  This motor turns a  mechanical tuning shaft on the klystron via a reduction gear box.  I f the correction voltage Is zero, then the motor doesn't  turn, i f there is a D.C. correction voltage, then 60 cycles A.C. is obtained, the phase depending on whether the D.C. correction voltage is negative or positive.  The motor then turns in the  direction determined by the phase of the 60 cycle A.C. This Is actually a servo-mechanism and removes only slow variations in the frequency of the klystron.  SCANNING  XTAL  KLYSTRON DETECTOR  XTAL KLYSTRON  MIXER  AND  AMPLIFIER  AMPLIFIER  DETECTOR  PHASE  SENS.  DETECTOR  MOLECULAR  ABSORPTION FIG.  To be facing page 15  6  METHOD  A b s o r p t i o n  2.4  T h i s as  a  o f  the  Method  method  r e f e r e n c e  uses  frequency  k l y s t r o n  i s  A B . C . c o r r e c t i o n  of  the  two  o f  the  k l y s t r o n .  f r e q u e n c i e s  10,11) w h o  have  One c i r c u i t  a  s c a n n i n g  a b s o r p t i o n p e r i o d i c the  used  and  on  a m p l i f i e d ,  d e t e c t o r ,  where  of  the  output  two  r e f l e c t o r The  l i n e  f a c t o r  appendix  o f  the  w i d t h  f o r  i s  o f  made  A A ) .  a c c u r a c y .  can  method  f o r  s t a b i l i z i n g  but  not  the  v a r y i n g  an  at  t o  W . D .  ( r e f . o f  8,9,  ammonia. I n  at  t h i s  some  covers  the  f r e q u e n c y s i g n a l  A o f  i s  t h e n  s e n s i t i v e i n  f r e q u e n c y  d e v e l o p e d  i n  the  and  i s  l o c k s i s t h a t  o s c i l l a t o r  r e s o n a n t  due  d i f f e r e n c e  i s  n o t i c e d  a  phase  a b s o r p t i o n be  i s  r e f l e c t o r  f r e q u e n c i e s .  T h i s  a  the  the  ( r e f . 8 ) .  D . C . v o l t a g e  k l y s t r o n  gaseous I t  w i t h  T h i s  s t a b i l i z e d the  e n t e r  to  a b s o r p t i o n d i f f e r e n c e  frequency  c e l l  k l y s t r o n . to  the  modulated  i t s  gas  the  spectrum 6  l i n e  frequency  others  k l y s t r o n ' s  D . C . v o l t a g e  ent  to  the  compared  k l y s t r o n s .  (see  frequency  s c a n n i n g and  and  f i g .  i n  to  method  i n v e r s i o n  sweep  i n  t h i s  I n  o f  a p p l i e d  Lamont  s t a b i l i z e d  occurs  d e t e c t e d ,  i s  and  a b s o r p t i o n the  frequency  o f  shown  The  the  the  i t  the  k l y s t r o n  a b s o r p t i o n  m o d u l a t i o n  H . R . L .  i s  m o l e c u l a r  p r o p o r t i o n a l  d e v e l o p e d  used  frequency.  l i n e  the  development  m a i n l y  or  E s s e n t i a l l y ,  w i t h  s i g n a l  N o r t o n ,  c i r c u i t  i n t e r m e d i a t e  s o u r c e .  i s  The  I . E .  atomic  compared  l i n e .  H e r s h b e r g e r ,  an  f r e q u e n c y  to o f  a p p l i e d i t s  the  a  the  f r e q u e n c y .  d e t e r m i n i n g  t h i s one  t o  i s  an  f i x e d c a v i t y .  e x c e l l frequency,  C  XTAL  A VIT Y  B  AT  TENUATOR  4 TO LOAD  3 XTAL  A  KLYSTRON  BUFFER  AMPLIFIER AI 1. F. OS c.  PHASE  BUFFER  SENS.  DETECTOR  POUND'S  FIG .  A .C .  CIRCUIT  7  To be f a c i n g page 16  2.5  A.C. Method There are three variations of this method.  v a r i a t i o n i s due to R.V.  first  Pound ( r e f . 3 » 5 ) » th® other two are  mentioned by E.F. Grant ( r e f .  12).  The Pound c i r c u i t shown i n f i g . 7, A cavity of resonant frequency s t a l s are on arm 2 and 4.  The  >>.  employs a magic tee.  i s on arm 1;  two mixer cry-  The operation of this c i r c u i t can be  explained q u a l i t a t i v e l y by the following arguments.  As i n the  Pound D.C. method, the k l y s t r o n output i s divided between the load and the s t a b i l i z i n g c i r c u i t , the attenuator causing the majority of the energy to reach the load.  The energy present  i n arm 3 divides equally between arms 1 and 2. arm 1 i s not reflected by the c a v i t y i f v * v if y^y  #  .  tf  The energy i n , but i s r e f l e c t e d  i f the energy i s r e f l e c t e d , i t divides evenly  between arms 4 and 3.  That part i n arm 3 Is l o s t to the atten-  uator and that part i n arm 4 i s mixed at c r y s t a l B with a s i g n a l from the I.F. a u x i l i a r y o s c i l l a t o r .  Hence there are two side  bands v ^ t v * ; v ^ t h e frequency of the k l y s t r o n , frequency of the a u x i l i a r y o s c i l l a t o r .  =. the I.F.  These bands are r e -  f l e c t e d and evenly divided between arms 1 and 2.  Those entering  arm 1 can be neglected as they give r i s e to only second order effects. inal  Those entering arm 2 mix at c r y s t a l A with the o r i g . We then have at c r y s t a l A, three frequencies  and  V-v*  •  —  output used from c r y s t a l A i s at the  I.F. frequency which has a voltage o f f » £  £*/C/<~*  $  ^(.w^*).  KLYSTRON TO  PHASE  nfl  SENS.  AUX. I.F.  LOAD  CAVITY  OSC.  DETECTOR I,  XTAL  F.  AMPLIFIER  CAVITY  DETECTOR  MODULATION FIG.  METHOD  8  KLYSTRON TO  1 PHASE  AUX . I. F. O S C .  LOAD  CAVITY  SENS.  DETECTOR  FREQUENCY  I. F.  XTAL  AMPLI F I E R  DETECTOR  MODULATION FIG.  METHOD  9 To be f a c i n g page 17  as shown by Pound, $  and  /»n are constants of the c i r c u i t ,  i s the phase s h i f t of >^  which depends on the length to  the cavity and the frequency difference of v - .  .  v  this <c<m &  It i s  which gives the required information to produce  a p o s i t i v e or negative correction voltage.  The voltage of  detected at c r y s t a l A i s then amplified and mixed i n a phase sensitive detector with a reference signal from the same auxiliary oscillator.  The output of the phase sensitive  detector contains a D.C.  component (see appendix A) which i s  the correction voltage applied to the r e f l e c t o r of the klystron. The second and t h i r d variations of this A.C. method are shown i n f i g . 8 and 9.  The method shown i n f i g . 8 modul-  ates the resonant frequency of the cavity by vibrating some part of the cavity such as a diagram or some object placed i n the cavity as a reed.  The other method In f i g . 9 modulates  the frequency of the klystron.  The operation of both these  c i r c u i t s i s s i m i l a r as It i s only the difference v - v determines the D.C.  correction voltage.  0  which  The detailed operation  of this c i r c u i t s h a l l be l e f t f o r chapter 3» but a sketch of i t s action i s given now. enter the cavity.  Microwaves generated  i n the k l y s t r o n  I f an external load i s used only a small  amount need enter the s t a b i l i z i n g c i r c u i t .  As the  frequency  of the microwaves or the resonant frequency of the cavity i s modulated we can say that the difference v->£  i s constantly  18 changing, hence the amplitude of the output from the cavity i a changing due to the resonance curve of the c a v i t y .  Moreover,  the phase of t h i s output w i l l depend on the sign of  .  This signal i s detected, amplified, and compared i n a phase sensitive detector with a s i g n a l from the same a u x i l i a r y o s c i l lator.  As shown i n appendix A, there i s a D.C. component i n  the output of the phase s e n s i t i v e detector. This D.C. voltage i s the correction voltage applied to the r e f l e c t o r of the klystron. One may note a feature lacking i n a l l the methods with the exception of the l a s t two variations of the A.C. method. This p a r t i c u l a r feature i s that the cavity i s a transmission type as f a r as the regulating c i r c u i t i s concerned so that one does not depend on r e f l e c t i o n s from the cavity. 2.6  Combination of Methods In addition to these d i f f e r e n t methods, one can combine  two, such as the servo-mechanical and say the Pound's A.C. methods as W.F. Gabriel and F.A. Jenks have successfully done (ref. 13, 14).  We may note however, that as we now have two  correcting systems or loops, there w i l l be some balance f r e quency that does not coincide with the resonant frequency of the cavity.  This combination of methods i s a f a i r l y good way  of s t a b i l i z i n g the frequency of a microwave o s c i l l a t o r when one i s interested i n absolute s t a b i l i z a t i o n , as the servomechanical method corrects for the slower variations while the  KLYSTRON  AMPLIFIER OR  CAVITY  MOTOR  3 P A R AM.  RES. SCOPE  A M P LI F I E R  PROPOSED  ADAPTION FIG.  To be f a c i n g page 19  10  O F  D.C, METHOD  electronic method corrects f o r the faster v a r i a t i o n s .  Farther,  the electronic method can act as an anti-hunt c i r c u i t f o r the servo-mechanical method.  Gabriel used t h i s combination i n  conjunction with the measurements of the d i e l e c t r i c of gases where an absolute frequency control i s necessary.  Because of  this necessity, great e f f o r t was spent to assure that the resonant frequency of the c a v i t y remained constant by minimizing the effects due to such factors as temperature and humidity fluctuations. 2.7  F e a s i b i l i t y of the Various Methods to the Present Problem As stated previously the chosen method must be such  that the s t a b i l i z a t i o n action and paramagnetic resonance must not i n t e r f e r e with one another. I f i t was attempted to use either of the D.C. methods the c i r c u i t would have to look something l i k e that shown i n f i g . 1G.  Microwaves from the klystron f i n d t h e i r way to the  cavity, some then being r e f l e c t e d and some transmitted.  Those  transmitted through the c a v i t y could be used f o r observing paramagnetic resonance and those r e f l e c t e d from the c a v i t y could be used f o r the s t a b i l i z i n g c i r c u i t .  There i s , however,  a serious f a u l t that the r e f l e c t i o n c o e f f i c i e n t of the c a v i t y i s altered by the presence of a paramagnetic resonance.  Thus  i f the regulation c i r c u i t i s working so that v - v„ , and i f one i s changing the D.C. magnetic f i e l d so that a paramagnetic absorption occurs, the condition of no r e f l e c t i o n i s upset,  20  hence the descriminator would have a D.C. output and the klystron would detune.  Minor d i f f i c u l t i e s arise by the f a c t  that not a l l the microwave energy reaches the c a v i t y and a D.C. system i s d i f f i c u l t to s t a b i l i z e .  We can therefore say  that the D.C. system i s not f e a s i b l e for the present problem. The absorption method i s obviously not applicable f o r the klystron frequency i s locked onto a constant frequency and not the varying resonant frequency of a cavity. The A.C. method devised by Pound has a serious f a u l t s i m i l a r to that described f o r the D.C. method since Pound's A.C. method depends on r e f l e c t i o n s from the cavity.  Another  f a u l t manifests i t s e l f by the presence of side bands i n the cavity which would inconvenience paramagnetic resonance.  Also,  degenerative frequency modulation can occur by cancellation of I.F. i n the microwave descriminator. In comparison to the previous methods the A.C. methods involving frequency modulation of the klystron or cavity modulation do not contain any of the mentioned f a u l t s of the other methods.  No use i s made of any r e f l e c t e d  microwaves,  thus the presence of a paramagnetic absorption i n the c a v i t y doesn't a f f e c t the s t a b i l i z a t i o n c i r c u i t .  I t may also be noted  that the f u l l amount of the microwave energy from the klystron enters the cavity.  Another advantageous feature i s that  there i s zero I.F. signal from the cavity when y * high gain amplifier may be used.  , hence a  The frequency modulation  method lends i t s e l f to the use of a higher searching frequency than the cavity modulation method.  A high modulation frequency  i s desirable since information i s collected more frequently than i f a lower modulation frequency i s used.  Further, the  cavity modulation method presents several mechanical d i f f i c u l ties not present i n the frequency modulation method.  Because  of these reasons the frequency modulation method was chosen for frequency s t a b i l i z a t i o n of the r e f l e x klystron. There are several minor disadvantages to this method which manifest themselves as only second order e f f e c t s .  They  are the following. (a)  Since the frequency of the klystron i s modulated, the klystron w i l l work back and f o r t h over a small part of the p a r t i c u l a r mode of operation.  I f a mode i s c a r e f u l l y  examined, i t w i l l be noted that there e x i s t small jumps i n the power output.  These small jumps w i l l manifest  themselves i n the form of noise introduced into the spectrometer. (b)  There i s the p o s s i b i l i t y of the introduction of a magnetic pickup loop into the spectrometer when the frequency s t a b i l i z a t i o n i s i n operation. However, t h i s aspect exists f o r any type of s t a b i l i z e r used.  (c)  One would expect the modulation of the frequency I t s e l f to increase the error i n the measurement of frequency at which paramagnetic resonance occurs; but this i s not  22  necessarily the case.  The error of the frequency  measurement without s t a b i l i z a t i o n i s of the order of (10  to 20)  megacycles.  10,000 and an operating  Now with a cavity of a Q of frequency of 25 kilo-mega cycles  per second, one needs to sweep the frequency through a maxium of o n l y 5 megacycles per second f o r successful operation  of the s t a b i l i z i n g system.  It can thus be seen  that the error i n the frequency measurements w i l l not be increased  by a noticeable  amount.  POWER  XTAL KLYSTRON  SUPPLY  F I L T E R  CAVITY  A UX.  AND  OSC.  NETWORK  CST.  P H A S E DETEC  DETAILED METHOD  M A T C H ING  BUFFER I.F.  TIME  DETECTOR  PHASE  SENS. TOR  BLOCK  S  HIFTER  DIAGRAM  F O R FREQUENCY To be facing page 23  I. B UFFE R  O F FREQUENCY STABILIZATION  F.  AMPLIFIE R  MODULATION F I G . I I  23  CHAPTER I I I  THE FREQUENCY MODULATION METHOD OF FREQUENCY STABILIZATION  Chapter II showed the superiority of the frequency modulation method for s t a b i l i z i n g the klystron. s t a b i l i z a t i o n c i r c u i t was b u i l t . of such a system i s presented.  Such a  In this chapter the operation A description of the c i r c u i t s  b u i l t i s also given. 3.1  Operation of the C i r c u i t A detailed block diagram of the s t a b i l i z a t i o n system  i s shown i n f i g . 11.  An a u x i l i a r y o s c i l l a t o r provides a  signal which i s applied to the r e f l e c t o r of the klystron thereby frequency modulating the output. a u x i l i a r y o s c i l l a t o r and klystron.  A buffer section isolates the The frequency modulated  microwaves enter the cavity which e s s e n t i a l l y converts the frequency modulation to an amplitude modulation.  This ampli-  tude modulation i s detected by a c r y s t a l detector. signal i s i l l u s t r a t e d i n f i g . 12.  The detected  The frequency modulation of  the microwaves changes the frequency i n the cavity by an amount 4 V at a rate equal to the frequency of the a u x i l i a r y o s c i l l ator.  As the amplitude of the microwaves or i n other words the  envelope follows the shape of the cavity resonance curve, we can see that i f the frequency of the klystron equals the resonant frequency  V, of the cavity, we then obtain a detected  — • A v «—  DETECTED  SIGNAL FIG.  12  FROM  CAVITY  To be f a c i n g page 24  signal at a frequency double that of the a u x i l i a r y o s c i l l a t o r . I f v*.y we then get a detected signal at a certain phase and 0;  at the a u x i l i a r y o s c i l l a t o r frequency; i f >>-y, , we obtain a detected signal 1 8 0 ° out of phase with the y * * , case, which can e a s i l y be seen by considering  fig. 1 2 .  I f the frequency  i s increasing  then for v ? v , the s i g n a l has a negative slope,  while for  »„ i t has a positive slope.  Thus the phase of  the detected signal gives us the information as to whether a positive or negative D.C. correction voltage i s required. The detected signal i s amplified, a f t e r passing through a matching section and enters a phase sensitive detector.  To  perceive a change i n phase of this s i g n a l , the phase s e n s i t i v e detector must have a reference s i g n a l from the same a u x i l i a r y oscillator.  This i s supplied v i a a buffer section and a phase  s h i f t i n g network.  The phase s h i f t i n g network allows adjustment  of r e l a t i v e phases so that maximum D.C. correction s i g n a l i s obtained i n the output of the phase s e n s i t i v e detector as the amplitude of this D.C. component involves  a  S , $ =. phase  difference between the two signals (see appendix A).  A low  pass f i l t e r cuts out a l l the A.C. components i n the output of the phase sensitive detector while a network giving a time constant determines the time response of the complete c i r c u i t .  The  D.C. correction voltage i s then applied to the r e f l e c t o r of the klystron so that to  V,  .  i s lessened or v i s brought closer  '.i e XII  To be f a c i n g page 25  Top View of the Frequency S t a b i l i z i n g System  25 It can be noticed that there i s no D.C. voltage when  v  correction  i s at a p o s i t i o n where the slope of the  cavity resonance curve i s zero.  Thus i f v * v  i s no correction voltage, also i f v  a  , then there  jumps i n the region where  the cavity resonance curve has zero amplitude, then again there i s no D.C.  correction voltage.  This behaviour shows that  a correction to the frequency v only occurs for frequency fluctuations which remain on the cavity resonance curve. 3.2  Circuitry The c i r c u i t r y of the i n d i v i d u a l components i n the block  diagram w i l l now  be described.  The complete c i r c u i t i s con-  tained i n three chassis. The a u x i l i a r y o s c i l l a t o r and buffer sections were put i n one chassis (smaller chassis i n Plate III IV) while the matching network, I.F. amplifier, phase s e n s i t i v e detector and phase s h i f t i n g network were put i n a second chassis (Larger chassis i n Plate III and IV).  The low pass  f i l t e r and time constant were placed i n the "klystron box" which, as i t s name suggests, contains the klystron.  A l l compon-  ents were shielded with brass so that 500 k i l c y c l e s used e l s e where i n the spectrometer would not i n t e r f e r e with the frequency regulating c i r c u i t . also was  Further shielding of i n d i v i d u a l components  employed. The a u x i l i a r y o s c i l l a t o r i s a 10.7  megacycle per second  c r y s t a l o s c i l l a t o r giving high frequency s t a b i l i t y , as a change i n the frequency of the a u x i l i a r y o s c i l l a t o r would  6AK5  6AK5 . 30K  —  6AK5  2  >30K.  >00K  R.F.C.  JT  •OOi"  SOOKi  '5O0K  J  X  OOS/ff  TO KLYSTRON REFLECTOR  cos" zoom  B. 6A.Q5  6AK6  XTAL  0  r"\/WW"  "y  SOJl  «0O5/lf  >/WW-  P  400,  SOK?  J l  '005yHt  >SOOK  REFERANCE SIGNAL  R.F.C.  —  R.F.C.  D  w 3vKw /I0W 0A2  T -II-  300V 50mA  ft ft ~p00£yrf  CIRCUIT OF OSCILLATOR AND BUFFER SECTIONS  FIG-.  13  6 3 V.  ~~poOS/if fa Q  6AU6  6AK5  6AU6  6AU6  AMPLIFIER O U T P U T MONITOR 3 3 K  RFC  RFC  I—AAAA  +-/00V  R.F.C  R.F.C.  -01/1f  -01/if_[|_ .OOS/<f  R.F.C.  R.F.C.  R.F.C  R.F.C  R.F.C  R.F.C.  mm  - L >oo5/tf  asm\  j-|H  -005/1f  00S/1  oos/iF  \ :  • V  #  f-l/ll c • IOK D  zr Zo/ytf  - = 29*/^  3K«/W.  •  i i/tL  ro"ooo)_  -  lljil  TO  G'  11/iL =  20/yif  H  T  ZSoJl  6AS6fil.  jr CIRCUIT  K L Y S T R O N BOX  OF MATCHING NETWORK, AMPLIFIER, PHASE SENS. DETECTOR AND PHASE SHIFTER  005" T  K  TO KLYSTRON POWER  SUPPLY  26  present a spurious phase change at the phase sensitive detector. The buffer sections consist of a low gain amplifier stage followed by a cathode follower for d r i v i n g the s i g n a l through cables. The  c i r c u i t i s shown i n f i g . 13,  ( r e f . 15,  16).  The c r y s t a l detector i s a 1K26 located i n the wave guide.  The matching network i s a Robert's network ( r e f . 17)  designed to present a non reactive impedance to the c r y s t a l detector.  The  I.F. amplifier i s a broad band, f i v e stage tuned  amplifier with a gain of about 1 0 ^ .  The phase sensitive detect-  or consists of a dual control pentode, a 6AS6 at the voltage of the klystron's r e f l e c t o r .  D.C.  The phase s h i f t e r for the  reference s i g n a l consists of a v a r i a b l e , lumped parameter, delay l i n e designed to give a maximum of 1 8 0 ° phase s h i f t (ref. 18).  For further phase s h i f t one can s h i f t the phase of  the s i g n a l i n the amplifier by interchanging I.F. transformer.  two leads on  an  The phase can be obtained to within 1 0 ° of  the maximum adjustment; t h i s i s s u f f i c i e n t as the  -*cr*  i s f a i r l y unsensltive to angular dependence when S^o  $  function  ,  The  c i r c u i t i s shown i n f i g . 1 4 . Other phase sensitive detectors  such as a diode bridge  c i r c u i t or a 6BE6 as a dual control pentode were t r i e d , however the 6AS6 was s h i f t e r , R.C.  found to be the most s a t i s f a c t o r y .  For the phase  networks were t r i e d but found unsatisfactory at  I.F. frequencies, due  to stray capacities.  E  o  F  o  G o H  o  J  °  K T O  1—  o P O W E R  P H A S E  S U P P L Y  S E N S .  ( S E E . F I G . i4)  VIA  D E T E C T O R  CIRCUIT  OF "KLSTRON FIG.  To be f a c i n g page 27  15  BOX"  The c i r c u i t of the k l y s t r o n box i s shown i n f i g . 15. The time constant of the frequency regulating c i r c u i t i s determined by R^ and C^ while the condensor C  2  acts as the  f i l t e r for the A.C. components i n the output of the phase sensitive detector. The leads from the power supply f o r the klystron enter the chassis containing the phase s e n s i t i v e detector and then enter the klystron box which contains the shielded k l y s t r o n . The klystron power supply c i r c u i t i s shown i n f i g . 16 and the c i r c u i t of the power supply f o r the amplifier, o s c i l l a t o r and buffer sections i s shown i n f i g . 17*  CHAPTER IV,  THE PERFORMANCE OF THE FREQUENCY STABILIZATION SYSTEM  In this chapter the performance  of the c i r c u i t s descri-  bed i n chapter I I I i s discussed, a few simple calculations are made to i l l u s t r a t e i t s operation.  Experimental performance i s  also given. 4.1  Some Calculations One may consider the frequency s t a b i l i z i n g c i r c u i t to  be b a s i c a l l y as shown i n f i g . 18. back loop.  k'y  I t i s shown just as a feed-  Due to l i m i t a t i o n s of the apparatus, the frequency  gtroty  T  St*bV  0  P*rcK*nny.Het\c  It'll*}  Loop Figure 18 v  of the klystron w i l l not equal the resonant frequency V„  of the cavity.  29  I f we define 0- - the gain of the feedback loop and the cavity ( v o l t s / frequency) ^ ( v s a n o r i g i n a l frequency deviation of v from v»  before  stabilization tfly's the frequency deviation of v  from y  0  after s t a b i l i z a t i o n  T s s e n s i t i v i t y of klystron r e f l e c t o r (frequency/volts) then CrJLv' i s the r e s i d u a l correction voltage. residual frequency deviation i s the unstabilized  The resultant c^v  minus  the change towards >& caused by the applied error voltage l e .  d '= v  S  <lv'  ^-TCr  = TVfi - y  or  being the s t a b i l i z a t i o n factor.  (1)  We can now see that the  loop i s e s s e n t i a l l y one of negative feedback. To i l l u s t r a t e the performance of this loop, one can calculate the tendency to correct an i n i t i a l frequency deviation  J-v of V .  If V  i s the amplitude of the 10.7 mega-  cycles per second applied to the r e f l e c t o r of the klystron, then the frequency modulation of the microwaves w i l l have an amplitude of  ^  -  ;  a  V  being the t o t a l frequency sweep.  It i s now assumed that the resonance curve of the cavity has a guassian shape. for  This assumption i s reasonable  these calculations since only approximations are attempted.  Actually the shape of the c a v i t y resonance curve i s not important as the Q of the c a v i t y i s high and we are not i n t e r ested i n the shape of the t a i l of the curve.  30 On the gaussian assumption, i t can be shown that the cavity resonance curve w i l l have a shape defined by the following. 0<Tv) = 00*)  -^£ -v«>*v  c  .  . ^(xJ^2^t c  (2)  i s defined as the square root of the power l e v e l of the microwave at the c r y s t a l detector.  This d e f i n i t i o n takes  account of the cavity resonance and any attenuation between the c a v i t y and crystal^detector.  present  • • . B&> ) 0  then i s the  square.root of the power l e v e l of the microwaves at the c r y s t a l detector when at the peak of the c a v i t y resonance curve. When the kylstron frequency i s modulated  where oiv =. "v-">^ , the error which i s to be corrected.  The  output from the cavity i n terms of the square root of power i s t  I f f~Cv) i s written i n a f o u r i e r series and the c o e f f i c i e n t of the sin**/* term i s calculated, the amplitude of the 10.7 megacycle component leaving the cavity i s obtained. amplitude i s given by  ~TT  As shown i n Appendix B, f o r  ^. •  x.  .  s i m p l i f i c a t i o n that  .  -jr and ei** c-  atlon can be made to  This  .  —  an approxim-  c^v  which i s almost i d e n t i c a l to the  31 It i s experimentally known that the c r y s t a l detector detects this s i g n a l according to a square law.  Thus, a f t e r amplifica-  tion of the detected s i g n a l , we obtain a voltage of £ z  CA  K  x  A-  - -  -  -  -  -  _  ^  _  - - (4)  the amplification of the I.F. amplifier  ^ - the proportionality constant f o r the c r y s t a l detector. This i s the voltage entering the phase s e n s i t i v e detector which i s out of phase by an amount $ with the reference voltage E . (  Appendix A shows that the D.C. output of the phase s e n s i t i v e detector i s given by "-p.c.  £  - - ( 5 )  A^£  where ^  - the conversion transconductance  The D.C. correction voltage i s given by W+ .RL  (6)  AC  where tf a u  the load resistance of the phase s e n s i t i v e detector.  Thus the tendency to correct  $v =  WT  -  Combining equations  ?I  S>  £; fLT  +P.c.R*-7  is  "  -  "  -  ~  -  (7)  2,3,4,5,6,7> we find that  B \ V ^ S * ' ^  L  ^  H  ^  i s a measure of the force p u l l i n g the klystron frequency  towards the cavity resonant frequency.  This force tends to  increase or decrease the frequency depending whether <£*a. $ i s positive or negative. Equation 8 shows that i f the error zero, then the tendency for correction i s zero.  i s large or Actually, i n  accordance with equation 1, the s t a b i l i z i n g system reduces djy to  ctv  /  i n absolute values.  When the error i s  c£v'  ,  the tendency towards correction i s balanced by the " s t i f f n e s s " or the reaction of the loop against correction. It may  be noted that these c a l c u l a t i o n have assumed  that the c i r c u i t regulates immediately, constant of the loop i s zero.  i . e . that the time  In practice, a time constant  i s used which w i l l modify the expressions obtained.  The  time  constant a c t u a l l y prevents hunting and has a smoothing action to the corrections. 4.2  Experimental Performance The s t a b i l i z a t i o n loop managed to lock the klystron  frequency to the cavity resonance frequency to a f a i r l y good degree.  Two l i m i t i n g factors were found i n the s t a b i l i z i n g  system.  Blocking can occur i n the high gain amplifier, i f the  c r y s t a l i s run a t a high l e v e l or i f s u f f i c i e n t attenuation i s n ' t present i n the  /^-wave c i r c u i t .  Pickup can occur i n the  high gain a m p l i f i e r .  This pickup originates, i n spite of  complete shielding, from the reference voltage phase s h i f t e r contained i n the same chassis as the amplifier.  Hence, the  magnitude of the reference voltage and the gain of the amplif i e r cannot both be a maximum value simultaneously. Direct frequency measurements could not be made, however the order of magnitude of the quantities calculated i n section (4.1) can be estimated i f a reasonable Q value of 1 0 * Is assumed f o r the ^-wave cavity.  Further the klystron  o s c i l l a t e s at about 25 kilo-megacycles. The long term frequency s t a b i l i t y over a period of a few hours (a test was made over four hours) i s s u f f i c i e n t to cause the amplitude of the microwaves leaving the cavity to be reasonably constant, the changes present can be ascribed to the mode of o s c i l l a t i o n i n the klystron.  This action implies  that the s t a b i l i z a t i o n factor of the regulating loop i s of the order of 20 or higher i-c.  -L  .  For a resonance  curve at 25 kilo-megacycles, and a Q of 10 ,  <L v  2 megacycles and s t i l l be on the resonance curve.  can be up to I f <A v'  is  100 k i l o c y c l e s or less then the amplitude of the microwaves leaving the cavity w i l l be f a i r l y close to the maximum value* The measured. K siSWitfl  various parameters i n equation 8 of (4.1) were They were found as follows. The c r y s t a l constant  This value was measured with a 30 megacycle wave  modulated at 1000 cycles.  The easy assumption i s made that K  has the same value at microwave frequencies. r e f l e c t o r s e n s i t i v i t y T i s 100 k i l o c y c l e / v o l t .  The klystron B(v.)  is  taken as 5xlO~3 since about 25 microwatts of power are at the  34  crystal detector,  ^, , E  i s  °o*it 2500 mlcromfaies,  Zoki\  is  a  the amplitude o f the k l y s t r o n modulation s i g n a l i s z J ?  A  }  while  the r e f e r e n c e v o l t a g e i s seven v o l t s . E q u a t i o n 8 then becomes, '»fc»i W  coit-tf  ( - >^' c  0  s  J7^\)  i s 500 k i l o c y c l e s , t h e c o r r e c t i o n tendency i s  Thus i f  k i l o c y c l e s or i f cL-y i s one megacycle,  the c o r r e c t i o n  tendency  is;*? 4*^4cycles. A good t e s t o f the c o n t r o l o f the s t a b i l i z i n g l o o p i s i t s a c t i o n when the r e f l e c t o r v o l t a g e c o n t r o l i s changed manually.  I t i s found t h a t the s t a b i l i z i n g l o o p manages t o  l o c k the r e f l e c t o r v o l t a g e , and the frequency o f the k l y s t r o n , so that the manual c o n t r o l makes no d i f f e r e n c e over  a large  range. In c o n c l u s i o n , the frequency o f the k l y s t r o n has been s t a b i l i z e d t o a t l e a s t one p a r t i n 2.5.10' t o the resonant frequency o f the c a v i t y used f o r paramagnetic  resonance.  frequency s t a b i l i t y , i f p r e s e n t w i t h magnetic  field  This  stability,  makes i t p o s s i b l e t o use the spectrometer as a narrow band instrument, thereby i n c r e a s i n g the s e n s i t i v i t y by a f a c t o r o f about  100;  35 APPENDIX A  If two signals at the same frequency are fed into a phase sensitive detector,  then there i s a D.C, component i n  the output. Let the two signals be ^  ust and F^+^feJ+S). In  a phase s e n s i t i v e detector there exists some type of nonl i n e a r i t y present.  Let i t be assumed that the type of non-  l i n e a r i t y present i s as followst f*-* where  Tj ,(k,*^«*) '-  • •* ? i  X  J  (1)  cy i s the t o t a l transconductance of the detector shown to  I t i s known that the output current i s  **+i(yt f  * ' \f £  _  _  -  () 2  upon substitution of (1) into (2)  +  -f  E," B^ ^L^."uv^t  +•  — —  ^)  It can be shown that  upon substitution of (4) Into  * where  r  t\ =  (3)  —JAH  J  SL  » ) are c o e f f i c i e n t s of the A.C, components.  It can be seen that there exists a D.C. component varing  as the cosine of the phase difference  6  between the  36 two s i g n a l s , given by the f i r s t term of (5)*  It i s considered  that only the f i r s t order term i s important i n this component.  The D.C,  ± C4,  current i s then given by equation  ?' ' x^S B  D.C,  £  i s known as the conversion  -  -  transconductance.  -  (6),  (6)  37 APPENDIX B  Consider the i n t e g r a l f o r a and b ^ 1.  It  o  where  As a and b  / the exponential factor can be written as a ?  series as the following  ^i?****?_ a? x ^ c ^  -r^cUr hence  ^/  ^-t°c&  + 7/  '  7  ^ ^  —  ' — ' —  ( ) 2  ^  (3) where C  p  i s given by (2)  Further as  fr-/)d*-3)-  • • /  since a and b 4. / the f i r s t few terms w i l l give a good approximation.  Consider the terms up to p=8. +  L  %  ***  I*  I f one considers the terms up to the t h i r d power, then  x - *(»•)  -£  - - () 3  Now consider the expression  -  (4)  I f e"^ sinh (a) i s written i n a s e r i e s , and only terms up to the t h i r d power are considered, the following Is obtained.  FjL»>^  e  '  C  ^ [-/  It can be noted that F approximation  as given by (5)  to I as given by (3).  the following approximation R  f  v  \  -  t +(v  (5)  (  i s a reasonable  I t can then be said that  i s v a l i d f o r c\  - c ^ * ^ . >C-  -O-'*^-  K  /> «c j  HAMMOND 1 6 7 E  FIGURE 1 ?  IIOVAC  TYPICAL  LOW R I P P L E , H I G H 2 5 0 - 3 7 5 VOLTS  REGULATION DC  POWER  SUPPLY  25-200 M A  o  REFERENCES  1.  B. Bleaney and K.W.H. Stevens, Rep. Prog. Phys.  16, 108 (1953) 2.  H.A. Buckmaster Ph.D. Thesis, University of B r i t i s h Columbia (1955)  3.  R.V.Pound, Rev. S c i . Inst. ! £ , 490 (1946)  4.  R.V.Pound, Rev. S c i . Inst. 18, 132 (1947)  5.  R.V.Pound, Proc. I.R.E. ^ , 1405 (1947)  6.  W.G. T e l l e r , U.C. Galloway, Z.P. Zaffarano, Proc, I.R.E. 36, 794 (1948)  7.  V.C. Rideout, Proc. I.R.E.  767 (1947)  8.  W.D. Hershberger, L.E.Norton, R.C.A. Review 2, 38 (1948)  9.  W.V. Smith, J.L.G. de Quevedo, R.L. Carter, W.S.Bennett Journ. Appl. Phys. 18, 1112 (1947)  10.  H.R.L. Lamount, Physics 1 £ , 446 ( 1 9 5 D  11.  H.R.L. Lamount, E.M. Hicfcing, B r i t . Journ. of Appl. Phys.  2, 182 (1952) 12.  E.F. Grant, Proc. I.R.E. . 2 2 , 943 (1949)  13.  W.F. Gabriel, Proc. I.R.E. 40, 940 (1952)  14.  F.A. Jenks, Electronics 20, 120 Nov. (1947)  15.  The Radio Amateur's Handbook, 129 (1953) P. 130-131  16.  Langford and Smith Radiotron Designers Handbook, Radio  17. 18.  Corporation of America 316, P. 316-327. H.C. Torrey and C.A. Whitmer, Crystal R e c t i f i e r s , Radiation Laboratory Series, V o l . 15> P. 223 (McGraw-Hill) Elmore and Sands, E l e c t r o n i c s , P. 38 (McGraw-Hill)  

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