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Design of a stable 150 kw 23 mhz amplifier for the triumf crm. Brackhaus, Karl Heinz 1972

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DESIGN OF.A STABLE 150 KW 23. MHZ.AMPLIFIER FOR THE TRIUMF CRM by KARL HEINZ BRACKHAUS B.A.Sc, University of British Columbia, 1970 ( A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in the Department of Engineering Physics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Apr i l , 1972 In present ing th i s thesis in pa r t i a l f u l f i lmen t of the requirements for an advanced degree at the Un ivers i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying o f th i s thes i s fo r s cho la r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i c a t i on o f th i s thes is for f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of The Un ivers i t y of B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT This thesis discusses the design of a stable 150 KW 23MHz RF system for the TRIUMF CRM cyclotron. The required characteristics of this system are presented with emphasis on the amplitude and phase modulation constraints. The composition of an amplifier system satisfying the power, bandwidth and noise requirements i s discussed. Both the i n i t i a l and present PA designs are presented, as i s the design of the driver amplifier. Also included i s a discussion of the choice of tubes and RF ci r c u i t s . The usefulness of feedback control in satisfying the RF s t a b i l i t y requirements is shown. The conditions a stable feedback system must satisfy are also given. Two amplitude control systems (drive control and screen control) are designed using Bode techniques. A d i g i t a l simulation of these systems using an el e c t r i c a l analogue i s presented. Implementation and results are discussed. i i i TABLE OF CONTENTS Page 1. SYSTEM DESCRIPTION ' 1 1.1 General Requirements 1 •  1.2 RF Modulation Constraints 1 1.2.1 RF Amplitude Modulation Constraints 2 1.2.2 RF Phase Modulation ? 1.3 RF System Description 7 2. RF AMPLIFIER DESIGN 16 2.1 General Design Considerations 16 2.1.1 Achieving the Required Voltage and Power 16» 2.1.2 Bandwidth Requirements 17 2.1.3 Achieving Waveform Purity r 20 2.2 Main Power Amplifier 31 2.2.1 Original Design 31 2.2.2 Present Design 34 2.3 Driver Amplifier Design 37 2.3.1 Specifications 37 2.3.2 Tube Selection 1 . , 38 2.3.3 Driver RF Circuits 48 3. AMPLITUDE CONTROL SYSTEM DESIGN 55 3.1 System Element Transfer Functions 55 3.2 Drive Control System 63 3.3 Screen Modulating System 77 4. CONCLUSIONS 88 5. FOOTNOTES 89 6. A SELECTED BIBLIOGRAPY 90 LIST OF TABLES Page I Average Power and Voltage Gain per Amplifier Stage 17 II Design Data for Maximally Flat Staggered Quadruple 19 III Chart for Noise Bandwidth Calculations 28 IV Typical Operating Conditions of the ML-7560 , 33 V El e c t r i c a l Characteristics of the Eimac 4CW250,000 36 VI Typical Operating Conditions of the 4CW250,000 Tetrode in the CRM Amplifier 37 VII Specifications for 3 Stage Driver Amplifier 38 VIII Maximum Output Power of the Tubes considered for the Output ; Stage of the Driver Amplifier 39 IX Minimum Power Input to DA-PA Coupling Circuit for a given value of Q 40 X Operating- Conditions for the Eimac 4-1000A near maximum Output 44 XI El e c t r i c a l Characteristics of the Eimac 4-1000A 45 XII E l e c t r i c a l Characteristics of the RCA 6146A Beam Power Pentode 46 XIII Typical Operating Conditions of the RCA 6146A 46 XIV E l e c t r i c a l Characteristics of the 6CL6 Power Pentode 48 XV Routh Table for the Approximate Characteristic Equation 65 V LIST OF FIGURES Page 1. RF Accelerating Voltage; RF out of Phase with Beam 2 2. Relationship between m/f and Modulating Frequency 4 3. Plot of m Maximum allowable Mod. Amp./RF Amp} against Modulating Frequency (fm) 6 4. Plot of m (= Maximum allowable Pulse Height/RF Amp.) against Pulse Length, tp 8 5. Plot of Maximum Permissible Amplitude of Sinusoidal Phase Modulation vs Modulating Frequency (No Amp. Mod. Present) 9 6. Block Diagram of the TRIUMF CRM RF System 10 7. Effect of Lumped Capacitance on the Voltage Standing Wave of a Transmission Line 12 8. TRIUMF CRM Transmission Line (for the Fundamental) 13 9. Coaxial Structure of Cyclotron Dees 15 10. Plot of Asymptotic Efficiency (Ea) against Total Conduction Angle (Theta) 16 11. Minimum Bandwidth Requirement for Driver Amplifier 18 12. Power Supplies for the PA (4CW250,000) 23 13. Change in Plate Swing (Ep) for a Change in Plate Voltage (Ebb) 24 14. Amplifier considered for Thermal Noise Calculation 27 15. Harmonic Content vs Conduction Angle 30 16. Pi Network Output Circuit 31 17. Schematic of Triode (ML-7560) Power Amplifier 32 18. Schematic of Main CRM Power Amplifier 35 19. Single-ended Grid Neutralization Drawn as a Bridge Circuit 34 20. Power Input to Tank and Pi Circuits 39 21. Operating Line of the 4-1000A 42 22. Schematic of CRM Driver Amplifier 49 23. Equivalent Circuit of Transmission Line-Resonator System 56 24. Plot of the Output RF Amplitude for Varying Screen Voltages (4CW250,000 Power Tube) 60 25. RF By-pass Circuit at the Screen of the 4CW250,000 . 61 26. Frequency Response of the RF By-pass Circuit at the Screen of the 4CW250,000 " 62 27. Block Diagram of Uncompensated Drive Control System 63 v i Page 28. Open Loop Frequency Response of the Uncompensated Drive Control System 64 29. Block Diagram of Drive Control System with Step Error i n the Output 66 30. System of Figure 29 Redrawn with Step Error as only Input 66 31. Frequency Response of the Lag-Lead Compensator 68 32. Open Loop Response of the Compensated Drive Control System 69 33. Circuit used for the ECAP Simulation of the Drive Control System 71 34. Frequency Response of Drive Control System with Error Input at the Plate of the PA 73 35. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used; FB Amp. has 24.1 db of Gain) 74 36. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used; FB Amp. has 32.1 db of Gain) 75 37. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used; FB Amp. has 240 db of Gain) 76 38. Block Diagram of Proposed Screen Modulating System 77 39. Block Diagram of Screen Modulating Circuit 78 40. Screen Modulator 78 41. Regulation of the Screen Supply 79 42. Equivalent Block Diagram of Figure 41 79 43. Open Loop Frequency Response of the Screen Modulating Feedback System with Lag-Lead Compensation (Screen Modulator is Uncompen-sated) 81 44. Open Loop Frequency Response of the Screen Modulating Feedback System with Lag-Lead Compensation (Screen Modulator is Compensated) 82 45. Simulation of Screen Modulator Function Block 83 46. Closed Loop Frequency Response of the Screen Modulating System (Error Input at the Plate of the PA) 84 47. Plot of Change in Resonator Voltage Amplitude for a Unit Step Change in RF Amplitude at the PA Plate (Screen Modulation Control used; Screen Modulator Uncompensated) 86 48. Plot of Change in Resonator Voltage Amplitude for a Unit Step Change in RF Amplitude at the PA Plate (Screen Modulation Control used; Screen Modulator Compensated) 87 V l l LIST OF PLATES Page I Top View of Driver Amplifier (Cover Removed) showing the 4-1000A and i t s Output Circuit; the Input to the Transmission Line i s on the Right-hand Side 52 II Front View of Driver Amplifier (Cover Removed) showing the 6CL6 and i t s Associated Circuitry 53 III Bottom View of Driver Amplifier (Cover Removed) showing the Filament Chokes and RF Transformer Coil; Filament Transformer on the Right 54 ACKNOWLEDGMENT I am much indebted to Dr. K. L. Erdman for his guidance in my studies and in the preparation of this thesis. Thanks are also due Mr. R. Poirier and Mr. C. Hartin for their helpful suggestions in the design of the driver amplifier and to Mr. H. Simmonds for doing most of the fabrication. The discussions with Mr. R. H. M. Gummer concerning the design of the feedback control systems were especially helpful; he must also be given credit for the excellence with which he constructed the required devices. • . < r Special thanks are also due my wife, Bonnie, for typing this thesis. 1 CHAPTER 1. SYSTEM DESCRIPTION 1.1 General Requirements This t h e s i s w i l l d e s cribe the design of the RF system b u i l t f o r the TRIUMF CRM c y c l o t r o n . An e x c e p t i o n a l f e a t u r e of t h i s system i s the extreme s t a b i l i t y r e q u i r e d of the RF waveform i f the energy r e s o l u t i o n d e s i r e d of the c y c l o t r o n (4H£_ ^ 2x|0=£) i s to be achieved. The KE steady s t a t e RF requirements f o r the TRIUMF c y c l o t r o n have been c a l -c u l a t e d ; ^ those a p p l y i n g to the CRM RF system may be b r i e f l y l i s t e d as f o l l o w s : (a) a frequency of 23 KHz, (b) a power output of 150 KW, (c) a peak c a v i t y v o l t a g e of 100 KV, (d) a frequency s t a b i l i t y of & 1.25 p a r t s i n 10^ f o r maximum duty, f a c t o r andt7.5 p a r t s i n 10^ f o r s i n g l e t u r n e x t r a c t i o n , and (e) a v o l t a g e amplitude s t a b i l i t y o f ± 2 p a r t s i n 10^ f o r maximum duty f a c t o r and* 2.5 p a r t s i n 10-> f o r s i n g l e turn e x t r a c t i o n . In a d d i t i o n , the d e l i c a t e nature of the e l e c t r o n i c i n s t r u m e n t a t i o n at TRIUMF demands that the l e v e l of RF r a d i a t e d be extremely low. I t has been found^ that spurious r a d i a t i o n at the TRIUMF s i t e must be kept below a l e v e l of .5^*V/m, a l e v e l 20 times lower than that s t i p u l a t e d by the Department of Transport. 1.2 RF Modulation C o n s t r a i n t s The s t a b i l i t y requirements l i s t e d i n the above s e c t i o n gave the maximum p e r m i s s i b l e s t a t i c d e v i a t i o n of a waveform parameter from i t s d e s i r e d v a l u e . However, disturbances to the system are not s t a t i c i n nature, so an estimate must be made of the p e r m i s s i b l e amplitude of time v a r y i n g d e v i a t i o n s i n frequency, phase and amplitude. Since the frequency s y n t h e s i z e r has a short term frequency s t a b i l i t y of l e s s than 5 p a r t s i n 10^, only amplitude and phase v a r i a t i o n s were considered when examining the CRM requirements. That i s , i f R then f o r (a) maximum duty f a c t o r : R allowed ^25 R s y n t h e s i z e r (b) s i n g l e turn e x t r a c t i o n : R allowed i*1.5 R s y n t h e s i z e r 2 i f there i s no .amplitude or phase modulation present. Figure 1 shows how both the amplitude of the resonator RF (V) and i t s phase (0 m ) w i t h respect to the i n s t a n t at which a beam pulse crosses the a c c e l e r a t i n g gap w i l l a f f e c t the a c c e l e r a t i n g v o l t a g e (VA). Note that the e f f e c t of phase e r r o r s introduced i n t o the RF system i s twofold: (a) the a c t u a l change i n phase w i l l i n troduce a phase e r r o r (b) the r a t e of change of phase w i l l i n t r o d u c e a frequency d e v i a -t i o n which w i l l , due to the resonant nature of the system, lower the resonator v o l t a g e . I d e a l l y , the resonator v o l t a g e should be maintained constant at the d e s i r e d l e v e l (Vo=IOOKV ) w i t h the beam pulses always c r o s s i n g the a c c e l e r a t i n g gap at the peak of the RF waveform (9«\=0). F i g . 1. RF A c c e l e r a t i n g Voltage; RF out of Phase with Beam 1.2.1 RF Amplitude Modulation C o n s t r a i n t s (No Frequency or Phase Modulation Present) A. S i n u s o i d a l Modulation Assume that the gap voltage i s modulated s i n u s o i d a l l y , w i t h the voltage remaining constant as the p a r t i c l e passes through the gap. That i s , let the energy gained per pass through the acceleration gap be (q x vress) where q = particle charge and V r e s s = gap voltage Hence, when amplitude modulation is present, the total energy gained by a particle w i l l be N N KET= l 2qVo ( l+m cos(w^ n&t •* 0)) = H q V r 9 S (1.1) n=o n=0 Vo = magnitude of fundamental RF m = ratio of modulating freq. amplitude to fundamental amplitude 1 x<7m = freq. of modulating signal rad. sec. At = time between impulses = l/2time for 1 rev. =* 1 x IO-'7 sec. j$ = phase of modulating signal at instant of particle injection N = twice the total no. of rev. one particle makes The factor (2) is present because the resonators are to work in the push-pull mode. The value of KEj may be approximated by substituting an integral for the sum of the sequence. Thus, i f At i s sufficiently small, one may write: KET= 2 N q V o 4 \ cos (w*t+ 0) dt = 2 N q V o + w § ^ 0 sin(wmtf+0)-sin0 C1'2) tf = total acceln. time 250fx sec. Assuming that reasonable accuracy requires that the period of the sinusoid be at least 100 times as long as the time (At) between terms of .the sequence for (KE^), then the above approximation is adequate for modulating frequencies below 100 KHz. (That i s , we require fmZ 10~ 2 = 10 5 HZ.) "LX It is not anticipated that higher modulating frequencies w i l l be en-countered. The energy resolution desired now requires that L A K E ^ ~ -^ 5^ |sin(wmt<+0) - sin 0 | < £ (1.3) Fig. 2. Relationship between m/e and Modulating Frequency 5 Hence s u b s t i t u t e : 8 = wmtf S = € m and s o l v e f o r 0 . ^ |sin(©+#) - sin$| < 8 ( 1 ' 4 ) The s o l u t i o n s vary between extremes f o r which 0=0 and $ =TT/Z. . The f i r s t places the more s t r i n g e n t requirements on the amplitude of modu-l a t i o n at low f r e q u e n c i e s . Thus s o l v i n g i ) 1 sin 9|<o9 ($=0) (1.5) I D Icose-i|<Se (0="tf/2) (i."6) f o r values of 0 = 2^ f^tf and S = gives t-he r e l a t i o n s h i p between f m andm ' Figure 2 gives the r e s u l t i n g r e l a t i o n s h i p s between fm and S3, f o r 0 = 0 and 0=1*72. " . * Noting t h a t below about 1 KHz the p e r m i s s i b l e upper bound on —• i s given for$( = 0 , w h i l e that above t h i s frequency i t i s defined by the lowest p o i n t s on the curves f o r 0=^/2, one may c o n s e r v a t i v e l y d e f i n e the o v e r a l l bounds on i E as: f I f m4l . 3 K H z UL - <{ ^ (1.7) € 1(7.8* I0)f m fw>l.3KHz A p l o t of m = amp, modulating s i g n a l i n d e c i b e l s against modulating amp. fundamental frequency i s given i n Figure 3. B. Rectangular Pulse Amplitude Modulation An estimate was made of the r e s t r i c t i o n s on the amplitude and d u r a t i o n of a s i n g l e r e c t a n g u l a r amplitude pulse superimposed on the steady s t a t e resonator RF amplitude. Assuming the worst c a s e — t h a t i s , t h a t the s t a r t of the pulse c o i n c i d e s w i t h entry i n t o the c y c l o t r o n of a p a r t i c l e to be a c c e l e r a t e d — t h e n the t o t a l energy gained by that p a r t i c l e w i l l be KE X = 2qVo (N t mn) Vo = steady s t a t e amplitude of the a c c e l e r a t i n g RF v o l t a g e N = t o t a l number of a c c e l e r a t i n g impulses per p a r t i c l e = 2500 n = number of a c c e l e r a t i n g impulses f o r which the amplitude pulse p e r s i s t s Fig. 3. Plot of m = Max. allowable Mod. Amp./RF Amp. against Modulating Frequency (fm) / m = Vp_ where Vp = pulse height Vo £ = energy r e s o l u t i o n r e q u i r e d = 2 x 10 tp = pulse length Then the r e s t r i c t i o n on the energy gained by the p a r t i c l e i s | A K E I K E mn N < € (1.8) L e t t i n g n = _tp_ gives the r e s t r i c t i o n t m t p < £ N A t - 5*10 (1.9) Figure 4 shows t h i s r e s t r a i n t . 1.2.2 RF Phase Modulation C o n s t r a i n t s (No Amplitude or Frequency Modulation Present) C a l c u l a t i o n s s i m i l a r to those of part A of 1.2.1 have been done f o r s i n u s o i d a l phase modulation. That i s , i t was assumed that the phase The r e s u l t a n t r e s t r i c t i o n s on the magnitude of AQ are shown i n Figure 5, where i t i s apparent that f o r low frequencies (fm £ 10^ Hz) the r e s t r i c t i o n s on the amplitude of RF phase v a r i a t i o n s become i n c r e a s i n g l y r e l a x e d . This i s because each new beam pul s e i s i n j e c t e d i n t o the c y c l o t r o n w i t h zero i n i t i a l "phase e r r o r by means of a c o n t r o l system that monitors the resonator RF and feeds p a r t i c l e bunches i n t o the beam l i n e at the proper times. 1.3 RF System D e s c r i p t i o n The RF system b u i l t to s a t i s f y the CRM requirements i s shown i n Figure 6. I t i s apparent that the system may be d i v i d e d i n t o two f u n c t i o n a l l y d i f f e r e n t — t h o u g h not independent-—subsystems: a system to generate the. r e q u i r e d RF, and a system to r e g u l a t e i t s amplitude and phase. The f o l l o w i n g i s a b r i e f d e s c r i p t i o n of the main RF f u n c t i o n b l o c k s . e r r o r (0m) was a f u n c t i o n 9 m - A© sin2TTf<at (1.10) — FREQ/HZ — >^ Reference Phase Synthe-sizer Phase S h i f t e r Phase C o n t r o l F-B A m p l i f i e r Phase Detector Amp. Modulator D r i v e r A m p l i f i e r (4 -1000A) Main Power A m p l i f i e r (4CW250,000) Transmission Line-Resonator System Screen Modulator ] Amplitude Detector ] Amplitude Con-t r o l F-B Amp. F i g . 6. Block Diagram of the TRIUMF CRM RF System 11 RF Syn t h e s i z e r (Rohde and Schwarz type ND 30 M) This device i s the primary s i g n a l source of the RF system. The manufacturer claims a frequency v a r i a t i o n { 5 x 10-9/l°C. f o r ambient temperatures ranging from +10°C. to +30°C. and a long term d r i f t due to aging of l e s s than 5 x 10 -^/month. I t s maximum output v o l t a g e i s .5 Vrms i n t o a 50-A-load. Hence, to s a t i s f y the CRM v o l t a g e and power requirements, the RF a m p l i f i e r chain must provide v o l t a g e and power gains of at l e a s t 1.4 x 10^ and 3 x 10? r e s p e c t i v e l y . RF D r i v e r The RF d r i v e r takes the output from the s y n t h e s i z e r (or the amplitude modulator when the d r i v e c o n t r o l system i s i n operation) and boosts t h i s input s i g n a l to the l e v e l r e q u i r e d to d r i v e the main power a m p l i f i e r . The power r e q u i r e d (400 watts) i s con s i d e r a b l y l e s s than the 2500 watts t h i s stage i s capable of. F i g u r e l l . i n d i c a t e s i n d e t a i l the makeup of t h i s device. Main RF Power A m p l i f i e r 3 This stage, designed and b u i l t by C o n t i n e n t a l E l e c t r o n i c s , provides the 150 KW of RF power r e q u i r e d by the CRM c y c l o t r o n . The s i n g l e t e t r o d e tube (EIMAC 4CW250000) employed r e q u i r e s a d r i v e power of only 150 wa t t s ^ f o r an output of 162 KW. This i s a power gain of » 10-^, and i t i s obtained w i t h an e f f i c i e n c y of about 75 per cent. For c i r c u i t d e t a i l s see Figure 18. RF Transmission L i n e A resonant c o a x i a l t r a n s m i s s i o n l i n e (Figure 8) i s employed at TRIUMF to t r a n s f e r the output of the f i n a l power a m p l i f i e r to the CRM resonators. A resonant l i n e (VSWR ~ 30) was chosen p r i m a r i l y because i t reduces the s e n s i t i v i t y of the tube's load to changes i n the resonator c h a r a c t e r i s t i c s . As i n d i c a t e d i n Figure 8, t h i s l i n e has 3 tuning c a p a c i t o r s which (1) reduce the p h y s i c a l length of the l i n e ( f o r a s p e c i f i e d e l e c t r i c a l length) and (2) f a c i l i t a t e the matching of the power tube to the resonator load. The f i r s t e f f e c t i s i l l u s t r a t e d i n Figure 7, where A and B i l l u s t r a t e the v o l t a g e standing wave before and a f t e r the i n t r o d u c t i o n of a c a p a c i t o r (C2) i n a par t of the l i n e where the impedance i s i n d u c t i v e . The value of C2 i s chosen so that the e l e c t r i c a l l e n g t h 12 CAPACITIVE INDUCTIVE ADD CAPACITOR SUCH THAT c | | z b - ^ z c ^ ELECTRICAL L E N G T H = lj/g X (B) <m ELECTRICAL LENGTH = 1 ^ X & F i g . 7. E f f e c t of Lumped Capacitance on the Voltage Standing Wave of a Transmission L i n e RESONATORS COUPLING LOOP C ! C2 OOO »"^-T0 COUPLING LOOP ////// / / / / SCALE 1:20 14 of the l i n e i s increased by an amount that r e s u l t s i n an i n d u c t i v e input impedance (Zin) w i t h a p a r a l l e l r e s i s t i v e component equal to the load impedance r e q u i r e d by the tube. The c a p a c i t o r C3 i s then chosen so t h a t , i n p a r a l l e l w i t h the output capacitance of the tube, i t w i l l c ancel the i n d u c t i v e component of Z i n , thereby presenting the tube w i t h i t s r e q u i r e d load impedance. Capacitor C l , by modifying the impedance t e r m i n a t i n g the t r a n s m i s s i o n l i n e , permits g r e a t e r freedom i n the choice of C2 and C3. Coupling to the tube i s achieved through a s e r i e s (D.C. b l o c k i n g ) c a p a c i t o r (C4); c o u p l i n g to the resonators i s achieved by means of a loop. During normal o p e r a t i o n , the power l o s s between these 2 p o i n t s i s about 2000 watts; s i n c e t h i s power i s d i s s i p a t e d p r i m a r i l y at the current nodes, an excessive temperature r i s e at these p o i n t s i s avoided by blowing c o o l i n g a i r through the region between the conductors. Resonators The a c c e l e r a t i n g s t r u c t u r e (RF load) used at TRIUMF i s unusual because i t has dees which are i n the form of */4 resonant c a v i t i e s (see Figure 9). To use e x c i t a t i o n at the i o n r o t a t i o n frequency would have re q u i r e d these s t r u c t u r e s to be p r o h i b a t i v e l y l a r g e ; i n s t e a d , the frequency chosen (23 MHz) i s the 5th harmonic of the r o t a t i o n frequency, thus reducing the s i z e by a f a c t o r of 5. The Q of these resonators i s about 6000; hence to get the r e q u i r e d 200 KV-* dee-to-dee, approximately 150 KW of RF power i s needed. F i o . 9. Coaxial Structure of Cyclotron Dees lb •CHAPTER 2. RF AMPLIFIER DESIGN 2.1 General Design Considerations 2.1.1 A c h i e v i n g the Required Voltage and Power The techniques r e q u i r e d to achieve the power and voltage gains needed by the CRM RF system are w e l l known—a b r i e f summary of the important ideas w i l l be given here. Since one i s working at a high frequency (f = 23 MHz), tuned a m p l i f i e r s must, of course, be used. A l s o , s i n c e a high output power i s d e s i r e d , i t i s imperative that the input DC power be e f f i c i e n t l y converted to usable RF output power. This i s important because i t leads to: (a) lower costs f o r power (b) r e l a x e d c o o l i n g requirements and (c) lower p l a t e d i s s i p a t i o n requirements. As shown i n Figure 10, hig h e f f i c i e n c y i s obtained by operating the tube such that the t o t a l p l a t e conduction angle i s l e s s than about 180° (Class C). 100 k 90 -= 80 70 60 50 L-0° 90° J 180° 270° — ^ 360° Theta F i g . 10- P l o t of Asymptotic E f f i c i e n c y (Ea) against T o t a l Conduction Angle (Theta) 1/ Table I i n d i c a t e s that to o b t a i n the r e q u i r e d output power there must be at l e a s t 3 or 4 stages i n the CRM RF a m p l i f i e r chain. The a c t u a l number chosen depends l a r g e l y on the c a p a b i l i t i e s of the f i n a l power tube used. That i s , once an output tube has been chosen, the output power requirements d i c t a t e the d r i v i n g power requirements; these i n turn determine the choice of d r i v i n g tube. This process i s repeated u n t i l the d r i v i n g requirements are met by the s i g n a l source. n Gp Gv 1 7.5 x 10 6 7 x 10 4 2 2.74 x 10 3 2.65 x 1 0 2 3 1.9 x 1 0 2 41.2 4 52.3 16.3 5 23.7 9.3 T o t a l v o l t a g e g a i n r e q u i r e d = 7 x 10^ T o t a l power gain r e q u i r e d = 7.5 x 10° n = number of stages Gp = average power gain/stage Gv = average v o l t a g e gain/stage Table I . Average Power and Voltage Gain per A m p l i f i e r Stage 2.1.2 Bandwidth Requirements To act as a guide i n the design of the c o u p l i n g c i r c u i t s , an estimate was made of the bandwidth requirements of the CRM d r i v e r a m p l i f i e r . Since t h i s design work was done at a time when i t was expected that under c e r t a i n 6 ° c o n d i t i o n s 0 the Operating frequency would be increased by 3 percent, i t was considered h i g h l y d e s i r a b l e to design the d r i v e r a m p l i f i e r w i t h a bandwidth s u f f i c i e n t to accommodate t h i s change without r e t u n i n g . Only the d r i v e r a m p l i f i e r was to be broadbanded s i n c e the load on the f i n a l stage (resonators) would be retuned. A d r i v e r w i t h a s u i t a b l e bandwidth may be achieved most simply through the use of synchronously s i n g l e tuned stages, each having a s u f f i c i e n t l y l a r g e bandwidth. As shown i n Figure 11, the mimimum o v e r a l l d r i v e r bandwidth (Bo) may be taken to be 3 percent xa of the normal o p e r a t i n g frequency ( f o ) . F i g . 11. Minimum Bandwidth Requirement f o r D r i v e r A m p l i f i e r This leads to an estimate of the minimum stage bandwidth r e q u i r e d (Bn) by means of the r e l a t i o n s h i p Bn = Bo (2.1) ( 2 l / n _ 1 } l / 2 where Bo = o v e r a l l bandwidth = .03 fo Bn = stage bandwidth n = number of stages. Since 4 tuned c i r c u i t s are used i n the d r i v e r , i t i s ' r e q u i r e d that Bn = 2.29 Bo = 2.29 (.03 f o ) . ' (2.2) Hence the Q per stage must be l e s s than . f_c = 14. (2.3) Bn Note that w i t h synchronous s i n g l e tuned stages the o v e r a l l bandwidth i s always l e s s than the stage bandwidth. I f the above r e s t r a i n t (2.3) on Q i s too severe, one may then stagger tune the a m p l i f i e r . In t h i s case, the o v e r a l l bandwidth i s l a r g e r than the stage bandwidth; however, to obt a i n t h i s d e s i r a b l e r e s u l t more e f f o r t must be expended i n tuning the a m p l i f i e r . For a maximally f l a t response, the c i r c u i t s of the d r i v e r must be tuned^ as shown i n Table I I . No. of C i r c u i t s C i r c u i t Center Freq.. C i r c u i t Bandwidth 2 f c .46 Bo .38 Bo 2 f c .19 Bo .92 Bo Table I I . Design Data f o r Maximally F l a t Staggered Quadruple The r e s t r a i n t s on the stage Q's are now con s i d e r a b l y reduced: i n s t e a d of Equation 2.3, the stage Q's must be Ql-,2 ^ 37 (2.4) and Q 3 > 4 £ 89 where the stages having these Q's are not re q u i r e d to be i n any p a r t i c u l a r order. Maximal f l a t n e s s i s not very important i n t h i s case; hence Bo could be f u r t h e r increased by overstaggering. Some time a f t e r the d r i v e r was b u i l t , i t was decided to drop the requirement f o r a 3 percent frequency s h i f t , thus reducing the bandwidth requirements of the RF a m p l i f i e r s . The bandwidth requirements are now set by the maximum d r i f t i n the n a t u r a l frequency of the resonators during warmup. This i s because the RF system i s f i r s t run i n a s e l f - o s c i l l a t o r y mode when the system i s turned on. Since the n a t u r a l frequency of the " c o l d " resonators w i l l d i f f e r by l e s s than .5 percent from the frequency of the system during normal o p e r a t i o n , the o v e r a l l bandwidth (Bo) of the d r i v e r may be c o n s e r v a t i v e l y set to .01 f o . For a d r i v e r c o n s i s t i n g of 4 synchronous s i n g l e tuned c i r c u i t s , the r e s t r a i n t on the Q per c i r c u i t i s now reduced to Q £ fo = 44. (2.5) 2.29 Bo Since t h i s r e s t r a i n t i s e a s i l y met, the present d r i v e r a m p l i f i e r i s not stagger tuned. 2.1.3 A c h i e v i n g Waveform P u r i t y The a t t i t u d e adopted i n the design of the CRM RF a m p l i f i e r system has been to f i r s t e l i m i n a t e as f a r as p o s s i b l e a l l sources which w i l l i n t roduce n o i se i n t o the RF chain and then to reduce the remaining noise using feedback systems. I t must be noted that the e f f e c t of noise introduced i n t o the RF chain i s cumulative: n o i s e introduced i n t o the a m p l i f i e r ' s i n i t i a l stages i s e s p e c i a l l y troublesome s i n c e i t i s a m p l i f i e d by the subsequent stages. With t h i s e f f e c t i n mind, i t was decided that during normal operation the d r i v e r a m p l i f i e r would be d r i v e n w e l l i n t o s a t u r a t i o n . This reduces s i g n i f i c a n t l y the output due to noise s i g n a l s introduced i n stages previous to the main power tube s i n c e , when s a t u r a t e d , the p l a t e current of the d r i v e r (4-1000A) i s v i r t u a l l y independent of i t s g r i d v o l t a g e . Under these c o n d i t i o n s the amplitude v a r i a t i o n s of the RF ' output are due almost e n t i r e l y to sources of n o i s e i n the main power a m p l i f i e r (4CW250,000). Frequency and phase v a r i a t i o n s w i l l , of course, remain unreduced by t h i s method of o p e r a t i o n . In order of importance, the sources of modulation i n the CRM RF a m p l i f i e r are (a) detuning of resonant c i r c u i t s (b) v i b r a t i o n of tube elements (tube microphonics) (c) power supply r i p p l e and (d) thermal n o i s e . These w i l l be now discussed i n t u r n . A. Detuning of Resonant C i r c u i t s Since the CRM RF chain w i l l be d r i v e n at a f i x e d frequency, a s h i f t i n the resonant frequency of any of the tuned stages w i l l i ntroduce both phase and amplitude e r r o r s i n t o the output. This may be i l l u s t r a t e d most simply by c o n s i d e r i n g a s i n g l e simply tuned stage f o r which the g a i n may by w r i t t e n i n the form A(jw) = Ar • (2.6) 1 + jQ(w/wo - wo/w) 21 where Ar = gain at resonance Q = stage Q wo = resonant frequency w = d r i v i n g frequency. For s m a l l changes i n resonant frequency, a f r a c t i o n a l change i n gain i s obtained A(.jw) Ar 1 (2.7) .1 + 2 ( 8 / B ) / where S = w - wo (change i n resonant frequency) B = stage bandwidth. The a c t u a l change i n gain i s A |A(jw)| = -2Ar ( 6/B) 2. (2.8) Since the change i n gain i s p r o p o r t i o n a l to (&/.B)2 = (&/w) 2Q 2 a high Q c i r c u i t w i l l i n troduce large, d e v i a t i o n s i n amplitude f o r s m a l l d e v i a t i o n s i n resonant frequency. The resonators w i t h t h e i r very h i g h Q w i l l t h e r e f o r e s e r i o u s l y a f f e c t the RF amplitude as t h e i r resonant frequency changes. Hence, i f no other c o r r e c t i v e measures were taken, the f r a c t i o n a l change i n the resonant frequency of the resonators would have to be c o n t r o l l e d so that A w r < 1.2 x l C T 4 ^ (2.9) wr where £ i s the d e s i r e d amplitude s t a b i l i t y . The phase s h i f t due to the detuning of a s i n g l e tuned c i r c u i t may be derived from Equation 2.6 as A & - ~2Q(&wr/wr) radians (2.10) where (Awr/wr) i s a s m a l l f r a c t i o n a l change i n resonant frequency. Since the resonators have a Q of about 6000, they w i l l be the p r i n c i p a l source of phase e r r o r s . Because the magnitude of the RF amplitude and phase e r r o r s due to resonator detuning i s l a r g e , a resonator tuning system i s being i n s t a l l e d . The r a t e of change of amplitude and phase w i l l , however, be s m a l l , s i n c e the e r r o r s are mechanical and thermal i n o r i g i n . This means that the 22 feedback systems employed (resonator tuning, amplitude and phase feedback) to c o r r e c t these e r r o r s w i l l be able to reduce them below the l e v e l s s p e c i f i e d i n Chapter 1. B. Tube Microphonics This form of output d i s t o r t i o n ( c o n s i s t i n g of low frequency amplitude and phase modulation) i s caused by the r e l a t i v e motion of the elements of a vacuum tube. In a l a r g e power tube such as the 4CW250,000, many complex modes of v i b r a t i o n are p o s s i b l e ; i n t h i s tube f i l a m e n t motion i s most important, being the p r i n c i p a l cause of microphonic n o i s e . Since an a c t u a l mechanical v i b r a t i o n i s i n v o l v e d , anything which j a r s or v i b r a t e s the tube w i l l cause t h i s e f f e c t . T y p i c a l cuases are mechanical v i b r a t i o n s from nearby equipment t r a n s m i t t e d to the tube v i a the f l o o r , the v i b r a t i o n of c o o l i n g fans, v i b r a t i o n due to coolant (water) flow, and the v i b r a t i o n of power transformers i n s t a l l e d i n the cabinet. Filament motion may a l s o be caused by the i n t e r a c t i o n of t h e i r own, or w i t h e x t e r n a l , magnetic f i e l d s . T y p i c a l noise values f o r the 4CW250,000 are -70 to -82 db. 8 Since the noise l e v e l s quoted f o r the 4CW250,000 are con s i d e r a b l y higher than the t o t a l a l l o w a b l e noise l e v e l of -94 db, great care must be taken to e l i m i n a t e the sources of microphonics. That i s , the tube must be i s o l a t e d from sources of mechanical v i b r a t i o n and from e x t e r n a l magnetic f i e l d s . This r e q u i r e s that the main DC power transformers must not be mounted i n the same cabinet as the power tube; coolant flow must not be t u r b u l e n t and fans must be v i b r a t i o n f r e e . DC f i l a m e n t s u p p l i e s g i v e f u r t h e r n o i s e r e d u c t i o n s , as would mesh f i l a m e n t s , i f they were a v a i l a b l e f o r the 4CW250,000. C. Power Supply R i p p l e Any v a r i a t i o n i n the l e v e l of p l a t e and b i a s supply vol t a g e s (Figure 12) w i l l cause a change i n the amplitude of the output RF v o l t a g e ; the r i p p l e on the output of these DC s u p p l i e s t h e r e f o r e must be r e s t r i c t e d to very low l e v e l s . This i s not a s e r i o u s problem f o r the d r i v e r stages of the RF a m p l i f i e r chain where the power and voltage requirements are q u i t e low. That i s , the DC s u p p l i e s f o r these stages may be e a s i l y r e g u l a t e d . S a t u r a t i n g the d r i v e r f u r t h e r reduces the problem, l e a v i n g the PA as the p r i n c i p a l source, of r i p p l e - r e l a t e d amplitude modulation. 4CW250,000 JT GRID SUPPLY 8 0 0 V IA PLATE SUPPLY 2 0 K V 12,5 A SCREEN SUPPLY 1_ i FILAMENT SUPPLY F i g . 12. Power Supplies f o r the PA (4CW250,000) From Figure 13 i t i s seen that AEp ~ .75 AEbb (2.11) where AEp = change i n the output RF amplitude AEbb = change i n the DC p l a t e v o l t a g e . Hence, i f an amplitude s t a b i l i t y of -100 db i s demanded, then the r i p p l e on the p l a t e supply must be r e s t r i c t e d to l e s s than -99 db. That i s , f o r (2.12) AEp / Ep 1 = -100 db To* i t i s r e q u i r e d to have A Ebb / I^JL = -99 db Ebb 105 (2.13) i f the p l a t e supply i s the only source of modulation. In the CRM a m p l i f i e r , t h i s c r i t e r i o n i s met by a s e r i e s regulated DC supply .9 ( I f r e g u l a t i o n was not a v a i l a b l e , the r i p p l e on the output RF could be.reduced by i n t r o d u c i n g a s u i t a b l e f i x e d f r a c t i o n of the r i p p l e to the g r i d . ) The 0 2 4 6 8 10 12 14 16 18 20 P L A T E V O L T A G E - K I L O V O L T S Fig. 13. Change in Plate Swing (Ep)•for a Change in Plate Voltage (Ebb) ZD change in output amplitude for a change in screen voltage is shown in Figure 24, which indicates that AEp ~ 8 (2.14) A E c 2 whereAEc2 is the change in screen bias. The s t a b i l i t y required of the screen bias supply therefore may be given as A E c 2 / /Ep \ 6 (2.15) Ec2 \ \Ec27 8 where €. is the allowable fractional change in plate swing. Taking the plate swing and DC screen voltage as 15 KV and . 8 KV respectively requires that for € = -100 db, A E c 2 must be less than -92.6 db in the absence of other sources of modulation. Ec2 A similar calculation for the control grid indicates that the ripple on i t s DC bias must also be restricted to a level of less than -93 db. The frequencies of the modulation introduced w i l l be the ripple frequencies associated with the DC supplies. These frequencies are rather low; the highest (that of the 6 phase plate supply) is 360 Hz. Since the effectiveness of the amplitude feedback system increases with decreasing frequency (see Figure 34 ), this system is able to significantly reduce the amplitude modulation caused by ripple on the plate and bias supplies. An AC filament supply is another source of amplitude modulation. This modulation i s the result of (a) the change in potential along the filament caused by the IR drop of the filament current (b) the action on the plate current by the magnetic f i e l d associated with the filament current and (c) the change in filament temperature due to a change in the magnitude of the filament current. The f i r s t cause is the most important. In this case, the voltage drop along the filament (cathode) causes this electrode to be biased with respect to ground; i f one end of the filament is grounded, then the other w i l l oscillate about ground by an amount equal to the filament supply voltage. This may be partially remedied by placing the ground near the midpoint of the filament. This is most easily done by connecting the 26 p l a t e r e t u r n leads to a center-tap on the output of the f i l a m e n t transformer (see Figure 17). The v o l t a g e drop i n the f i l a m e n t now w i l l cause the negative h a l f of the f i l a m e n t to supply more e l e c t r o n s than the p o s i t i v e h a l f . However, si n c e the current drawn i s p r o p o r t i o n a l to the 3/2°power of the p l a t e to cathode v o l t a g e , the r e d u c t i o n i n current from the p o s i t i v e h a l f of the f i l a m e n t i s not equal to the i n c r e a s e i n current from the negative h a l f . Consequently, the p l a t e current increases whenever f i l a m e n t current f l o w s ; that i s , the p l a t e current i s modulated at twice the f i l a m e n t supply frequency. The magnetic f i e l d produced by the f i l a m e n t current w i l l d e f l e c t the e l e c t r o n s f l o w i n g to the p l a t e ; consequently, the p l a t e current i s decreased s l i g h t l y whenever f i l a m e n t current flows. Again, the p l a t e current i s modulated at twice the f i l a m e n t supply frequency. The e f f e c t of the f i l a m e n t magnetic f i e l d w i l l tend to cancel the e f f e c t of the f i l a m e n t v o l t a g e drop; by p r o p e r l y choosing the f i l a m e n t geometry and v o l t a g e , the modulation produced by an AC f i l a m e n t w i l l be reduced to a very low l e v e l . The t h i r d way i n which an AC f i l a m e n t supply may modulate the p l a t e c u r r e n t — t h r o u g h c y c l i c v a r i a t i o n s i n f i l a m e n t t e m p e r a t u r e — i s f a r l e s s s i g n i f i c a n t than the f i r s t two. This i s because the thermal c a p a c i t y of the f i l a m e n t s i n the tubes used i s so h i g h that the v a r i a t i o n i n f i l a m e n t temperature d u r i n g a c y c l e i s not l a r g e enough to s i g n i f i c a n t l y a f f e c t the p l a t e c u r r e n t . Since t h i s e f f e c t depends on the power d i s s i p a t e d i n the f i l a m e n t , the consequent modulation need not have a s i n u s o i d a l waveform; i t s frequency w i l l be twice that of the f i l a m e n t supply. The most e f f e c t i v e way to e l i m i n a t e the f i l a m e n t as a source of modulation i s to use DC f i l a m e n t s u p p l i e s — t h i s w i l l a l s o e l i m i n a t e the problem of microphonics caused by the i n t e r a c t i o n of the magnetic f i e l d s of the f i l a m e n t strands. DC f i l a m e n t s u p p l i e s may not be used w i t h some tubes because the voltage drop along the f i l a m e n t would s i g n i f i c a n t l y a f f e c t the tube's performance (that i s , a l t e r the g m of the tube). In our case, t h i s i s not a problem because the f i l a m e n t voltage i s l e s s than .1 percent of the p l a t e supply v o l t a g e . D. Thermal Noise At the noise levels of interest at TRIUMF, the most familiar source of random noise—thermal n o i s e — i s of no concern. This is illustrated in the following brief calculation in which i t is assumed the amplifier consists of two stages (Figure 14). El DRIVER PA Gv2i 166 hi Gv = voltage gain, Vo = RMS thermal noise voltage on resonators Fig. 14. Amplifier considered for Thermal Noise Calculation The RMS noise voltages generated at the inputs may be calculated using the formula E = y 2kTp R* (2.16) where E = RMS noise voltage generated in the resistance R (ohms) k = Boltmann's constant = 1.38 x IO""23 joule/°K T = temperature, °K R = resistance, ohms f3 = noise bandwidth. For a synchronous single tuned amplifier, the noise bandwidth may be calculated from the formula P = B n j dx (1 + x 2)n (2.17) where Bn = bandwidth of a s i n g l e stage /rad \ sec n = number of stages. This i n t e g r a l may be evaluated by l e t t i n g Z(n) = $/Bn and f i r s t e v a l u a t i n g Z ( l ) . ( Z ( l ) was found to be 11/2.) Then f o r a cascade of n stages, Z(n) may be found by r e c u r s i v e l y e v a l u a t i n g Z(n) = fl — 1 \ z ( n - 1 ) . (2.18) \ 2 ( n " 1 } / Since the o v e r a l l bandwidth (Bo) i s given by Bo = Bn(2l/n - 1 ) 1 / 2 (2.19) the f o l l o w i n g Table ( I I I ) was constructed. n Z(n) Bn/Bo P/Bo = m 1 1.57 1.0 1.571 2 .785 1.55 1.220 3 .589 1.96 1.155 4 .491 2.30 1.129 .5 .423 2.59 1.097 Table I I I . Chart f o r Noise Bandwidth C a l c u l a t i o n s The output noise v o l t a g e may now be simply evaluated f o r n o i s e introduced by Rj_ and Since the resonator Q (=6000) i s much l a r g e r than a l l other system Q's, t h i s value may be used f o r both cases. Hence E = 2 y kTRf nm' = 4.6 x 10-K>yTRm' (2.20) where f c ^ 2.3 x 10 7 Hz and m i s taken from Table I I I . 2V E]_, the thermal noise introduced by R]_, w i l l be the dominant thermal noise source i f the driver i s not saturated. In this case, there w i l l be 4 stages in the amplifier—therefore m = 1.129. Taking T = 100° C gives ' Ei = 6.68 x 1CT8 v. (2.21) Since there is a voltage gain of about 2 x 10^, the corresponding RMS thermal noise component at the output w i l l have a level of about "Vol = 1.3 x 1CT2 v. (2.22) If the driver i s Saturated, the principal source of thermal noise w i l l be the 2.5 K-fL. resistance at the input to the main power amplifier. In this case, there is only 1 stage of amplification—therefore m = 1.571. Taking T = 100° C gives E 2 = 5.56 x 10 - 7 v. (2.23) Then, due to the PA voltage gain of 166, the RMS thermal noise in the output w i l l have a value of = 9.2 x 10~5 v. (2.24) Both V D j and VQ2 are RMS values; however, even though the instantaneous values of thermally produced noise at the output may reach considerably higher levels, the sources previously discussed s t i l l contribute far more to the output noise. Shot and partition noise, the two other sources of random noise in a vacuum tube amplifier, may similarly be disregarded. Class C Amplifier Operation (Effect on Waveform) Efficiency considerations dictate the use of class C operation in an RF power amplifier. Since in this case the plate current flows in pulses, the output signal w i l l consist of the fundamental (input) frequency plus a high percentage of harmonics as shown in Figure 15. Although the restrictions on the harmonic content of the output are not as severe as those on i t s modulation (the second harmonic must be reduced to less than .5 percent) the percentage of harmonic content shown in Figure 15^^ is intolerable. 30 0 —§s» © = t o t a l conduction angle P = percent harmonic content (fundamental = 100%) F i g . 15. Harmonic Content vs Conduction Angle An i n t e r e s t i n g f e a t u r e i l l u s t r a t e d by t h i s graph i s that f o r a t o t a l conduction angle near 180° the t h i r d harmonic content i n the output may be almost e n t i r e l y e l i m i n a t e d , w h i l e the second harmonic i s reduced to about 45 percent of the fundamental. A more s i g n i f i c a n t r e d u c t i o n i n harmonic content i s obtained, however, because tuned c i r c u i t s are used. Consider the simplest case: the s i n g l e tuned stage. The r e d u c t i o n i n gain f o r the second harmonic may be obtained by s u b s t i t u t i n g w = 2wo i n Equation 2.6: 1 * (2.25) A(2wo) A (wo ) 1.5 Q where ! 25i 10; A(2wo) 1 = 1.3% A(wo) I 31 This equation i n d i c a t e s that s u f f i c i e n t l y high a t t e n u a t i o n of harmonics may be obtained by using a simple tank c i r c u i t w i t h a s u f f i c i e n t l y high Q. However, a r b i t r a r i l y l a r g e Q's are not allowed s i n c e these would v i o l a t e the bandwidth requirements given i n S e c t i o n 2.1.2. I f grea t e r harmonic a t t e n u a t i o n i s r e q u i r e d , the low pass P i network shown i n Figure 15 may be used. (This network a l s o has good impedance matching a b i l i t i e s . ) i i I I I I I W- Pi SECTION P>! F i g . 16. P i Network Output C i r c u i t No problem w i t h harmonic content has been experienced during the opera-t i o n of the CRM RF s y s t e m — t h e t r a n s m i s s i o n l i n e (Figure 8) cou p l i n g the 4CW250,000 to the resonators provides s u f f i c i e n t harmonic a t t e n u a t i o n . 2.2 Main Power A m p l i f i e r 2.2.1 O r i g i n a l Design A c i r c u i t diagram of the f i r s t RF power a m p l i f i e r b u i l t f o r the TRIUMF CRM i s shown i n Figure 17. This a m p l i f i e r used a Machlett t r i o d e ^ (ML-7560) i n a s e l f - b i a s e d , grounded cathode c o n f i g u r a t i o n . A combination of g r i d leak and cathode b i a s was used; the l a t t e r provided p r o t e c t i o n FILAMENT U<jJJ TRANSFORMER JTTTX Fig. 17.^  Schematic of Triode (ML-7560) Power Amplifier 33 should the drive have been accidentally removed. The output circuit was the resonant transmission line discussed in Section 1.3. Neutralization, very important in a triode amplifier, was provided by the c o i l L3 connected in parallel with the capacitor Cg. The parallel combination of L3, and the plate to grid capacitance (75pF) was to be resonated at the operating frequency to eliminate the plate to grid feedback path. This form of neutralization (coil neutralization) is effective at only 1 frequency; hence, i f the frequency of operation is changed, the neutralizing c i r c u i t must be readjusted. Since feedback at other frequencies is only slightly affected, the tendency of an amplifier to act as a tuned plate tuned grid oscillator is not appreciably reduced. Typical operating conditions of the ML-7560 triode are given in Table IV 1 2. These were never fully realized because severe problems with parasitic oscillations caused this design to be abandoned. DC Plate Voltage 20 KV DC Grid Voltage -700 V Plate Swing 17.6 KV Grid Swing 940 V DC Plate Current 8.75 A DC Grid Current .51 A Fundamental Plate Current. 15.9 A (peak) Fundamental Grid Current .94 A (peak) Input Power 175 KW Output Power 139 KW Drive Power 517 W Efficiency 79 % Required Load Resistance 1100 Ohms Table IV. Typical Operating Conditions of the ML-7560 2.2.2 Present Design The present CRM RF a m p l i f i e r , designed and b u i l t by C o n t i n e n t a l E l e c t r o n i c s , i s shown i n Figure 18. Although a grounded cathode c o n f i g u r a t i o n i s used, t h i s a m p l i f i e r d i f f e r s c o n s i d e r a b l y from the previous one. The tube used i s a tetrode (Eimac 4CW250,000); the screen g r i d of t h i s tube reduces s u b s t a n t i a l l y the p l a t e to g r i d feedback capacitance (Cpg a 1.2pF). The i s o l a t i o n of p l a t e and g r i d c i r c u i t s i s f u r t h e r increased by p l a c i n g them i n separate compartments w i t h the tube socket mounted i n the w a l l d i v i d i n g these two compartments. The screen and f i l a m e n t by-pass c a p a c i t o r s are b u i l t i n t o t h i s socket. Even though t h i s a m p l i f i e r i s l e s s s u s c e p t i b l e to p a r a s i t i c o s c i l l a t i o n s than the previous one, n e u t r a l i z a t i o n must s t i l l be used; i n t h i s case single-ended g r i d n e u t r a l i z a t i o n i s employed. To use t h i s method, the input resonant c i r c u i t i s taken s l i g h t l y o f f ground by means of the by-pass c a p a c i t o r C. The v o l t a g e across t h i s c a p a c i t o r , which i s out of phase w i t h the g r i d v o l t a g e , i s then fed back to the p l a t e v i a Cn to provide n e u t r a l i z a t i o n . Since t h i s i s e f f e c t i v e l y a c a p a c i t i v e bridge c i r c u i t (see Figure 19), t h i s form of n e u t r a l i z a t i o n i s e f f e c t i v e f o r a wide band of frequencies. NEUTRALIZATION FOR Cn/C = Cpg/Cgf F i g . 19. Single-ended G r i d N e u t r a l i z a t i o n Drawn as a Bridge C i r c u i t 35 -A/W- "WV" 1000 <2W 'iHf 4CW250,000 PLATE CHOKE Cn 6 — 6 0 PLATE SUPPLY Hi TRANSMISSION LINE TO 3000 RESONATORS IMF R F CHOKE o n r r — 20000 I 10000 FILAMENT SUPPLY FEEDBACK SCREEN SUPPLY CROWBAR SIGNAL DENOTES PART OF TUBE S O C K E T Fig. 18. Schematic of Main CRM Power Amplifier J U Separate DC supplies are used to provide the fixed bias shown in Figure 18. Although more expensive, this design has advantages: with fixed bias there is no danger of tube overload should the drive be removed; greater f l e x i b i l i t y in setting the DC conditions also results. In addition, the amplitude of the output RF may be varied by adjusting the screen bias. This option, not present in a triode amplifier, was used to provide an amplitude control system u t i l i z i n g feedback control of the screen bias voltage. Since the restrictions on the amplifier Q given in Section 2.1.2 were found d i f f i c u l t to meet, a grid swamping resistor (R^) is included in the ci r c u i t . To lower the Q of the input circuit to an acceptable level, this resistor must dissipate up to 250 watts; consequently, i t is water cooled. Table V gives the el e c t r i c a l characteristics of the 4CW250,000. Note that the maximum plate dissipation allowed is 250 KW. At 75 percent efficiency and an output of 150 KW, the dissipation w i l l be only 50 KW, well within the tube's rating. Table VI gives typical operating conditions of this tube (in the CRM PA). Filament: Thoriated Tungsten Maximum Filament Voltage Maximum Filament Current Direct Interelectrode Capacitance, Grounded Cathode: Input Output Feedback Maximum Ratings: DC Plate Voltage DC Screen Voltage DC Plate Current Plate Dissipation Screen Dissipation Grid Dissipation Table V. El e c t r i c a l Characteristics of the Eimac 4CW250,000 12.0 V 640 A 775 pF 130 pF 1.2 pF 20 KV 2.5 KV 40 A 250 KW 3.5 KW 1.5 KW 37 DC P l a t e Voltage DC G r i d Voltage DC Screen Voltage P l a t e Swing G r i d Swing DC P l a t e Current DC G r i d Current Fundamental P l a t e Current Fundamental Gr i d Current Input Power Output Power Drive Power E f f i c i e n c y Required Load Resistance 19 KV -800 V 800 V 15.9 KV 950 V 12.2 A .27 A 23 A (peak) .51 A (peak) 232 KW 182 KW 243 W 78 % 690 Ohms Table VI. T y p i c a l Operating Conditions of the 4CW250.000 Tetrode i n the CRM A m p l i f i e r 2.3 D r i v e r A m p l i f i e r Design 2.3.1 S p e c i f i c a t i o n s In S e c t i o n 2.1, the RF system requirements regarding power g a i n , bandwidth and noise r e d u c t i o n were discussed; Table VII summarizes the r e s u l t s a p p l i c a b l e to the 3 stage d r i v e r a m p l i f i e r . Note that the power output quoted i s the minimum d r i v e required to obt a i n an output of about 150 KW from the PA tube; " l o s s e s " r e f e r s to power l o s t i n the coupling c i r c u i t and PA g r i d swamping r e s i s t o r . D r i v e r Power Output >517 W + Losses " (ML-7560) >150 W + Losses (4CW250,000) Q of Tuned Driver C i r c u i t s A11<C 14J Synchronous, S i n g l e Tuned C i r c u i t s L3% Frequency S h i f t 2 C i r c u i t s < 89 T s t a g g e r Tuned 2 C i r c u i t s < 37 \_3% Frequency S h i f t A l l < 44 ) Synchronous, S i n g l e Tuned C i r c u i t s |_No Frequency S h i f t D r i v e r Output Noise <S^ -94 db ( D r i v e r Unsaturated) Table V I I . S p e c i f i c a t i o n s f o r 3 Stage D r i v e r A m p l i f i e r 2.3.2 Tube S e l e c t i o n The tubes f o r the d r i v e r a m p l i f i e r were chosen, i n order, from the output to the input of the a m p l i f i e r . Each was chosen on the b a s i s of ga i n , input-output i s o l a t i o n , and output power. At the time the d r i v e r was designed, the PA power tube being used was the Machlett ML-7560; as i n d i c a t e d i n Table V I I , t h i s tube r e q u i r e d considerably more d r i v e power than the present tube being used (Eimac 4CW250,000). On the b a s i s of the d r i v e requirements of the ML-7560, 3 Eimac power tetrodes were considered f o r the output stage of the d r i v e r : 4-250A, 4-400A, and 4-1000A. Tetrodes, r a t h e r than t r i o d e s , were considered because the former have much lower i n t e r n a l feedback coupling and lower d r i v i n g power requirements ( u s u a l l y < 1 percent of output power). Assuming a t y p i c a l e f f i c i e n c y of 75 percent, Table V I I I i n d i c a t e s the maximum output power which could be expected of these tubes. 39 Tube No. Pd (Watts) Po (Watts) Pd = 4-25OA 250 750 Po = * 4-400A 400 1200 4-1000A 1000 3000 maximum allowed p l a t e d i s s i p a t i o n maximum power output Table V I I I . Maximum Output Power of the Tubes considered f o r the Output Stage of the D r i v e r A m p l i f i e r To help i n the choice of the d r i v e r a m p l i f i e r (DA) output tube, an estimate was made of the minimum output necessary to s a t i s f y the Q requirements of t h i s stage. To t h i s end, the c i r c u i t s i n Figure 19 were considered; s i n c e the minimum capacitance that may be used i n these c i r c u i t s i s the output capacitance of the f i n a l DA tube and the input capacitance of the PA, an estimate may be made of the minimum power which must be fed i n t o the c o u p l i n g c i r c u i t to o b t a i n a given Q. The v o l t a g e (V) i n both cases was taken to be the r e q u i r e d peak RF v o l t a g e on the g r i d of the PA. (a) Tank PDT. DT TCfV (b) P i L ci C2 P D K =.TCfvf C 2 1 + C2 Q V. c l ( f o r Q >10) F i g . 20. Power Input to Tank and P i C i r c u i t s 40 Table IX gives the power that must be fed into the tank circuit i f the DA tube is the 4-1000A and the PA tube is either the ML-7560 or the 4CW250,000. (The cir c u i t used i s shown in Figure 20 (a), where C is the sum of the tube capacitances.) Q Required Power (KW) ML-7560 4CW250.000 10 1.22 2.04 20 .61 1.02 30 .41 .67 40 .31 .51 50 .24 .41 60 .20 .34 70 .17 .29 80 .15 .25 Driver Tube = 4-1000A Output Capacitance (C D) of the 4-1000A = 8pF Input Capacitance (Cj_) of the ML-7560 = 200pF Input Capacitance (C^) of the 4CW250,000 = 775pF C = C Q + C± Vg (ML-7560) £Z 900v Vg (4CW250,000) Oi. 600v Table IX. Minimum Power Input to DA-PA Coupling Circuit for a given value of Q If the Pi circuit is used (Figure 20 (b)) with C]_ = C D and C 2 = C^, then one may write pD T L = C i P D T - (2.26) Co If the ML-7560 is used, P n = 25 P D T; i f the 4CW250,000 is used, Ppi^ = 100 Pj)X- Since additional reactance must be added to properly tune the cir c u i t s , the actual power required w i l l be at least 1.5 times the figures given in Table IX, but lower than the P ^ quote above. If a 3 percent shift in drive frequency must be handled by a synchronous single tuned driver, only the 4-1000A w i l l adequately meet the power requirements. Even though the 3 percent frequency shift was discarded, the 4-1000A is s t i l l a good choice because i t can easily satisfy the present power requirements without being run near i t s maximum ratings; also, i f more power is 41 r e q u i r e d , there i s a considerable reserve a v a i l a b l e . Before a tube to d r i v e the 4-1000A can be chosen, the ope r a t i n g c o n d i t i o n s of the 4-1000A must be c a l c u l a t e d . This i n f o r m a t i o n i s a l s o necessary f o r the design of the b i a s and coupling c i r c u i t r y . The a n a l y s i s of a c l a s s C a m p l i f i e r tube i s s e m i g r a p h i c a l , u t i l i z i n g the f a c t that the operating l i n e of the constant current curves of the given tube i s a s t r a i g h t l i n e . This l i n e i s s t r a i g h t because a tuned load i s used. That i s , i f the vo l t a g e on the g r i d of the tube i s Egg = E c l + E g cos wt, (2.27) then the vo l t a g e on the p l a t e of the tube w i l l be Epp = E^ - Ep cos wt (2.28) where Egg, E ^ = instantaneous g r i d and p l a t e v o l t a g e s E^cl = g r i d b i a s E^ = DC p l a t e v o l t a g e Eg = g r i d swing and Ep = p l a t e swing. On the constant current c h a r a c t e r i s t i c s of the tube (see Figure 20), the r e l a t i o n s h i p between Egg and Epp then appears as a s t r a i g h t l i n e : E g g = (- I^Epp + ^ E c l + |gEh.y (2-29) The a c t u a l a n a l y s i s c o n s i s t s of s p e c i f y i n g an op e r a t i n g l i n e and then c a l c u l a t i n g the d e s i r e d q u a n t i t i e s from data p o i n t s on t h i s l i n e . To s p e c i f y the ope r a t i n g l i n e f o r a given screen b i a s , the g r i d and p l a t e b i a s plus g r i d and p l a t e swing must be f i x e d . P o i n t s on the op e r a t i n g l i n e are then found that are 15° (conduction angle) apart. Using the values of voltage and current obtained from these p o i n t s , an approximate harmonic analysis-'- 3 i s made of the p l a t e , c o n t r o l g r i d , and screen g r i d c u r r e n t s ; that i s , the magnitude of the DC and fundamental ( d r i v i n g frequency) components are found. The operating l i n e given f o r the 4-1000A i n Figure 21 shows t h i s tube operating near maximum output; to f i n d the DC and fundamental current the equations I D C = (-5A + B + C + D + E + F)/12 (2.30) 300 A.B.C.D.E.F.G. ARE 15° APART Fig. 21. PLATE VOLTAGE — VOLTS Operating Line of the 4-1000A EIMAC 4-1000A TYPICAL CONSTANT CURRENT CHARACTERISTICS SCREEN VOLTAGE — 500 VOLTS . PLATE CURRENT — AMPERES SCREEN CURRENT — AMPERES GRID CURRENT — AMPERES DC P L A T E VOLTAGE 7000 43 and Ipp = (A + 1.93B + 1.73C + 1.41D + E + .52F)/12 are used, where I-QQ = DC component of the p l a t e current pulse Ipp = peak fundamental component of the p l a t e current pulse and A, B , C, D, E, F = the instantaneous values of current taken from the operating l i n e . This a n a l y s i s i s done f o r the p l a t e current to f i n d the power output and p l a t e d i s s i p a t i o n , ' f o r the g r i d current to f i n d the d r i v e power and g r i d d i s s i p a t i o n , and f o r the screen current to f i n d the screen d i s s i p a t i o n . The process i s repeated u n t i l an op e r a t i n g l i n e i s found that gives the d e s i r e d output power w i t h a high e f f i c i e n c y (^75 percent) and without exceeding the maximum r a t i n g s of the tube.. Then, i n order f o r the tube to operate as c a l c u l a t e d , the given b i a s and d r i v e must be provided, as w e l l as the proper load impedance f o r the tube, where the loa d impedance i s given by = Peak fundamental v o l t a g e . (2.31) Peak fundamental current The op e r a t i n g c o n d i t i o n s c a l c u l a t e d f o r the 4-1000A based on the o p e r a t i n g l i n e i n F i g u r e 21 are given i n Table X; Table XI gives the e l e c t r i c a l r a t i n g s f o r t h i s tube. 44 DC Plate Voltage DC Grid Voltage DC Screen Voltage Plate Swing Grid Swing DC Plate Current DC Grid Current DC Screen Current Fundamental Plate Current Fundamental Grid Current Input Power Output Power Drive Power Plate Dissipation Grid Dissipation Screen Dissipation Efficiency Required Load Resistance 5 KV -200 V 500 V 4.4 KV 350 V .71 A .04 A .12 A 1.24 A (peak) .08 A. (peak) 3.57 KW 2.73 KW 13.1 W .84 KW 5.1 W 61.5 W 76% 3550 Ohms Table X. Operating Conditions for the Eimac 4-1000A near maximum Output 45 Filament: T h o r i a t e d Tungsten Maximum Filament Voltage 7.5 V Maximum Filament Current 22.7 A Dirent I n t e r e l e c t r o d e Capacitance, Grounded Cathode: Input 32.4 pF Output 9.4 pF Feedback .35 pF Maximum Ratings: DC P l a t e Voltage 6.0 KV DC Screen Voltage 1.0 KV DC P l a t e Current .7 A P l a t e D i s s i p a t i o n 1.0 KW Screen D i s s i p a t i o n 75 W Gr i d D i s s i p a t i o n 25 W Table XI. E l e c t r i c a l C h a r a c t e r i s t i c s of the Eimac 4-1000A The tube chosen to d r i v e the 4-1000A i s an RCA 6146A (see Table X I I ) . This i s a beam power pentode w i t h an i n d i r e c t l y heated cathode; consequent t h i s tube provides high stage i s o l a t i o n and w i l l be f r e e of f i l a m e n t hum. As Table XII shows, t h i s tube i s capable of an output power of 48 watts which i s co n s i d e r a b l y l a r g e r than the maximum d r i v e requirement of the 4-1000A ( 13 W). However, even i f the d r i v e requirement of the 4-1000A i s very s m a l l , a s i g n i f i c a n t amount of power must be d i s s i p a t e d i n the cou p l i n g c i r c u i t r y to s a t i s f y the d r i v e r Q requirements. For example, i f only the tube c a p a c i t i e s are used, the tank c i r c u i t of Figure 20 (a) must d i s s i p a t e about 18 watts i f a stage Q of 10 i s to be achieved. Since the 4-1000A r e q u i r e s l e s s than 18 watts of d r i v e under normal o p e r a t i n g c o n d i t i o n s , a r e s i s t o r must be added to lower the Q by d i s s i p a t i n g the excess power. T y p i c a l o p erating c o n d i t i o n s f o r the 6146A are shown i n Table X I I I . 46 Filament Voltage (AC/DC) 6.3 V Filament Current 1.25 A Trans conductance 7000 JJ* mhos Direct Interelectrode Capacitances: Input 13 pF Output 8.5 pF Feedback .24 pF Maximum Ratings (CCS): DC Plate Voltage 600 V DC Screen Voltage 250 V DC Grid Voltage -150 V DC Plate Current 140 mA DC Grid Current 3.5 mA Plate Dissipation 67.5 W Table XII. E l e c t r i c a l characteristics of the RCA 6146A Beam Power Pentode DC Plate Voltage 500 V DC Screen Voltage 170 V DC Grid Voltage -66 V Grid Swing 84 V (peak) DC Plate Current 135 mA . DC Screen Current 9 mA DC Grid Current 2.5 mA Driving Power .2 W Output Power 48 W Efficiency 70% Required Load Resistance 1500 Ohms Table XIII. Typical Operating Conditions of the RCA 6146A 47 The maximum d r i v e power re q u i r e d by the 6146A (.2 W) i s much l a r g e r than the a v a i l a b l e power output from the frequency s y n t h e s i z e r (5 mW) ; however, under normal operating c o n d i t i o n s (output about 18 W), the 6146A w i l l r e q u i r e only a few m i l l i w a t t s of d r i v e . This would seem to i n d i c a t e that the s y n t h e s i z e r could normally be used to d r i v e the 6146A. However, t h i s cannot be done i f the stage Q requirements are to be met; that i s , i f the input c i r c u i t of the 6146A i s a tank c i r c u i t using only the input capacitance of t h i s tube i t i s found that Q P i n = 2.3 ' (2.32) where P i n = power d i s s i p a t e d i n g r i d c i r c u i t of the 6146A Cin = 13 pF and Vg = 50 V (peak) = RF d r i v e v o l t a g e r e q u i r e d . Hence, f o r a Q = 10, the s y n t h e s i z e r would have to supply 230 mW; f o r a Q = 70, the s y n t h e s i z e r would have to supply 14 mW. Since the s y n t h e s i z e r i s capable of only 5 mW, another stage must be added. An RCA 6CL6 power pentode (Table XIV) was chosen to d r i v e the 6146A. Although t h i s tube has an input capacitance (11 pF) that i s almost as l a r g e as that of the 6146A, the 6CL6 r e q u i r e s an RF g r i d v o l t a g e of l e s s than 1.5 v o l t s (peak). Because the energy storage i n the input capacitance depends on t h i s v o l t a g e squared, i t i s found that Q P i n < 1.8 x 1 0 - 3 (2.33) where P i n = minimum power to be d i s s i p a t e d i n the g r i d c i r c u i t of the 6CL.6' and Q = stage Q r e q u i r e d . Consequently, the d r i v e requirements of t h i s stage may e a s i l y be met by the s y n t h e s i z e r : a 0 of 10 re q u i r e s a power d i s s i p a t i o n of only .2 mW. 48 Filament Voltage (AC/DC) 6.3 V Filament Current .65 A D i r e c t I n t e r e l e c t r o d e Capacitance (without e x t e r n a l s h i e l d ) : Input 11 pF Output 5.5 pF Feedback .12 pF Maximum Ratings: DC P l a t e Voltage 300 V DC Suppressor G r i d Voltage 0 V DC Screen Voltage 300 V DC G r i d Voltage -50 V DC P l a t e Current 30 mA DC Screen Current 7.2 mA P l a t e D i s s i p a t i o n 7.5 W Transconductance 1.1x10" mhos Table XIV. E l e c t r i c a l C h a r a c t e r i s t i c s of the 6CL6 Power Pentode 2.3.3 D r i v e r RF C i r c u i t s A c i r c u i t diagram of the present d r i v e r a m p l i f i e r i s shown i n Figure 2 2; P l a t e s 1 to 3 show the top, f r o n t and bottom of the d r i v e r w i t h covers removed. The c i r c u i t r y of the d r i v e r must provide proper i n t e r s t a g e c o u p l i n g ; that i s , i t must (a) present the proper load impedance to each tube (b) provide the r e q u i r e d RF d r i v e v o l t a g e s and (c) t r a n s f e r power e f f i c i e n t l y . (This i s imperative i n the output stages where the power generated i s l a r g e . ) This c i r c u i t r y must a l s o s u f f i c i e n t l y attenuate the harmonics of the d r i v e frequency that are generated by Class C o p e r a t i o n of the tubes. Any tendancy of the a m p l i f i e r to break i n t o spontaneous o s c i l l a t i o n i s , of course, i n t o l e r a b l e . To prevent t h i s , n e u t r a l i z i n g c i r c u i t s are used to reduce p l a t e to g r i d c o u p l i n g , w h i l e p a r a s i t i c suppressors are added to + 6 KV DC 4-300V DC Q + 6 0 0 V DC 0 PS2 FROM -6 6.3 V A C SYNTHESIZER 0 5 0 V DC 0 + 150 V DC O 180 V DC Fig. 22. Schematic of CRM Driver Amplifier 50 l o a d the g r i d and p l a t e c i r c u i t s f o r frequencies much higher than the ope r a t i n g frequency. Since the a b i l i t y to f u n c t i o n w i t h a 3 percent s h i f t i n d r i v i n g frequency i s no longer required of the CRM RF system, the d r i v e r c o n s i s t s of synchronous s i n g l e tuned stages w i t h c i r c u i t Q's l e s s than 44. Since the stage requirements are not a l l the same, s e v e r a l d i f f e r e n t types of s i n g l e tuned c i r c u i t s are u t i l i z e d . The output c i r c u i t of the 4-1000A i s a modified Pi x^»15 c i r c u i t . I n i t i a l l y , a t a n k - c i r c u i t w i t h loop c o u p l i n g was t r i e d to match t h i s tube to the 50-O- t r a n s m i s s i o n l i n e . I t was found that when the loop was coupled l o o s e l y enough to provide the proper load impedance, the Q became e x c e s s i v e l y h i g h . A P i c i r c u i t was then b u i l t . When p r o p e r l y matched, i t had a Q of about 30. This Q s a t i s f i e d the bandwidth requirements, but the c i r c u l a t i n g current (equal to Q times the input current) heated the tank c i r c u i t e x c e s s i v e l y . The present output c i r c u i t i s a m o d i f i c a t i o n of the P i . By tapping the in d u c t o r as shown, inductance was added i n s e r i e s w i t h the p l a t e , hence lowering the input shunt capacitance of the P i . T h i s lowered the Q and reduced the he a t i n g of the i n d u c t o r . To reduce the chance of p a r a s i t i c o s c i l l a t i o n s , the p a r a s i t i c suppressor (PS2) was added. The c i r c u i t c o upling the 6146A to the 4-1000A was o r i g i n a l l y a P i c i r c u i t . I t was to have been used i n conj u n c t i o n w i t h the 4-1000A i n a grounded screen c o n f i g u r a t i o n which i t was hoped would e l i m i n a t e the need f o r n e u t r a l i z a t i o n . Because long leads and f l o a t i n g s u p p l i e s were r e q u i r e d , the i s o l a t i o n of the 4-1000A's p l a t e and g r i d was l e s s than i n a conve n t i o n a l grounded cathode c o n f i g u r a t i o n . Since the f l o a t i n g s u p p l i e s presented a s a f e t y problem, and si n c e the need f o r n e u t r a l i z a t i o n had not been e l i m i n a t e d , the output stage was changed to i t s present grounded cathode c o n f i g u r a t i o n . In a d d i t i o n , the g r i d c i r c u i t of the 4-1000A was changed to a transformer-coupled (tuned secondary) c o n f i g u r a t i o n x ^ i n order to s i m p l i f y the n e u t r a l i z a t i o n of t h i s tube. This was accomplished by r a i s i n g the secondary of the transformer o f f ground by means of a 1000 pF c a p a c i t o r (Cng) and then coupling t h i s p o i n t to the p l a t e u s i n g c a p a c i t o r Cn. (Cn i s a s e c t i o n of f o i l placed next to the a i r chimney surrounding the 4-1000A.) The 5.6 KSL r e s i s t o r placed across the 51 secondary of the transformer lowers the Q of t h i s stage to the r e q u i r e d l e v e l . The coupling between the 6CL6 and the 6146A c o n s i s t s of a P i c i r c u i t w i t h r e s i s t i v e l o a d i n g at the g r i d of the 6146A. A P i c i r c u i t i s used not because a wide impedance tr a n s f o r m a t i o n i s r e q u i r e d , but because these two tubes are r e l a t i v e l y f a r apart. By using a P i c i r c u i t and p l a c i n g the r e q u i r e d c a p a c i t o r s near the tubes, the inductance of the l e a d i s i n c o r p o r a t e d i n the i n d u c t o r of the P i . Transformer coupling u t i l i z i n g a tuned secondary i s used at the input to the 6CL6. To minimize the reactance i n t h i s c i r c u i t and t h e r e f o r e minimize the power d i s s i p a t i o n r e q u i r e d to a t t a i n a given Q, no capacitance i s added to the input c i r c u i t (input capacitance of the 6CL6 CS 11 pF). Resonance i s obtained by s l u g tuning the transformer. Plate I. Top View of Driver Amplifier (Cover Removed) showing the 4-1000A and i t s Output Circuit; the Input to the Transmission Line i s on the Right-hand Side Bottom View of Driver Amplifier (Cover Removed) showing the Filament Chokes and RF Transformer Coil; Filament Transformer on the Right 55 CHAPTER 3'. AMPLITUDE CONTROL SYSTEM DESIGN Two amplitude control systems were designed and built for the TRIUMF CRM RF system. For use when the driver amplifier is not saturated, a drive control system is used which controls the amplitude of the output RF by appropriately modulating the synthesizer signal. When the driver is saturated, this form of control is not p o s s i b l e — i n this case, the resonator RF amplitude is controlled by adjusting the screen grid voltage on the 4CW250,000. 3.1 System Element Transfer Functions Before the amplitude control systems may be analyzed as a whole, the input-output relationships of a l l system components must be found. Briefly, these are (a) transmission line-resonator system (b) RF chain (c) resonator voltage detector (d) input RF amplitude modulator (e) Hewlett-Packard programmable power supply (f) PA plate amplitude response to PA screen voltage modulation and (g) RF by-pass circuit on the screen of the PA • It was assumed that a l l other components to be added would be broadband enough so that their frequency response could be ignored. A. Transmission Line-Resonator System The input-output amplitude relationship of the transmission l i n e -resonator system (1 dee) was found using the lumped parameter cir c u i t of Figure 23 to model the actual distributed system assuming a fixed source frequency, wo. 56 PA + VRES TRANSMISSION LINE RESONATORS Fig. 23. Equivalent Circuit of Transmission Line-Resonator System To find the output amplitude response to a small amplitude modulation at the input to the transmission line, the input was taken to be Vg(t) = Im (V (1 + ku(t)))el wot) ( 3 > 1 ) where V = i n i t i a l steady state amplitude k<3^  1 i s the fractional increase in input amplitude as a result of step amplitude modulation. The output i s then of the form Vres = Im ((a(t)eJ 4^  (t) ) ejw 0t) Vg ( 3 , 2 ) where a ( t ) e J ^ is the complex resonator voltage amplitude transfer function. It was found a ( t ) e 3 ^ ( t ) = & ROCQ + $ ( R ^ + R 2C 2) + j ( R 0 S 0 + 8 ( R ^ + R ^ ) ) (3.3) where 5 = ku(t) y = 1+8 Co = cos.^o So = sin 9o Cl = cos ((b^ - w Q)t +8i) s l = sin ((b^ - w Q)t C 2 = cos ((b 2 - w Q)t + 0 2) S2 = s in ( (b 2 - w Q)t +e2) 57 R J - R ^ R2 = R 2 e a 2 t * The constants 6Q, © i , 0 2, al> a 2> Ro> Rl> R2 c a n n o t D e given exp l i c i t l y in terms of the equivalent ci r c u i t parameters, since their determination involved a computer solution of the circuit's fourth order characteristic polynomial. From the computer solution, i t was found that 8 Q, 0 i , 8 2 ^ 1 and b-^'X wo, b 2 Os* wo; consequently, a very good approximation would be to take Co. C 1 } C 2 ~ 1 S0> sl> S 2 0. It was found by comparing the actual and approximate solutions for the amplitude response that the error varied from about 1.5 x 10 - 4% at t = o to about 2 x 10-7% at t = 50 yu sec. when the input was a step. Hence, one may take the amplitude response to be A aj^sCt) = kVRo(l + k i e a ^ + A2ea2t) u(t) where k 1 = input step amplitude ai = -2.00 x 10 4 sec" 1 a 2 = -5.23 x 10 5 s e c - 1 Taking the Laplace transform this becomes { (3.4) Time constants from computer solution. A *RES (S) = kVRo(l + Ar + A? ) S S-ai S-a 2 (3.5) R0 = Steady State Resonator Amp.  Corresponding Steady State Input Amp. £ 5. A i , A 2 are the relative amplitudes of the two exponential decay terms. To satisfy the i n i t i a l conditions (that i s , Aa(t) = o at t = o) one must have 1. + A x + A 2 = o (3.6) Ai = -1.0417 (from computer solution). The small signal input to output amplitude response function T(S) may now be found for the transmission line-resonator system. T(S) = AaR E S s(S) R n ( l + S/ko) (3.7) l i n TST (1 + Syko)(l + S^ X) 58 where oCQ = 1.966 x 10 4 cr 2 x IO 4 sec" 1 oC± = 5.227 x 105 ~ 5.2 x IO 5 s e c - 1 2 = 7-° x 1 0 ° s e c - 1 . B. RF Chain The amplitude response of the RF chain was estimated by examining the step response of the system when the PA was loaded by the transmission line which was terminated by a 50 ohm dummy load. It was found that the output, measured at the dummy load, had a rise time of about 3 x 10~6 seconds. This then corresponds to a Q of about 200—a reasonable figure for the overall RF system. That i s , Q = wo* ~ 21C x 22 x 10 6 x 3xl0~ 6 „ 200. (3.8) 2 2 Consequently, the transfer function for the RF chain was taken to be A a o u t - • ^ = K (3.9) A a i n 1 +'YS 1 + S/3.3 x 10$-where 4 K = ratio of output to input steady state amp. — 2..*<o ^ = time constant cr 3 x 10-6 sec. C. Resonator Voltage Detector The dominant time constant of this device i s determined by the R-C combination i n the cathode cir c u i t of the detecting tube. We have a time constant V = RC = 180 pF x 100 KA. = 1.8 x IO - 5 sec. Therefore, the detector transfer function may be taken as: T(S) = KD ^ KD (3.10) 1 + 1.8 x 10-5 x S 1 + S/6 x 10*-4 where KD = IO - 3 = Steady State Detector Output Steady State Resonator Voltage 59 D. Input RF Amplitude Modulator This function is performed by a Hewlett-Packard double balanced mixer (Model 10514A)• Since this device has a band width in excess of 50 MHz, i t s frequency characteristic w i l l be disregarded in the following calculations. » E. Hewlett-Packard Programmable Power Supply The frequency characteristics of this device were taken from i t s service manual. Its half power frequency is given as 20 KHz with a voltage gain variable from 0 to -10. Therefore, i t s transfer function may be written as: T(S) = AyHP = - KHP (3.11) AVin l + s/a a = 2Hx 20 x 103 rad. A, 1.25 x 10 5 rad. sec. sec. Kjjp = gain (taken as 10 i n a l l following calculations) . F. PA Plate Amplitude Response to PA Screen Voltage Modulation It i s necessary to know A.Vp i f a screen modulating system is to be A V g 2 analyzed. A Vp = change in the RF amplitude at the plate of the 4CW250,000 in response to a change in the screen voltage of this tube. The time constant of such a change w i l l be extremely .short and may therefore be neglected. The magnitude of Ayp was estimated from the constant A V g 2 current characteristics of the Eimac 4CW250,000 tube by drawing load lines corresponding to the same operating conditions on curves for different screen voltages. That i s , load lines were found for the different screen voltages of 400, 800, 1000 and 1200 volts (the characteristics available at that time). These load lines had the same load resistance (RL), DC plate voltage (Eb), control grid bias (Ec^) and grid drive (Eg). RL = 690 _D-Eb = 18,000 volts Eci = 500 volts Eg = 600 volts peak OU R|_ = 6 9 0 Eg = 6 0 0 V (peak) E b = 1 8 0 0 0 V E C | = 5 0 0 V BIAS Fig. 24. Plot of the Output RF Amplitude for varying Screen Voltages (4CW250,000 Power Tube) 61 The results obtained are shown on Figure2A where one sees that Vp is an approximately linear function of Vg 2 and that Ayp /v 8. AVg 2 G. RF By-Pass Circuit on Screen of PA Figure 15 below shows the RF by-pass circuit which connects the modulated DC screen supply to the screen of the 4CW250,000 power amplifier tube. RD represents the dynamic resistance of the screen. That i s , . RD = AVg? • A I g 2 A V H P 4C7U.H y T T T -500 72JUH A l a 2 -nrrr 5 0 0 pF (3.12) Fig, 25. RF By-pass Circuit at the Screen of the 4CW250,000 Using the same load lines as those used for finding AVp , i t was AVg 2 possible to findAVg 2. However, from the nature of the curves i t was A l g 2 possible to find I g 2 for Vg 2 equal to only 1000 and 800 volts. Thus V§2 I g 2 1000 800 Therefore, .95A .48A. RD = AVg? ,» 1000 - 800 = 425.5 JX. A l g 2 ~ .95 - .48 (3.13) For the purpose of these calculations, RD was consequently taken to be 425.fl.. The frequency response (db magnitude and phase) of the screen circuit was then found using the Ecap computer program. A plot of the results i s shown on Figure 26, from which one sees that i f a control system with a phase crossover frequency below 5 x 10^ rad. 8 x 104Hz sec. is adequate, then this circuit may be ignored in control calculations. Fig. 26. Frequency Response of the RF By-pass Circuit at the Screen of the 4CW250,000 63 3.2 Drive Control System A. Uncompensated Open Loop Response Having found the transfer functions of the components of the proposed drive control system, one has a system as shown in Figure 27. RF CHAIN Kl 1 + S/3.3 x 105 MODULATOR TL-RES SYSTEM K 2 ( l + S/7 x 10b) (1 + S/2 x 10 4)(1 + S/5.2 x 10 5) VOLTAGE DETECTOR IO" 4 1 + S/6 x 10 4 DAC REFERENCE Fig. 27. Block Diagram of Uncompensated Drive Control System Note that the output of the voltage detector has been decreased by a power of 10 to make i t s output compatible with the DAC voltage reference. From Figure27, one may find the open loop transfer function of the system: GH = K(l + S/7 x 1Q6)  (1 + S/2 x 10 4)(1 + S/6 x 10 4)(1 + S/3.3 x 1<)5) (1 + S/5.2 x 10 5) C3.14) where (K) is the DC gain of the loop. The Bode plot of equation 3.14 is given in Figure as. Since positive phase and gain margins in most cases ensure a stable closed loop system, we see that, based on this criterion, the maximum stable open loop gain of the system w i l l be 40 db - 18 db = 22 db. A check of this s t a b i l i t y limit may be made by applying the Routh st a b i l i t y criterion using, however, an approximation of (GH) to simplify calculations. 65 Let GH = K . (3.15) (1 + S/2 x 10 4)(1 + S/6 x 10 4)(1 + S/3.3 x 10$) Then the characteristic equation of the system, 1 + GH = 0 becomes S3 + (4.1 x 10 5)S 2 + (2.76 x 10 1 0)S + (3.69 x 10 1 4) + K 1 = 0 K 1 = 3.96 x 10 1 4K S3 1 2.76xl0 1 0 S 2 4.1xl0 5 3.69xl0 1 4 + K 1 S 1 2.76xl0 1 0 - .09xl0 1 0 - .24xlO~5xK1 0 So 3.69xl0 1 4 + K 1 0 Table XV. Routh Table for the Approximate Characteristic Equation The characteristic equation represents a stable system (having roots with only negative real parts) i f the signs of a l l entrees of the f i r s t row of the Routh table (Tableau) are the same. Since K^O, this requires that 2.76 x 10 1 0 - .09 x 10 1 0 - .24 x IO - 5 K 1>0 (3.16) or K < 28 = 28.65 db This confirms the value 22 db as the maximum stable gain of our system. The f i n a l value theorem (Eqn 3.17) may now be used to estimate the reduction of resonator voltage errors by the uncompensated drive control system. f(oo) = lim f(t) = lim s F(S) (3.17) t-o-00 S-wO If a unit step error (1/S) should occur in the output, we may write e ( o o ) = ) lim s j l j GT s-*o IS \ 1 + G]Hi lim (3.18) s*o 1 + G^Hi 1 + K where our actual system configuration is as shown in Figure 29. 66 S T E P ERROR T L — RES S Y S T E M RF CHAIN DETECTOR DAC REF Fig. 29. Block Diagram of Drive Control System with Step Error in the Output l/S Fig. 30. System of Figure 29 Redrawn with Step Error as only Input Gi = 1 H-L = GH (system open loop transfer function) Figure 30 is equivalent to Figure 29. Therefore, since K = 22 db Ci 12.6, step errors In the output w i l l be reduced by a factor of = .074 = -22.6 db. 1 + 12.6 0/ B. Compensated Open Loop Response Since as large as possible a reduction of the amplitude errors is desired, an increase in the open loop gain is required. However, increasing the system gain above 22 db would lead to an unstable system unless: (a) the time constants of the system are decreased at the same time or (b) compensating elements are added to stabilize the system. An examination of the RF chain, transmission line-resonator system, and voltage detector shows that the system time constants can not be decreased significantly. Hence, compensation—either parallel or cascade—must be used in this case. Cascade compensation placed between the reference comparator and the input modulator is by far the most practical choice. Two cascaded phase lag circuits having a transfer function T ( S ) c o m p = Kc (1 + S/2 x 10 4)(1 + S/6 x H)4) (3.19) (1 + S/103)(1 + S/6 x IO 3) were tried f i r s t as compensation. From bode plot considerations this limited the system gain to less than 42 db and gave a phase crossover frequency of 3.0 x 10 4 rad. This would reduce the response to a step sec. error input by about 42 db, an improvement of about -20 db over the uncompensated case. However, the phase crossover frequency had been lowered — t h i s was not desirable since i t would reduce the effectiveness of this system when confronted with modulation in the kilohertz range. A better compensator would be constructed using phase lag-lead compensation (note the pole cancellation as before) of the form: T ( S ) c o m = Kc (1 + S/2 x 10 4)(1 + S/6 x 104) (3.20) (1 + S/a D)(l + S/ai) letting a Q = 10 rad. sec. ai = 6 x 10 5. The frequency response of this compensator is shown on Figured ; the open loop response of the drive control system using this compensation is given on Figure 32- The latter plot indicates that the maximum stable i 1 r w(rad/sec) Fig. 32. Open Loop Response of the Compensated Drive Control System 70 system gain was -then 64 db - 15 db = 49 db, a considerable increase over lag-lag compensation (simulation shows the limit is 64 - 11 = 53 db). In addition, the phase crossover frequency had been raised to. 2.7 x 10-* Hz, an important gain. It must be noted that the system gain in these two compensating schemes depended upon the compensator's lowest break point frequency which was arb i t r a r i l y chosen to be 10 rad. In both cases, the position sec. error constant (DC error) could be improved indefinitely by lowering this frequency and increasing the gain. This would not, however, improve the system response to amplitude errors having a frequency larger than about 10 4 rad. *i 1.6 KHz. The choice of (a^) as (6 x 10^ rad.) sec. sec. is approximately the maximum possible frequency in terms of ease of implementation and usefulness. C. Simulation Results It was deemed useful to examine the system closed loop frequency and time response. Since closed loop calculations with anything other than the simplest systems are extremely tedious, i t was decided to d i g i t a l l y simulate an e l e c t r i c a l analog of this control system using the Ecap circuit analysis program. Each system block was f i r s t modelled separately, i t s Ecap frequency response being checked against i t s Bode plot. Once a l l function blocks were correctly modelled individually, the system was then modelled by interconnecting, but not loading, the function blocks by means of the Ecap dependent current source ( T i j ) . — p=-6.e , ERROR Q&|<a-1NPUT ' - f - - l 6 - - < IK > ( \ 4 V I A A A — n | 1 1.66-10 V D f (? IK i<3 -FEEDBACK COMPENSATION -gs>;<3- -VOLTAGE DETECTOR Fig. 33. C i r c u i t used for the ECAP Simulation of the Drive Control System 72 i . Frequency Response Using the cir c u i t of Figure 33 , the open loop response of the drive control system was found and compared to the equivalent Bode plot (see Figure 32 ), showing (as expected) that the Bode plot is an accurate approximation except at system break points. The system closed loop frequency response was then found for a loop gain of 44 db (10 db gain margin, 40° phase margin) for a unit error input to the plate of the PA. This was done to examine the effect of amplitude modulation introduced by this stage. The output for the control loop both open and closed i s shown on Figure 34 . Note that the F-B system ceases to provide any useful error reduction at about 10 6 rad. = 160 KHz. sec. i i . Time Domain Response The time domain response of the compensated drive control system to a unit step error input to the plate of the PA was found using the Ecap transient response program. The results are shown in Figures 35 , 36, and . Note that without F-B, the output would be an exponential rise to (6.6) Vin with a time constant of 50yU.sec. Figure 35 shows a stable system response corresponding to a 10 db gain margin, 40° phase margin, and a unit step error input. Because of the nature of our amplitude tolerances, a smooth response of this kind is less useful than the response shown on Figure 3fc, which i s due to a system gain close to the s t a b i l i t y limit. However, when this limit is exceeded, an osc i l l a t i o n with an exponentially increasing amplitude, such as shown cn Figure 37, results. The choice of system gain must therefore be such as to place the system near the s t a b i l i t y l i m i t , but not so close that the amplifier d r i f t could cause the system to become unstable. ^ WITHOUT FEEDBACK -WITH FEEDBACK 10^ N4 IO*' w(rad./sec.) I0C Fig. 34. Frequency Response of Drive Control System with Error Input at the Plate of the PA Fig. 35. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used;. FB Amp. has 24.1 db of Gain) Fig. 36. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used; FB Amp. has 32.1 db of Gain) bsc. = 7 0 KHz A A = Change in Amplitude at the Resonator 10 14 18 22 26 3 0 t / 1 0 s e c . 37. Plot of Change in Resonator Voltage Amplitude after an I n i t i a l Unit Step Change in RF Amplitude at the PA Plate (Drive Amplitude Control used; FB Amp. has 240 db of Gain) 77 3.3 Screen Modulating System The proposed screen modulating system is shown in Figure 38 below. RF BYPASS CIRC. A V ° 2 ^ AVp AVg2 SCREEN MODULATOR F-B AMP A V p T.L.—RES SYSTEM VOLTAGE DETECTOR REF Fig. 38. Block Diagram of Proposed Screen Modulating System Note that two components of this system—the resonator voltage detector circuit and the transmission line-resonator system—are common to both amplitude control schemes. This indicates that the compensating amplifier used in the drive control system might work equally well as the F-B amp. in the screen modulating system. This is apparent when i t is noted that the proposed compensation was used to cancel the pole contributed by the voltage detector and also the lower pole due to the transmission l i n e -resonator c i r c u i t . The use of a common F-B amplifier considerably simplifies the amplitude control system. A. Screen Modulator Screen voltage modulation i s accomplished as shown in Figure 33 , where the variac i s used to set the DC screen voltage of the 4CW250,000. For purposes of control calculations, this arrangement is shown more simply as in Figure 40 t where the DC screen voltage is considered constant and hence does not enter into control calculations. Furthermore, the RF by-pass c i r c u i t , whose transfer function is shown in Figure 2ft, may be ignored i f an overall system phase crossover frequency lower /a than l O ^ rad. i s considered adequate to meet the amplitude e r r o r sec. t o l e r a n c e s . This w i l l be assumed to be the case unless measurements on the a c t u a l system show otherwise. Mains V a r i a c F-B S i g n a l F i l t e r e d DC Supply (s 800v) -fs> H. P. Program-mable Supply 1750.r 100.ru RF By-pass V g 2 F i g . 39. Block Diagram of Screen Modulating C i r c u i t FB S i g n a l ————gs> 10 See F i g . 26 AVg 2 1 + S/1.25 x 10 5 H. P. Prog. Supply RF By-pass F i g . 40. Screen Modulator 79 The screen arrangement as shown i n Figure 40 may be adequate; however, an improvement can be made by feedback compensating the Hewlett-Packard programmable power supply. This would provide advantages: (a) the system phase crossover frequency would be i n c r e a s e d , a l l o w i n g more system gain and (b) the DC screen supply would be r e g u l a t e d , removing—to a l a r g e degree—amplitude e r r o r s from t h i s source. Since the Hewlett-Packard supply has a simple p o l e , the e f f e c t of F-B compensation may e a s i l y be determined a n a l y t i c a l l y . The proposed F-B arrangement i s shown i n Figure 41 , where (H) i s chosen to be ( I O - 2 ) so that the DC screen reference (R) may be taken as 8 v o l t s . FB S i g n a l -4>> A V g 2 H F i g . 41. R e g u l a t i o n of the Screen Supply FB S i g n a l A/(L + HA) 1 + S/(l+HA)a AVg 2 F i g . 42. Equivalent Block Diagram of Figure 41 80 The equiva lent b lock i s shown in Figure 42.. For purpose of c a l c u l a t i o n , take A = 1 0 4 , which then gives Vg? ~ 10 2 = 10 2 . (3.21) e 1 + S/10 2a 1 + S/1.25 x 10 7 This c i r c u i t would then give approximately a 40 db reduct ion i n DC screen vo l tage e r r o r s , and move the modulating supply break frequency up to about 10 2 x 1.25 x 105 rad . ~ 2 x 10 6 Hz. sec . I f the amp l i f i e r p rov id ing the requi red 60 db of feedback has a 20 db/decade drop-off i n gain above a s ing l e break frequency, th i s feedback loop w i l l be abso lute ly s t ab l e . However, to increase the break frequency of the equiva lent b lock cons iderably above 1.25 x 10^ r a d . , the l o c a l F-B sec. amp l i f i e r must have a break frequency severa l decades above 1.25 x 10^ r ad . sec . Th is requirement would be very hard to meet; the re fore , one must s e t t l e fo r a lower o v e r a l l break frequency. In the remaining c a l c u l a t i o n s , a F-B compensated screen modulator having an equiva lent t r ans fe r func t ion T ( s > = 10 2 (3.22) 1 + S/1.25 x 10 7 w i l l be taken as the l i m i t on what can be achieved i n th i s d i r e c t i o n . B. Open Loop Response F igure 43 gives the open loop frequency response of the screen modulating system using an uncompensated screen modulator. A compensated modulator i s used fo r F igure 44. In both cases , the feedback amp l i f i e r p rov id ing the s i g n a l to the screen modulator provides the same compensation as was used i n the dr i ve con t ro l system; that i s , T ( S ) F _ B = K F_ B (1 + S/2 x 10 4 ) (1 + S/6 x 10 4 ) . (3.23) amp. (1 + S/10 3)(1 + S/6 x 10 5 ) fo r the feedback a m p l i f i e r . The Bode p lo t s i nd i ca t e that without screen compensation, the maximum system gain would be about 51 db, with a phase crossover frequency of 1.8 x 10 5 r ad . = 29 KHz. sec . T MAGf 0) tc re w(rad./sec.) Fig. 43. Open Loop Frequency Response of the Screen Modulating Feedback Svsten virh Lag-Lead Compensation ( Screen Modulator ± s Uncoip$ensatedT system with :ed) Fig. 44. Open Loop Frequency Response of the Screen Modulating Feedback System with Lae-Lead Compensation ("Screen Modulator is Compensated) V 83 When the screen compensation of the previous section i s used, allowable system gain is raised to about 62 db with a phase crossover frequency of 5.8 x 10 5 rad. = 92 KHz. sec. C. Screen Modulation System Simulation As for the drive control system, the Ecap program was used to analyze the behavior of an e l e c t r i c a l analog of this system. Since the only essential difference between the screen modulating system and drive control system is that the f i r s t has a screen modulator instead of an RF chain, a function block for the f i r s t (Figure 45 ) was substituted for the latter in the program. INPUT OUTPUT L = o x 10~ 8 (S creen Modulator Uncompensated) C = 8 x l C r 1 ^ (Screen Modulator Compensated) Fig. 45. Simulation of Screen Modulator Function Block i . Frequency Response Again, the closed loop system frequency response with respect to a unit amplitude error signal introduced at the plate of the PA was found. Figure i\<o shows the response for the screen with and without compensation. Also shown for comparison is a plot of the response with the F-B loop open. As is to be expected, the error reduction for low frequencies is in each case equal to 1 1 + Kp Fig. 46. Closed Loop Frequency Response of. the Screen Modulating System (Error Input at the Plate of the PA) 85 where Kp = position error constant Kp = DC gain in this case. If the modulating supply i s uncompensated, the graphs show that below about 10 3 rad. = 160 Hz, sec. the maximum error reduction w i l l be about -51 db. Above this frequency, the amount of reduction decreases by about 20 db per decade, the effect of F-B becoming minimal at about 105 rad. = 16 KHz. sec. i i . Time Response Using the Ecap transient response program and the electric analog circuits already described, the error output for an amplitude error at the PA plate was found. Figures 47 and 48 show the outputs for unit step error inputs to the PA plate for maximum F-B amplifier gain. In both cases, a significant decrease in the error as a result of increasing the feedback amplifier gain is seen. F i g . 47. P l o t of Change i n Resonator Voltage Amplitude f o r a Unit Step Change i n RF Amplitude at the PA P l a t e (Screen Modulation C o n t r o l used; Screen Modulator Uncompensated) Fig. 48. Plot of Change in Resonator Voltage Amplitude for a Unit Step Change in RF Amplitude at the PA Plate (Screen Modulation Control used; Screen Modulator Compensated) 88 4 CONCLUSIONS 4.1 RF Amplifier System The RF amplifier system described in this thesis has satisfied the steady state voltage and power requirements given in Section 1.1. The power required by the CRM cylotron (150 KW) is easily supplied by the f i n a l output tube which is capable of an output of up to 460 KW. Actual operation of the amplifier has indicated that i t i s stable: no parasitic oscillations have been observed. At present the longest period of continuous operation with a cavity voltage of 100 KV has been about 5 hours; longer periods of operation have not been possible due to problems with arcing in the resonators. 4.2 RF Amplitude Control System The two amplitude control systems described in this thesis were b u i l t with a common compensating feedback amplifier differing from the one proposed only in that i t s f i r s t break frequency was 79.6 Hz instead of 159.0 Hz. I n i t i a l tests on the operating systems showed results consistant with those calculated. For example, i t was found that both control systems showed a maximum error reduction of about 50 db which is very near to the calculated values. It was also found that the drive control system oscillated at about 50 KHz for excessive feedback gain. This compares closely with the results shown in Figures 2>t and 37 • The open loop error consisted mainly of a 120 Hz signal at about -30 db for the drive unsaturated and -35 db for the drive saturated. The 50 db reduction gained by closing the loop s t i l l l e f t the system performance short of the -94 db error ratio desired. The installation of DC filament supplies should improve this performance. To accurately evaluate the system, more comprehensive noise measurements (magnitude and frequency) w i l l have to be made in addition to checking the control system frequency response. The information provided by the latter measurements w i l l be needed to optimize the present feedback system settings or to suggest, i f necessary, improvements to the compensator. FOOTNOTES R. Richardson and M. K. Craddock, Beam Quality and Expected Energy  Resolution from the TRIUMF Cyclotron (Vancouver, 1969). 2R. R. Johnson, Tolerable RF Voltages at TRIUMF (Vancouver, 1969). -^Continental Electronics Manufacturing Co. is a subsidiary of Resalab, Inc., Dallas, Texas. 4The other 250 watts of drive required by this stage are dissipated i n the grid swamping resistor and in the tank c o i l . ^The peak voltage on each resonator i s 100 KV; push-pull operation of the 2 dees brings the gap voltage to 200 KV. The a b i l i t y to function with the operating frequency increased by 3% was i n i t i a l l y demanded since i t was desired to have a cyclotron with an optional, higher output energy. ^Thomas L. Martin, Jr., Electronic Circuits (Englewood C l i f f s , 1959), p. 195. ^These noise figures were obtained from correspondence with Continental Electronics. 920 KV series regulated DC supply, built by Cober-Electronics Inc., Stamford, Conn. 1 0Martin, p. 446. x xMachlett Laboratories, Inc., a subsidiary of Raytheon Co., Springdale (Stamford) Conn. x 2William M. Brobeck and Associates, Centre Region Model Power Amplifier (Vancouver, 1969), pp. 28-30. x 3"Tube Performance Computer," Eimac Application Bulletin, No. 5 (1952), pp. 1-5. x 4William L. Everitt, Communication Engineering (New York, 1932), p. 234. X ^ J . J. DeFrance, Communications Electronics Circuits (New York, 1966), p. 61. 1 6Samuel Seely, Electron-Tube Circuits, 2nd ed. (New York, 1958), p. 342. 90 A SELECTED BIBLIOGRAPHY Atkinson, P. Feedback Control Theory for Engineers. London, 1968. Auslander, David M. , Michael J. Rabins, and Yasundo Takahashi. Control  and Dynamic Systems. Reading, 1970. Bell, D., and A. W. J. G r i f f i n , eds. Modern Control Theory and Computing. London, 1969. Brobeck, William M. & Associates. Centre Region Model Power Amplifier. Vancouver, 1969. ' -DeFrance, J. J. Communications Electronics Circuits. New York, 1966. Everitt, William L i t t e l l . Communication Engineering. New York, 1932. Jameson, Robert A. Analysis of a Proton Linear Accelerator RF System and  Application to RF Phase Control. Los Alamos, 1965. Johnson, R. R. Tolerable RF Voltages at TRIUMF. Vancouver, 1969. Kendrick, S. H. Preliminary Design Considerations for the RF Phase Control  System for the LINAC. Chalk River, 1967. Ku, Y. H. Transient Circuit Analysis. Cambridge, 1965. Martin, Thomas L., Jr. Electronic Circuits. Englewood C l i f f s , 1959. Millman, Jacob and Samuel Seely. Electronics. 2nd ed. New York, 1951. Orr, William I. Radio Handbook. 17th ed. New Augusta, 1968. Peskin, Edward. Transient and Steady-State Analysis of Electric Networks. Cambridge, 1965. P o r c e l l i , G. Transient Analysis of a Resonant Cavity for a Separated  Orbit Cyclotron. Chalk River, 1966. Reference Data for Radio Engineers. 5th ed. Indianapolis, 1969. Richardson, J. R.. and M. K. Craddock. Beam Quality and Expected Energy  Resolution from the TRIUMF Cyclotron. Vancouver, 1969. Seely, Samuel. Electron-Tube Circuits. 2nd ed. New York, 1958. 91 Terman, Frederick Emmons. Electronic and Radio Engineering. 4th ed. New York, 1955. "Tube Performance Computer." Eimac Application Bulletin, Number 5 (1952), 1-5. Tuttle, David F., Jr. Electric Networks: Analysis and Synthesis. New York, 1965. Watkins, Bruce 0. Introduction to Control Systems. New York, 1969. 

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