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Characteristics of a reflection-type microwave modulator utilizing a reflex klystron operated in the… Domeier, Gordon Charles 1966

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THE CHARACTERISTICS OE A REELECTION - TYPE MICROWAVE MODUIATOR UTILIZING A REFLEX KLYSTRON OPERATING IN THE PASSIVE REGION GORDON CHARLES DOME IER B.Sc, University of Alberta, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Electrical Engineering .. We accept this thesis as conforming to the standards required from oandidates for the degree of Master of Applied Science Members of the Department of Electrical Engineering THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1966 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of • British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that per-mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that, copying or publi-cation of this thesis for financial gain shall not be allowed without my written permission,, Department of 0/^<^f n ca, I <7//7<?e/~/ n c, , <jL _^ The University of British Columbia, Vancouver 8'? Canada Date dtr, J 22. 6 & • ABSTRACT Experiments were carried out to determine the I characteristics of a reflection-type modulator. The modulator consisted of an E=plane T-junction that was terminated on the side-arm hy a reflex klystron operating in the passive region. Switching was accomplished hy applying a pulse to the repeller of the passive klystron. It was found that the switching characteristics were strongly dependent on the power level at the input to the modulator. Good switching characteristics were obtained at low power levels hut these deteriorated as the input power became comparable to that produced by the klystron when operating as an oscillator. Eor the particular klystron used, satisfactory switching was possible for input power levels approximately 5 to 10 dB less than the output of the switching klystron. It was also found that the modulator characteristics depended on the operating mode of the passive klystron* The desired operating mode was a compromise between power-handling capability and the switching rate. An attempt was made to explain the decrease in switching range at high input power levels by relating the observed results to an increase in the bunching parameter at the boundaries of the passive region. However, this did not ful l y account for the observed results. i i TABLE OE CONTENTS Page LIST OE ILLUSTRATIONS .................................. i v LIST OF T ABIES • o e 6 O o 0 « » » e o t > o » t > o o « « < r 0 o » « * 0 c « Q O 0 9 « « ' « O * * » ~V"i-UST OE SYTyCBOIS «#«*«* • o * * o « * « « * » * < » « » * e « * f t o a « * « « » * o * e » * *v*ii ACIOTOWIEDGEMENT c o e o » 0 O 0 * « 9 e a » o » « o c « o e 0 o o o e e * e o o o 9 o o o « * 2 t l 1* INTRODUCTION » * * o o & « » » i j ( i o f f » # « f f * » t r o » * # i » f f » f f D e O f l « * f f » « # 1 2. REE LEX KLYSTRON THEORY . 4 2.1 Small-Signal Theory 5 2.2 The Reflex Klystron as a Microwave Switching 3. EXPERIMENTAL 21 3.1 The Switching Klystron ........ 0 . . . . . « « r . . 21 %2 E-Plane •T-Junction Measurements 28 3-3 Static Switching Characteristics of the %4 Pulse Modulat ion Measurements o o . o . a o . o o o . o o a o 34 4 . DISCUSSION oo. a o » . » . ' . . . . . « . « ' . . « • . « • o » . o . . ' « . ' o e . o * . . o 46 4»1 Static Switching Tests »».*»•»'»»*»o • <ro *» o*.'o o» 46 4«2 Operation of the Reflex Klystron Near the Regenerative Boundary .............. . . . . . . . 0 * e 49 4.3 Pulse Letectxon .. o.. o o. o . . « o . <> e«- . & #o <r © o 0« 61 5 o C ONC LUS TONS » . « e o « . . e « 0 a « ' » o o . « » . « . « . * 0 * . » o o " o o » o . f t . v 66 APPENDIX I SCATTERING MATRIX ANALYSIS OE A T-JUNCTION 68 APPENDIX II PULSE COUPLING NETWORK 74 REFERENCES • • o « • o « s * & » o » « » » » « # v o « 0 a » » • © » • • • ' T T i i i LIST OF ILLUSTRATION'S Page Fig,' 2 ,1 Reflex Klystron in Schematic Form « • « « . . < , . » . . 4 Fig , 2,2 Equivalent Circuit of the Cold C a v i t y . . . . . . . . 10 Fig , 2.3 Loop-Coupled Cavity Equivalent Circuit . . . . . . 10 Fig . 2.4 Equivalent Circuit Referred to the Interaction F ig , 2.5 Admittance Diagram Showing Osci l lat ion, Regenerative Amplification, and Absorption Regions . . . . . . „ • ' . . . . . • . . • * * . . • • - * . . . . • . . . . • • • . . 15 F i g o 2o'6 E—Plane T—Junction « » . o « . « B » » ' » o o o « v « o e e IT F i g « 3*1 Basic Test Equipment Configuration * • . » • • »« • , . « . . 22 F ig . 3 «2 Klystron Mode Diagram ....v•.*•<>••••«»«»..»«• 23 F ig . 3.3 Smith Chart Plot of Normalized Input Admittance V S "V" . o . . . . . . . . . . . . . . . . . * , . o e o a o.PO ' b ' a o o&.O.. 25 r F ig . 3 . 4 Klystron-Cavity Q Curve 27 Fig.- 3.5 Scattering Coefficient Calculations . . . . . . . . . 29 Fig , 3.6 T-Junction Isolation Fig , 3.7 Test Equipment Setup for Static Tests 33 Fig , 3 . 8 Static Switching Curves Under Optimum Phasing F i g „ 3 . 9 Static Switching Curves Under Non-optimum Phasing Conditions « , « • • • * . , , . . . o . . , , o © , . o , . . 39 Fig , 3 .10 Test Equipment Setup for Pulsed Tests . . . . . . . 42 Fig , 3 « H Detected Carrier Pulse . . . . . . . * . o a « o o e » o « « o « . 45 Fig . 4»1 Minimum Output at OFF vs Incident Power . . . . . 47 F i g . 4.2 Relative Change of Output in dB from OFF to ON a o i > 0 ' 0 0 ' ' 0 ' i ? T » i O * o n f t O * o « o o o B o o * a » * « i t 4 a » e « w a o t ) O a « F ig . 4*3 Equivalent Circuit of Klystron Including F i g . 4 «4 W vs 1 with V as a Parameter . , « , » • » » » 0 0 « 56 iv Page Fig. 4«5 Repeller Current vs Incident Power . o W O O o o 60 Fig, 4«6 Equivalent Circuit of Detector System Under Steady—State Conditions 8 , o o , 9 « » o . , » o o o o o » o » * . 62 Fig, I—1 IT—Port Junction o » o , 0 o a 9 0 , o , » o o , , o , , » » , , 0 4 0 0 0 0 68 Fig, 1-2 Theoretical Switching Curve .......,,».,.»,.., 73 Fig, I I - l Pulse Coupling Network ,,,., 74 Fig, II-2 Modulating Pulse Measured Between Repeller Electrode and Anode 76 v LIST OE TABLES Page Table 3.1 Power Output of..the VA203B Klystron .......... 23 Table- 3.2 E-Plane T-Junction Scattering Matrix Elements Measured at 9000 MHz ......................... 31 Table 3.3 Pulsed Power Switching Data for the 5j Mode .. 43 Table 3.4 Pulsed Power Switching Data for the 6j Mode .. 44 Table 4»1 Data for Cal Table 4.2 Bunching Parameter X for the 5^ Switching Table 4.3 Bunching Parameter X for the 7j Switching 1 Tahle 4.4 Comparison of X _ and X , for the 5T * app calc 4 Swi*tciii^i^ Mod© © * © * o o * » » © * » o o o o » o o © o » o o © ' » © f f « 0 * 57 Table 4.5 Comparison of x a p p a n d x c a i c f o r ^ e 4^ SwJL"tcllill^ Mod.© t 9 M 9 f t « ' d « 0 S M f f « O f f a o o 9 f f o » f f 9 O f * « i 5S Table 1-1 Calculated and Measured T-JunGtion Parameters. 72 v i LIST OP SYMBOLS a - voltage attenuation factor a-,,ap....a - normalized incident waves at the ports of a junction h-,,h2.,..b - normalized reflected waves at the ports of a junction C • - equivalent cavity capacitance D - distance between grid and the repeller electrode d - spacing between the resonator grids G-^  and eQ - magnitude of electronic charge G" - sum of cavity conductance, beam loading conductance, o and electronic conductance G - generator conductance transformed to the interaction gap g - sum of generator and klystron conductance i - reverse convection current returning to the a interaction gap - current induced in the resonator - constant beam current from the cathode T l - fundamental component of induced current J (mX) m - Bessel function of f i r s t kind K - cavity transformation ratio L - equivalent cavity inductance Ji - self-inductance of the coupling loop M - beam coupling coefficient M' - mutual inductance between the coupling loop and the cavity inductance mo - rest mass of the electron Q — cavity quality factor V I 1 Qgx^ . - external cavity Q Q-^  - loaded cavity Q Q£ - loaded cavity Q when the electron beam is on QQ - unloaded cavity Q - modified unloaded cavity Q Q" - unloaded cavity Q when the electron beam is on o R - shunt resistance of the cavity R-, .R~ - output resistance of detector and input resistance of sampling oscilloscope respectively r - equivalent cavity resistance when losses are small S. . - reflection coefficient looking into the i ^ * 1 port of a junction th 3.. - emergent wave at the i port of a junction due 1*' to a wave of unit amplitude incident at the j ™ port t - time when electrons arrive at G ? from the repeller a space t' - time when electrons enter the repeller space V - amplitude of the gap voltage V - instantaneous value of gap voltage 8 V Q - constant resonator or beam voltage V r - repeller voltage VSWR - voltage standing wave ratio v Q - i n i t i a l electron velocity v(t') - velocity of electrons after passing through the interaction gap v 1,v 0,....v - higher order terms in electron velocity equation ± d n (2.1) W - absorbed power a. W. - incident power i n v i i i bunching parameter approximate value of bunching parameter X calculated value of bunching parameter X normalized input admittance of the klystron when Y-g is real normalized input admittance of the hot klystron referred to the plane of the detuned short beam loading admittance referred to the interaction gap normalized cavity admittance referred to the plane of the detuned short electronic admittance referred to the' interaction gap small-signal electronic admittance load admittance transformed to the interaction gap cavity admittance referred to the interaction gap normalized input impedance of the cavity normalized cavity impedance referred to the plane of the detuned short characteristic impedanoe of the external transmission line cavity coupling factor input reflection coefficient of the non-oscillating klystron input reflection coefficient at port 1 of the T-junction reflection coefficient of the termination on the side-arm of the T-junction fractional detuning off resonance average electron transit angle in the repeller space ix \ - wavelength in rectangular waveguide \i - electronic parameter 0 - average electron transit angle through the interaction gap w - angular frequency wQ - resonant frequency of the cavity AF - bandwidth between half-power points x 'ACKNOWLEDGEMENT Financial support through the National Research Council of Canada Block Grant A68 during the 1961-1962 and 1963-1964 terms and through a National Research Council Studentship for 1964=1965 is gratefully acknowledged. I would li k e to express my sincere thank's to Dr. M.M.Z. Kharadly for invaluable guidance during the latter stages of this project. I wish to thank Dr. A.D.-Moore for reading the manuscript and for his useful comments. Thanks are due to Messrs. .'J.E. Lewis, A.E. Shankowski, and D.J. Connor for assistance in proof-reading, Mr, A. MacKenzie for draughting work, and to Miss B. Rydberg for typing the thesis. x i 1. INTRODUCTION In microwave systems various types of modulators are used to produce RP power variations under a prescribed set of conditions. Of particular interest are microwave modula-tors where the output is a periodic train of pulses a few nanoseconds wide* For example, carrier pulses of widths ranging from 3 to 25 ns provide a convenient means of testing long waveguide antenna feeder sys tems» A display of reflections from individual transmission-line discontinuities on a time or distance scale reduces the effort required to locate hidden faults and con-struction errors in the feeder system. ; Several techniques have been ut i l ized to generate nanosecond carrier pulses. A gated travell ing wave tube modulator has been used by Beck and Mandeville. Semiconductor (2) diode pulse generators have been developed by Miyauchi, ( 3 ) Ito, and other workers. These particular devices have certain disadvantages. Travelling wave tube generators are generally very complex and expensive while semiconductor diode generators can, so far, handle only a few milliwatts of RF power without sacrif icing switching speed. . The microwave modulation system discussed in this thesis makes use of an ordinary reflex klystron as a switching element with the1 RF power supplied from a separate source. When used as a modulator the reflex klystron is not operated as an osci l lator , but is adjusted to operate as a passive device. 2 Metivier and A u doin^ f i r s t demonstrated a reflex klystron amplitude modulator where the tube operated in the passive region. Their technique utilized the variation of electron beam admittance with repeller voltage. The non-psciliating klystron terminated the side arm of an H-plane T-junction. The variation of input admittance with repeller voltage controlled the output power from the junction. (5) Whitford v has shown that a passive reflex klystron modulator may be used for the production of nanosecond-width carrier pulses with risetimes of approximately 1.5 ns. This value of pulse risetime is several orders smaller than the rise-time of pulses produced by the same klystron when used as an oscillator and switched in and out of oscillation by the appli-cation of a pulse to the repeller. The work discussed in this thesis is centred on the evaluation of the characteristics of a reflection-type modulator where the switching klystron provides a variable admittance termination on the side arm of an E-plane waveguide T-junction, A key point which is investigated is the relative change of output power between two specific states under high input power conditions. This is especially important from the point of view of pulse modulation. If the switching MLystron can tolerate a large input signal, the peak output power can be raised accord-ingly. The major points that are covered in this work are the followings (l) A study of the properties of a non-oscillating klystron t I I 3 under v a r i o u s c o n d i t i o n s when e x c i t e d by an e x t e r n a l source of RF power. ! (2) An i n v e s t i g a t i o n o f the c h a r a c t e r i s t i c s of the microwave m o d u l a t i o n network. (3) A comprehensive e v a l u a t i o n of the e x p e r i m e n t a l r e s u l t s . 4 2. REFLEX'KLYSTRON THEORY The essential features of reflex klystron theory are i discussed in this chapter in order to provide a basis for the description of the different modes of operation. In Section 2.1, f i r s t order small-signal osci l lator theory is presented and the application of the klystron as a switching element is considered in Section 2.2. A typical reflez klystron is shown in schematic form in Eig . 2.1. The origin of coordinates is the f i r s t cavity grid Gr^ . The dimension d is the spacing between the grids of V r lll-V Cavity Resonator / Electron Gun Assembly L d-Z Repeller Electrode J L Output Line Fig . 2.1. Reflex Klystron in Schematic Form the re-entrant section of the resonator. D i s the spacing between G^ and the repeller electrode. VQ is the constant resonator or beam voltage and V i s the repeller voltage. Both 5 voltages are measured with, respect to the cathode. 2 , 1 Small-Signal JTheory Simplified f i r s t order reflex klystron theory is (6 7 ) based upon the following assumptions: 1 ( 1 ) The retarding f i e l d in the space between Gg an& the repeller is uniform;.and directed parallel to the tube axis. ( 2 ) Cathode emission is space-charge limited. ( 3 ) Space-charge effects within the resonator and in the repeller space are ignored, (4) The cavity resonator has a large Q. Thus i t may be repre-sented by a lumped-element equivalent circuit in a narrow frequency range about resonance. (5) The amplitude, V, of the alternating voltage between G^  and G^  is very small compared to V Q, the beam voltage. Only terms of f i r s t order in V/VQ are retained in the simplified analysis.-(6) A l l electrons are collected after two transits of the interaction gap. Based on the above assumptions the f i r s t order theory of operation of 'the reflex klystron i s well known, A brief outline of this theory is given below. It is assumed that a voltage V- = V sinwt exists between the ideal grids which form the resonator interaction gap. Thus, electrons which enter the gap at G^  with an i n i t i a l (7 ^ velocity v Q leave grid G 2 with a velocity^ ; ' 2 v(t ) = v Q + (Jv-^  + \i v 2 + ... ( 2 . 1 ) 6 where 2e V ° 0 is the heam velocity e Q = magnitude of the electronic charge m = rest mass of the electron o and 0Q = ~ is the average electron transit angle through o the gap when no alternating f i e l d i s present. The coefficients. v l * v2* ot"9 Yn> ^ n are functions of the gap transit angle., 0Q, and the time at which an electron enters the intern-action gap. For small signals Eq. (2.1) "becomes (2.2) v(t') = v. where 0 U l ? sin (cot' - % o sin ^ M = — 3 r — - is the heam coupling coefficient and accounts for the effect of a fi n i t e gap transit angle. From Eq, (2.2) i t i s seen that the electron heam is velocity modulated. It leaves the interaction gap through and enters the repeller space where a uniform retarding electric f i e l d i s present. The electrons are brought to a stop and then travel back toward G^  i n the negative z-direction, If t is the arrival time at G0 of an electron emerging from a d. the repeller space, then the electron transit angle in the 7 repeller space i s given by 9 = wT = wt -,wt' ( 2 . 3 ) 3, By combining Eq. ( 2 . 2 ) with the equations of electron motion in a retarding f i e l d , Eq. ( 2 . 3 ) may be rewritten in the form t t 0 © = ut - wt = 9 + Xsin(wt - ^ ) ( 2 . 4 ) a n 2 where 2u v D 4u D 9 = ^ - — - — is the average transit -P.(V _ v ) ' ( i - - « E)v i n v o r ^ o o o angle in the repeller space when the alternating gap fields are no.t present, and X=fK (2.5) o X i s called the bundling parameter. By rearrangement of Eq. ( 2 . 4 ) we obtain 0 O wt = © + wt + Xsin(wt - ^ ) ( 2 . 6 ) a n - 2 Eq. ( 2 . 6 ) relates the electron arrival time,t ,to the departure a r time,t, with the gap voltage (or X) as a parameter. The current returning to the gap from the repeller region, the reverse convection current, can be calculated i f the electron distribution in both apace and time is known. When X ^> 1 , the electron arrival time, t , is a multiple-valued function of t . Thus the current density distribution is not a continuous function, and bunching is produced. By application (7) of the principle of conservation of charge i t can be shownv ' 8 that the reverse convection current entering the resonator gap is given by a 0 o 111=1 ( - l ) m J^(miX)co^mjwta-(©n+ m (2.7) where A Q = the constant component of convection current i = the constant beam current from the cathode o and J (mX) = Bessel function of f i r s t kind, m The current induced in the resonator may now be evaluated and i s given by (7) 0, \ „ .-i sin m rv, O m=l 2 wt - (© + 0 ) n -o ( 2 . 8 ) If we now consider the excitation of the resonator at the fundamental frequency^ w, only the fundamental component of induced current i s required. This is given by (2.9) s i n i l = 2 i o T J X(X) sin art _ ( 9 n + 0 o) + | Prom Eq. (2.9) and the relation for the gap voltage Y - Y sin wt the electronic admittance, Xg , referred to the interaction gap can be defined. Thus YE = GE + 3 BE = 2 1 MJn(X) o 1 V sin(© + 0 ) + j cos(9 + 0 n *o 0 n 'o ( 2 . 1 0 ) By using Eq. ( 2 . 5 ) , V can Toe eliminated and Eq. ( 2 . 1 0 ) becomes i 0 2 J X(X) -i 0 (© + 0 ) - ? n ro 2 ( 2 . 1 1 ) It can be seen from Eq. ( 2 . 1 1 ) that the phase of Yj, is dependent on while the magnitude varies with © as well as X. Since n n ©^ is related to V . the electronic admittance, Y ^ , is a function n r £i of repeller voltage. 2 . 1 . 1 Cavity Parameters A typical cavity resonator which is utilized in a reflex klystron i s of the re-entrant type. The f i e l d configura-tion is\ such as to provide a maximum electric f i e l d within the interaction gap in a direction parallel to the electron trajec-(6) tories along the tube axis. ; The cavity walls forming the interaction gap are composed of a fine grid structure which allows an electron beam to pass through the cavity. Coupling of microwave power from the cavity to an external transmission line is achieved by means of a loop,or an i r i s . In a narrow range of frequency about resonance the cavity may be represented by the lumped equivalent RLC circuit shown in Pig. 2 . 2 . C and Lare the equivalent capacitance and inductance of the resonator. R is the shunt resistance of the cavity corresponding to ohmic losses in the cavity walls. If losses are small, and the unloaded cavity Q is greater than 1 0 0 , the shunt resistance, R,may be replaced by a resistor, r, in series with I as shown in Pig. 2 . 3 . In this equivalent circuit the external transmission line is coupled to the cavity by means of 10 R C Fig. 2.2. Equivalent Circuit of the Cold Cavity o 1 Fig. 2»3» Loop Coupled Cavity Equivalent Circuit a loop with self-inductance,and mutual inductance5M . The normalized input impedance of the cavity referred to terminals 1-1 (Fig, 2.3) i s given hy 7 Z i n . X l M Z c = T~ = *T + 0 o (co M ' ) 2  o ' (2.12) Z r< 1 + 3— o. I r CO i +(TT) 'CO where Z q = characteristic impedance of the external'trans-mission line X^ = reactance of the coupling loop (assumed lossles and co = angular frequency. 11 X By choice of special reference planes spaced ^ apart in the ^ 1 (8) transmission line the term ^ — may he eliminated. v ' When the o cavity is tuned far off resonance the input impedance measured at these particular reference planes i s zero.' These reference planes are called planes of the detuned short. Now. referred to the plane of the detuned short, the normalized input impedance is given hy \ = 6 — s r < 2 - " > VO X CO CO o where and B = cavity coupling factor co L Q = —— is the unloaded cavity Q. o r • In a narrow hand of frequencies about resonance co co — CO ( £ - - » 2 ( — — S ) = 2 S ( 2 . 1 4 ) CO CO CO o • o Combining Eq„ ( 2 . 1 4 ) with E q . ( 2 . 1 3 ) we obtain Z c - 1 + J2Q r - Q 1 ( 2 . 1 5 a ) Q0 ext where Q ^ext ~ p - ^ e e x ^ e r n a - ^ - cavity Q„ The normalized input admittance referred to the plane of the detuned short i s given by 12 o 2.1.2 Klystron Input Admittance with the Electron Beam On When evaluating the input admittance of the reflex klystron the effect of the electronic admittance discussed in the previous section should he considered. In addition, the energy required to velocity modulate the heam as i t passes through the f i n i t e interaction gap should also he taken into consideration. This heam loading can he accounted for hy a heam loading admittance = + jB-g. Thus, the1 equivalent circuit of Fig. 2.3 can he modified hy adding circuit elements in parallel with C. This procedure is justified since the cavity constants r, I, and C as well as Y^ and Y^ are a l l referred to the interaction region with the gap voltage«V , as the independ-ent variable for circuit calculations. ?^ Referred to the plane of the detuned short., the normalized input admittance of the hot klystron i s given by. - ^ + J2«j£t + Y E % 5 i (2.16) U O 0 where Y^ = the electronic admittance as shown in Eq. (2.11) and Q Q i s the modified unloaded cavity Q given by m C Q = 77-—~7T— (2.17) o G R +GB G-£ is the cavity shunt conductance. G-g, the beam loading con?-ductance, accounts for the energy which is extracted from the 13 cavity fields in order to velocity modulate the electron heam. x Qext Now, i f in the third term of Eq, (2.16), y - 2 ^ is R replaced hy Qex^(Q~) ? (2.16) hecomes o yr s V + j 2 Q <T + Y E Q e x t ( ^ ) (2.18) Qo o Eq. (2.18) is a f i r s t order approximation to the input admittance of a reflex klystron. It can he seen that Y is a function of several variables 0 However, the most important consideration in this work is the variation of Y with repeller voltage when a l l other parameters are fixed. 2.1.3 Operating Regions of the Reflex Klystron The equivalent circuit shown in Eig. 2.4 represents (6 7) the klystron as observed from the interaction gap, 7 ' where Y L ~ G L = ^ e -'-oa^ admittance transformed to the gap Y B = + jB-g = the beam loading admittance referred to the interaction gap and Y^ = the cavity admittance referred to the gap. Pig. 2,4. Equivalent Circuit Referred to the Interaction Gap 14 Under steady-state conditions the reflez klystron (7) oheys the usual criterion for an oscillator, ' i.e. the sum of the circuit admittances equals zero, or Y E + Y R + Y B + Y L = 0 Separating real and'imaginary parts we obtain (2.19a) and G B + G R + G B + G L = 0 BE + BB + BR = 0 (2.191a) (2.19c) A necessary condition for oscillations to start is that the sum of the circuit conductances be less than zero, i.e, Re Y Es (2.20) where "Es = the small-signal electronic admittance. If the gap voltage 7, i s zero, X = 0 (Eq. 2 . 5 ) , ^(Xj/Xft?^, and the electronic admittance becomes Y B(X-*0) = Y E s O -3 ( ^ n + 0 o ) - f (2.21) When the klystron starts to oscillate the gap voltage increases and the coefficient J^(X)/X in Eq. (.2.11) decreases u n t i l Eq. (2.19h) is satisfied. The susceptance relation (2.19c) provides the information required to solve for the steady-state oscillation, frequency. Oscillations are possible for a l l values of © n and X such that Eq, (2,19a) is satisfied. The small-signal 15 admittance spiral and the circuit admittances are shown in Pig. 2.5. The oscillation region l i e s to the l e f t df the load line 0-0 . Pig. 2.5. Admittance Diagram Showing Oscillation, Regenerative Amplification, and Absorption Regions Output power from the klystron oscillator depends (6) on circuit loading and internal losses. The power produced is maximum when the fundamental component of induced current is maximum and Y-g is real and negative. This condition occurs when (©^ + 0 Q) equals 2rt(n + ^ ) , where n is a positive integer. It has been s h o w n t h a t i f Gf-^  i s very large, oscillations can he suppressed. If the electrode voltages are set to values which result in oscillation under normal circuit • loading, the input reflection coefficient of the klystron w i l l 16 be greater 'than unity in magnitude. When excited by an external RF source the reflex klystron functions as a one-port regenera-tive amplifier. The conductance condition denoting the boundaries of the regenerative amplification region is given by -(G L + GB + GR) <R .e [Y E s] < - (G B + GR) (2.22) ' The regenerative region i s shown as the-cross-hatched area in Fig. 2 ,5 . Now, consider the region on the admittance diagram shown in Fig. 2.5 where Re Y E s j ^ - ( G B + G R ) » In this region oscillations are not possible and the input conductance of the klystron is positive. The variation,of input admittance,with in this passive or absorption region can be utilized as a means of amplitude modulating an RF signal. For low-power input signals the simplified klystron analysis shown in Section 2.1 predicts a variation in Y^ proportional to the coefficient J^(X)/X, When the power incident on the passive klystron approaches a value equal to i t s output as an oscillator in the lowest mode, a more precise analysis is required to show the variation of Y^ with bunching parameter, X. A comprehensive analysis of electron bunching theory is (6) given by Hamilton, 2.2 The Reflex Klystron as a Microwave Switching Element In this section the use of a non-oscillating reflex klystron as an amplitude modulator of a separately supplied RF signal is considered^ The klystron is operated in the absorp-tion region. When a modulating waveform is applied to the 17 repeller electrode a corresponding variation of input admittance with 7^ is produced,* 2.2*1- Microwave Switching Network Since a reflex klystron is a one-port device, a means of separating the incident and reflected signals must he provided, A hybrid T-junction or a 3 arm T-junction may he used. The principal disadvantage of the hybrid junction is that i t can be matched over only a very narrow bandwidth, In this work a 3 arm E-plane T-junction has been u t i l i zed . Consider the E-plane T-junction shown in Eig . 2,6, The important characteristics are given below, A more detailed analysis of the junction is given in Appendix I, Main Arms Eig, 2,6. E-Plane T-Junction The power emerging from- the output arm due to power incident at the input arm is a function of the reflection coefficient of the termination on the side arm. In terms of 18 the junction scattering matrix the normalized f i e l d components at the ports of the junction are related in the following manners 311 S 12 S l 3 a l S 12 S 2 2 -s 1 3 a 2 (2,23) To, D ^ 1 3 S '33 let arm 3 he terminated in a load with reflection coefficient r 3 = r3 Arm 1 is fed by a matched generator an'd arm 2 i s terminated in a matched load* The normalized output at arm 2 is given hy h 2 = a-^  S. 12 3 _ (2.24a) and the input reflection coefficient at arm 1 i s given hy (2.24h) a-, 1 - Q S 3 J The output power from arm 2 is given by l 3 2 i 2 ~ a n s . r ? 3 i / D 12 (2.25) 2 . 2 . 2 Klystron-T-Junction Amplitude Modulator If a klystron operating in the passive region i s connected to the side arm of a T-junction, the system can he !9 used as an amplitude modulator through changing the repeller voltage. The output power from the Tujunction, at.arm 2, exhibits the greatest change when the shunt admittance at the junction changes from 0 to o o , This junction admittance, in turn, depends on the admittance looking into the klystron or on the input reflection coefficient, , at the klystron terminals. ! 7! i s related to the normalized input admittance in of the klystron by 1 in ' i n e ^ l - ^ J - . ( 2 - 2 6 ) 1 + Y [7^ varies both in phase and in magnitude with repeller voltage. It i s shown in Section 3.3 that the phase shift of P "between - l u l l end points decreases as the switching mode number m increases. The mode number m is defined by determining the phase angle (@ n + 0 Q) such that Y-g i s real. At these points (©n + 0 ) = 2jc(m + j ) . The entire branch of the admittance curve between th the regenerative boundary i s called the m switching mode.' An optimum switching mode i s one where the phase shift of ("7^  between end points approaches 180 degrees. Another important factor is the switching rate or rate of change of HT^  with V . Switching rate increases with ' mode number m in a manner similar to the increase of electronic (7) tuning rate of an oscillating klystron. ' 2.2,3 .Power-Handling Capacity of the Modulator The non-oscillating klystron may he expected to- switch power less than or equal to the power produced by the klystron 20 when operating as an oscillator. However, deterioration of the switching characteristics has heen observed w' to occur princi-pally at the boundary of the passive region. As the input power is increased, breakdown at the houndaries should begin at the highest switching modes. This can he seen from Eq, (2,5) whereby the hunching parameter,X,increases with mode number, m, © n is a function of m and i f Y/Y remains constant, X increases with V 21 3. EXPERIMENTAL In order to determine the characteristics of the microwave modulator (T-junctlon and switching klystron combina-tion) i t was f i r s t necessary to test the individual components of the system. Section 3.1 i s concerned with tests on the switching klystron. The T-junction scattering matrix and isola-tion measurements are discussed in Section 3.2, Static tests on the modulator are described in Section 3»3 while the results of pulse tests are given in Section 3.4* 3.1 The Switching Klystron The X-band klystron used was a VA203B/6975 which had an internal cavity, waveguide output, and mechanical tuning. The coupling factor of the main cavity was mechanically variable. This tube is normally used as a local oscillator with a nominal power output of 50 mW in a frequency range from 85Q0 to 9600 MHz. 3.1.1 Reflex Klystron Mode Diagram The schematic diagram of the basic microwave test setup is shown in Eig. 3,1. At a fixed value of beam voltage the klystron was adjusted for an operating frequency of 9000 MHz at the centre of the oscillatory mode. The oscillation modes were displayed on an oscilloscope. The data obtained from mode displays over a range of beam voltage from 200 volts to 350 volts are plotted in Eig. 3.2. X-13 Klystron Power Supply Power Meter Isolator and Pad I Directional Coupler and Bolometer Cavity Wavemeter Precision Slotted Component Rotary Line V Being Attenuator Probe and Tested Detector •> VSWR Meter Pig, 3.1. Basic Test Equipment Configaration IV) ro 23 100 150 200 250 300 350 Beam Voltage - Volts Fig. 3.2. Klystron Mode Diagram 3.1.2 Power Measurements Power output at the oscillatory mode centre was measured under CW conditions at a frequency of 9000 MHz with the heam voltage set to 250 volts. Results of the power measure-ment test are shown in Table 3°1° Table 3 , 1 Power Output of the VA203B Klystron (V = 250V. f = 9000 MHz) Oscillation. Mode Number, n Repeller Voltage Power Output dBm Power Output Milliwatts 5 6 7 207 1 3 1 80 + 16.8 + 15.7 + 1 2 , 5 47.9 37.2 17.8 24 3.1.3 Input Admittance of the Non-Oscillating Reflez Klystron Standard slotted l i n e techniques,details of, which (12) are described i n Sucher and Pox, ' were u t i l i z e d to carry out the measurements. The klystron was i n i t i a l l y adjusted i n the lowest o s c i l l a t o r y mode f o r an operating frequency of 9000 MHz and i t s parameters were not altered during subsequent ezperiments. A l l admittance curves of the passive klystron were referred to the plane of the detuned short of the cold cavity. These reference planes were found by detuning the cavity mechanically f a r off resonance and loca t i n g points along the slotted l i n e where the standing wave r a t i o was a minimum. At the extreme edges of the passive region the standing wave r a t i o was very high. When measurements were extended into the regenerative region, the standing wave pattern was found to be highly ir r e g u l a r and meter readings were er r a t i c and subject to sharp fluctuations. Standing wave patterns i n the boundary region were considered v a l i d only i f the spacing between minima was and i f the pattern near the minima was regular. The input admittance curves for the VA203B are shown i n Pig. 3-3a to 3.3d. The values of input admittance referred to the plane of the detuned short as a function of re p e l l e r voltage are plotted on a Smith chart. Incident power was varied i from + 6dBm jto + 19dBm f o r switching, modes with m = 5, 6, and , i 7. i Fig. 3 .3 . Smith Chart Plot of Normalized Input Admittance vs V r Fig. 3.3. Smith Chart Plot of Normalized Input Admittance 27 3.1.4' Cold K l y s t r o n - C a v i t y Q Measurement. The c o l d c a v i t y Q i s the value of Q measured with the e l e c t r o n heam o f f . The standard VSWR versus frequency technique (12) was u t i l i z e d ' f o r t h i s measurement. VSWR p l o t t e d a g a i n s t . frequency i s shown i n P i g . 3«4» F i g . 3.4. K l y s t r o n - C a v i t y Q Curve The VSWR at resonance was 2.20. Since the c a v i t y was over-coupled, the c o u p l i n g f a c t o r , B, was a l s o equal to 2.20. The VSWR f a r o f f resonance was'greater than 60, and th e r e f o r e transducer l o s s could he neg l e c t e d . Thus the h a l f (12) power VSWR could he d i r e c t l y c a l c u l a t e d ' and was found to he 7.17. As the h a l f power VSWR was known, the bandwidth between h a l f power p o i n t s could be determined and t h e r e f o r e f ! ^1 = AF c o u l d ^ e c a l c u l a t e d . was found to be 288. Hence, Q 0 = Qj.(p' + 1) = 923 and Q g x t = Q L ( £ - ± J * ) = 419. 28 3.2 E-Plane T-Junction Measurements The scattering coefficients of the T-junction were calculated from data obtained at the test frequency of 9Q00 MHz. The junction terminated the slotted line while a' 'precision shorting plunger provided a variable reactance termination on a second arm of the junction. A matched load, for which the VSWR was less than 1.01, terminated the third arm. The layout of test equipment used is shown in Eig. 3.1. The normalized input impedance referred to certain reference planes, known as (18) the characteristic reference planes of the junction, v ; was measured for a series of specified positions of the shorting plunger. A second set of measurements were carried out with the positions of the plunger and the matched load interchanged. Test data are plotted in the reflection coefficient plane in Eig.- 3.5a and 3.5h. The graphical construction necessary for calculation of the scattering matrix elements is shown on these diagrams. Fig. 3»5a shows the plotted data for measurements between arm 1 and arm 3 while Eig. 3«5b applies to measurements between arm 1 and arm 2. Scattering matrix elements derived from Fig. 3.5a and 3-5b are given in Table 3.2. Phase angles are measured with respect to the characteristic reference planes of the junction. Junction isolation, as defined in Appendix I, was (12) measured by a substitution techniquev ' in 100 MHz steps in a frequency range from 8600 MHz to 9500 MHz. Test results are' shown in Fig. 3.6. 29 Fig. 3.5a. Scattering Coefficient Calculations 30 Fig. 3.5b. Scattering Coefficient Calculations 31 Table 3.2. E-Plane T-Junction Scattering Matrix Elements Measured at 9000 MHz Eiemint Magnitude Phase Angle S±1 0.268 181.4 S 2 0.694 178.8 S n„ 0.624 180.2 13 S 2 2 0.270 187.2 S „ 0.446 179.0 33 Eig. 3.6. T-Junction Isolation Curve 32 3.3 Statio Switching Characteristics of the Modulator Switching characteristics of the modulator were determined hy means of static tests. The klystron was supplied with fixed electrode potentials and a continuous RF signal was fed into the input arm of the junction. The repeller voltage was varied slowly. In essence, the static tests pertain to virtually steady-state conditions in contrast to the transient conditions which prevail when the klystron is pulse modulated. 3.3.1 Test Equipment Configuration The test equipment setup used during static tests is shown in Fig. 3«7» The Varian X-13 klystron provided a continuous 9000 MHz input signal to the modulator. Incident power and frequency were monitored at Power Meter #1 and output power was measured at Power Meter #2. A squeeze-section phase shifter was placed between the switching klystron and the side arm of the T-junction so that the variable input admittance of the klystron could be correctly phased with, respect to the characteristic planes of the junction. 3.3.2 Test Conditions Experimental data were obtained under two sets of conditions. In the f i r s t case the repeller voltage of the switching klystron was set to a value corresponding to the boundary of the passive region. At this point the input admit-tance of the klystron was almost purely imaginary. Then the phase shifter was adjusted so that minimum power was obtained Power Meter #1 Isolator and Pad Directional Coupler and Bolometer Cavity Wavemeter I E-Plane Precision T-Junction —*>- Rotary —9" Bolometer Attenuator < Phase Power Shifter Meter #2 Power Switching Supply >• Klystron VA203B Pig. 3.7. Test Equipment Setup for Static Tests 34 at the output arm of the junction. Small changes in Y^ were required ,at the same time in order to ohtain the minimum power condition. This procedure i s analagous to that used in the case where a shorting plunger i s adjusted so that the plane of the short i s brought into coincidence with the characteristic plane in the side arm. This minimum output power condition was designated as the OFF position of the modulator. When the input power was increased, both the phase shifter and the repeller voltage were adjusted to produce the minimum possible output in the OPP position. After calibration in the OPF position, output power versus repeller voltage was recorded for 1 1 1 a range of input power. Test data for the 6j,- and 7^ -switching modes under optimum phasing conditions are plotted in Pig. 3.8a to 3.8d. Another set of tests, under fixed phasing conditions, were carried out. For'a low level input signal, the modulator was set at the OPF position by adjusting both the phase shifter and the repeller voltage: As the incident power was increased the phase shifter setting was not altered from the reference setting established at a low power level. Under this fixed phasing condition, power output versus repeller voltage for the three switching modes is shown in Fig. 3.9a to 3.9c. 3.4 Pulse Modulation Measurements The schematic of the test equipment used for pulsed tests is shown in Fig. 3.10. The modulator was i n i t i a l l y calibrated in the OFF 35 Pig-'. 3.8a. Static Switching Curve Under Optimum Phasing Conditions - 5T Switching Mode Fig . 3.810. Static Switching Curve Under Optimum Phasing Conditions - 6 j Switching Mode Fig. 3 . 8 3 . Static Switching Curve Under Under Optimum Phasing Conditions - 6 7 Switching Mode 38 Fig. 3.8d. Static Switching Curve Under Optimum Phasing Conditions - 7T Switching Mode 39 Fig. 3.9a. Static Switching Curve Under Non-optimum Phasing Conditions - 5j Switching Mode 40 Fig. 3 . 9 b . Static Switching Curve Under Non-optimum Phase Conditions - 6 j Switching Mode 41 a Ti U & O PH - P I +15 +10 +5 W. = + 16 dBm in V J i L 80 100 120 V p - Volts § Ti CD IS o -p +15 +10 +5 : v W. = + 19 dBm in 80 100 120 V r - Volts Pig. 3.9c. Static Switching Curve Under Non-Optimum Phasing Conditions - 7T Switching Mode RF Source and Power Monitor E-Plane T-junction Isolator Precision Attenuator Phase Shifter " Pulse Generator Detector Sampling Scope -ft-Switching Klystron VA203B ««— Pulse Coupling Network V Switching Klystron Power Supply V. 0 Fig a 3.10. Test Equipment Setup for Pulsed Measurements 43 position under the optimum phasing conditions discussed in Section 3=3.2. Output power was measured at the OPP point with a power meter. During i n i t i a l calihrations the pulse generator was off. Pulses were coupled to the repeller electrode hy means of the !pulse coupling network. This network isolated the pulse generator from the high repeller voltage but simultan-eously provided a path for the modulating waveform. This is discussed in Appendix II. The polarity of the modulation pulse was chosen so that the switching klystron would be driven into the ON position within the passive region.. The output from the modulator was detected and then displayed on a sampling oscilloscope. The deflection on the oscilloscope was noted. The peak pulsed output power in the ON position was measured by a substitution method. The pulsed power data for the' 5^ mode for a modulation pulse amplitude of 50 volts and a half amplitude width of 40 ns is shown in Table 3. Table 3.3. Pulsed Power Switching Data for the 5^ Mode Incident Power Peak Output Relative Change in dBm in dBm OPP to ON in dB + 10 +7.0 31.5 + 13 + 9.5 32.5 + 14.5 + 9.5 30.0 + 15.5 + 11.5 21.5 +17 +13.0 18.0 + 19.5 + 16.0 12.0 44 Table 3.4 shows, the pulsed power switching data for the 6^  mode with a pulse width of 40 ns and an amplitude of 40 volts. Tahle 3.4. Pulsed Power Switphing Data for the 6j Mode Incident Power Peak Output Relative Change in dBm in dBm OFF to ON in 9B + 10.0 + 6.5 29.5 + 13.0 + 8.8 31.8 + 16.0 + 12.2 16.6 + 19.0 + 15.6 10.1 3.4.1 The Detector Two types of detectors were used in these experiments, The f i r s t was a H-P 423A broadband coaxial detector, the output of which was large enough to produce a jitter-free oscilloscope trace. The envelope risetime was slightly less than 10 ns. In Fig. 3.11 an example of a pulse which was detected with the H-P 423A detector is shown. The horizontal scale is 10 ns per major division and the vertical scale is 10 mV per major division. The modulator input was 14.5 mW and the modulation pulse amplitude was 50 volts. The second type was a tuned detector u t i l i z i n g a 1N23C diode backed by a sliding plunger. When this detector was tuned for maximum sensitivity, the pulse envelope risetime was 15 ns. The output voltage from this detector was approximately three times that of the broad-band coaxial detector. The detected pulse envelope was found to exhibit a 20$ overshoot. The origin of the overshoot was traced to the pulse coupling network. This is discussed in Appendix II. Fig. 3.11. Detected Carrier Pulse 46 4 . DISCUSSION 4.1 Static Switching Tests The static switching curves shown in Pig. 3.8a to 3.8d were obtained under the optimum phasing condition discussed in Section 3 .3.2. These illustrate the characteristics of the modulator as a function of input power. For the production of pulses the two factors of importance are the minimum carrier output signal in the OFF position and the relative change in output from the OFF to the ON position. (The ON position was defined as the condition where the output power was a maximum.) The minimum output power versus input power is plotted in Fig. 4.1a to 4=lc. The sloping line on each figure i s the minimum output when a shorting plunger is located at a character-i s t i c :reference plane in the side arm of the junction. It can be seen that 'the minimum output begins to increase in a non-linear manner for input powers less than the power output of the individual modes when the klystron i s oscillating. The relative change in output power from OFF to ON (the switching range) is shown i n Fig. 4.2a to 4.2c as a function of incident' power. The switching range i s limited for two reasons. Fi r s t , the output power in the ON position i s not the maximum obtainable because the klystron switching curves (input admittance versus repeller voltage) are not ideal. For low input power the change in reflection coefficient phase angle between end points is not 180 degrees and for high input power the input admittance i s not purely imaginary. The second is the rapid increase of minimum output (as the input power is Fig, 4»1» Minimum Output at OFF T S Incident Power 48 PQ 30 xi © ttO o t> 10 H CP # +10 +15 +20 W^n-Inoident power - dBm (a) 5^ Switching Mode pp •a CO 9 03 O 0 t> •H -P c6 H O « 30 20 10 +10 +15 +20 W. -Incident Power - dBm in (h) 6^ Switching Mode $p 20 3 O d) t> •H - P cS H co P« 10 +10 *15 +20 Win»Incident Power - dBm (c) 7^ Switching Mode • Decreasing V X Increasing V Pig. 4.2, Relative Change of Output in dB from OFF to ON 49 increased) when the modulator is biased OPP, This is considered to he the major reason for the decrease in switching range. The dependence of the input admittance of the passive klystron on incident power i s illustrated in Fig. 3.3a to 3.3d. The most significant effect is the change in the input admittance, J Y , near the boundary of the passive region.. This has the greatest effect on the performance of an ON-OFF modulator. The i shift in phase of Y (under constant phasing conditions of the modulator) results in a degradation of the static switching curves as shown in Pig. 3.9a to 3.9c« 4.2.0 Operation of the Reflex Klystron Near the Regenerative Boundary The nonlinear increase in minimum output of the modulator (under optimum-phasing conditions) with increasing input power has been mentioned in Section 4.1. This occurs very close to the boundary of the passive region where the-measured values of input admittance (or reflection coefficient) are inaccurate because they depend on the measurement of very large VSWR. When the static switching tests were carried out, several effects were observed near the boundary region. For small input power the transition into the regenerative region was abrupt (input refection coefficient greater than unity) and was accompanied by a large- increase in output power. As the input power was increased a variation in repeller voltage toward the regenerative region resulted in a smoother increase in output. These observations would suggest that i f the power I 50 incident on the klystron became large enough, the bunching parameter might become so large that the input reflection coef-ficient near the regenerative boundary no longer attained a value of unity. If this occurred the minimum output when the modulator was biased OFF would be higher than expected. In the following sections an attempt is made to calculate the gap voltage, V, and subsequently the bunching parameter, X, under variable incident power conditions; 4.2.1 Calculation of the Cavity Transformation Ratio In the non-oscillating region the klystron can be represented by the equivalent circuit shown in Fig. 4.3. The Z . o -vVAW-K R E Fig. 4.3. Equivalent Circuit of Klystron Including Transformer components are referred to the interaction gap. They include cavity admittance, beam loading admittance, and electronic admittance. The transformer connecting the generator to the i equivalent circuit is assumed to have a constant real transfor-(11) mation ratio K under a l l conditions. Assume that the non-oscillating klystron is;excited by an RF source at the resonant frequency of the cavity and that 51 the r e p e l l e r v o l t a g e i s s e t such t h a t Y E i s p u r e l y r e a l . L e t ¥ he t h e power d i s s i p a t e d i n the c a v i t y . The gap v o l t a g e , V, i s r e l a t e d t o ¥ hy a where g = G + G & o u (4.D (4.2) Conductance G- r e p r e s e n t s the g e n e r a t o r conductance t r a n s f o r m e d t o the gap. G = G^ + G^ + Re 0 l l a (4.3) I n t h e e x t e r n a l t r a n s m i s s i o n l i n e t he n o r m a l i z e d i n p u t conductance i s ; g i v e n hy Re KG (4.-4) Prom resonant c a v i t y theory^®'^ the f o l l o w i n g e q u a t i o n may he d e r i v e d : where II ir £o Si (4.5)' and Q'k = l o a d e d c a v i t y Q when t h e e l e c t r o n heam i s on Q Q = unloaded c a v i t y Q under i d e n t i c a l c o n d i t i o n s . Combining Eq. (4.5) w i t h Eq. (4.4) we o b t a i n Re [V] - Kg 2j (4.6) S u b s t i t u t i n g the v a l u e o f g o b t a i n e d from Eq. (4.6) i n t o Eq. (4.1) y i e l d s 52 2 ^ From Eq. (4.7) we can solve for the transformation ratio K. ii K ^ Y -ft (4.8) a Q L where Y = normalized input admittance of the klystron when it II Y-p, i s real. Qrt and are given hy Q0 = - f 2 ^ (4.9) and "-4-= -4 + (4.10) QT CT wext L O II Q. By use of Eq. (4.9) and Eq. (4.10), the factor —£ may he Q L eliminated from Eq. (4.8) which reduces to v 2 K = ( | w - ) ( l + Y) (4.11) a In order to calculate K, the parameters Y, ¥ , and V must he measured. ¥ and Y can he measured as outlined previously. The gap voltage, V, however was estimated hy an indirect method. The VA203B klystron was tested under the same conditions used for input admittance measurements. A sensitive ( l uA F.3.D.) low resistance galvanometer was connected in series in the repeller circuit. With the repeller voltage adjusted so that i Y was real, the klystron was excited with an increasing value of incident power in the 8^ switching mode. (Ideally we would / 5 5 have preferred to calculate K for the 5^ mode hut this was impos-sible because the available RF'power was insufficient„) The input power, Wj_n? was increased u n t i l a positive, galvanometer deflection of % i " 0 ^ was. observed thereby denoting interception of electrons at the repeller, (The value of the.positive repeller current was required to be as small as possible.) Test results are shown in Table 4.1. Table 4.1. Data for Calculation of E V r VSWR W w i n c i'in 1 -V w = a 25S 1 - [7 Ixn W. in 55 2.5 50.5 mW 0.4 0.429 0,816 77 41.2 mW Using the above data the calculated value of K from Eq, (4.11) is 10.1 x 10^ ohms. 4.2.2 Calculation of V and X for the 5j and 7^ Switching Modes The value of K determined in the previous subsection w i l l be assumed to hold for.the 5j and 7^ modes. Thus we can proceed to calculate V and X, Rearranging Eq. (4»7) gives 54 where 2 K W a Re (Y !) i Q. (4.12) W = 1 - W i n i s t l i e P o w e r dissipated in : magnitude of the input reflection coefficient and Re(Y ) = normalized input conductance The values of V and X in Tahle 4.2 have been calculated for incident power levels of + 6 dBm and + 19 dBm for the 5^ switching mode. Table 4.3 shows the results under the above conditions for the 7^ switching mode. Table 4.2. Bunching Parameter X for the 5^ Switching Mode V r W. = m + 6 dBm W. = m + 19 dBm V X V X 223 26.5 1.14 177.2 7.64 230 24.2 1.04 127.6 5.50 240 22.7 0.98 86*2 3.72 260 16.4 0;71 74.2 3.20 270 15.7 0.68 73.6 3.17 280 16.1 0.70 77.1 3.33 290 17.5 0.75 96.2 4.14 300 24.3 1.05 114.1 4.92 310 28.1 1.21 149.5 6.44 320 28.0 1.20 177.6 7.66 330 28.2 1.22 183.8 7.94 55 Table 4.3° Bunching Parameter X for the 7T Switching Mode V r ¥. = in + 6 dBm in + 19 dBm Y X > V X 90 18.2 1.11 124.9 7.63 95 14.9 0.86 100.5 6.14 100 12.4 0.75 65.8 -3.95 105 10.7 0.65 62.9 3.83 110 8.9 0.55 78.7 4.81 115 8.7 0.53 155.0 9.55 The most significant feature of the results in Tables 4.2 and 4.3 is the variation in gap voltage over the switching mode even though the incident power i s constant. At. the centre of the non-oscillating region, both the gap voltage, V, and the bunching parameter, X, have their minimum values and they increase as the boundary region i s approached. 4.2.3 Variation of Bunching Parameter with Incident Power ¥hen the electron beam i s off and the cavity i s excited by RF power at the resonant frequency of the cavity 9 the voltage across the interaction gap increases as the square root of the dissipated power. The r a t i o of dissipated power to incident power i s fixed because the davity parameters are independent of the excitation^ ¥hen the electron beam i s on, the klystron circuit can be studied under the assumption that i t can be simulated by a lumped-element equivalent c i r c u i t ^ where the circuit 56 elements are referred to the interaction gap. The gap voltage, V, is related to the power dissipated as shown hy Eq. (4.1). 1 The electronic admittance^ Y^, and consequently, Y , i s a function of the hunching parameter (or gap voltage V), In Eig. . 4 . 4 the dissipated power, ¥ , has been plotted against the incident power, ¥ i n , with as a parameter. It can he seen that the relationship is linear. Erom Eq. (4,12) i t can he ¥. - Inoident Power :'inm¥ i.n Fig, 4 . 4 . ¥ vs ¥. with V as a Parameter a m r 2 seen that V varies linearly with ¥ and hence with ¥. .. Thus, a m the hunching parameter, X, varies as the square root of 11. . 57 4.2.4 Discussion of the Calculated Values of Bunching Parameter X The calculated values of hunching parameter; x c a]_ c> (Tables 4,2 and 4.3) are compared with those obtained by using Eg, (2oll) (X ) in Tables*4.4 and 4.5 for the 5T and 7T switching modes, respectively. Table 4 . 4 . Comparison of X a p p and X c a l c for the 5j Switching Mode V r X app : "^calc X _ /X calc' app 223 2.41 7.64 3.17 230 1.45 5.50 3.77 240 0.30 3.72 -12.4 * 260 1.93 3.20 1.67 270' Accuracy of Measured Susceptance Poor 280 1.04 3.33 3.20 290 1.31. 4.14 3.16 300 1.70 4.92 2.90 310 2.29 6.44 2.81 320 1.71 7.66 4.47 330 1.73 7.94 4.59 The values of X were obtained by using the input admittance app data shown in Pig. 3.3a and 3.3d. Since the input admittance was measured at the resonant frequency of the cavity, Im Y provides the major contribution to the input susceptance. With J x ( x ) V fixed, Im r ' Y E is proportional to — ^ — as shown in Eq. (2.11). * This value is inexplicable. 58 Table 4 . 5 . Comparison of x a p p a n d x c a i c f o r ^ e ^4 Switching Mode V r X app ^calc X , /X calc' app 90 3*27 7.63 2.33 95 2.68 6 ,14 2.29 100 2.38 3.95 1.66 105 Accuracy of Measured Susceptance Poor 1 1 0 2.0 •4.81 2 . 4 1 115 3.0 9.55 2.65 The power output of the switching klystron was +12.5 dBm in the highest mode (Table 3.1), therefore the admittance measured with = + 6 dBm was considered to he a small-signal value. Admittance measured at an incident power of + 19 dBm was considered J (X) to be a large-signal value. Por small signals — ^ — <^ The ratio of large-signal susceptance to small-signal susceptance 2J 1(X ) is — — — w h e r e X i s the approximate value of bunching app parameter under large-signal conditions. It can be seen that the values of X and X , u app calc differ considerably both in the 5^ and 7^ modes. The ratio X n /X is quite irregular but most of the values in the calc app 0 5^ mode were centred around a value of 3«3 and in the 7"| mode around 2,3. Errors in determination of Z can only account partially for this discrepancy as- i t is assumed that Z is constant for 59 a l l modes while X -, /X _ varies between 1,67 and 4*59 for the calc app two modes. It would appear that there are other factors which come into effect for different modes. The error in calculation (a) of K has been investigated hy other workers and is discussed in the following section, 4.2 ,5 Errors in Calculation of K The parameters necessary for the calculation of K were measured at the instant a very small repeller current was noted. Under simplified theory, the electrons constituting the current would be those which made one transit of the inter-action gap and acquired an energy corresponding to the gap volt— (a) -age«,V, However, Musson-Genonw/ has shown that the process of electron interception at the repeller is far from ideal. In an actual klystron electrons are produced not only from the cathode but also by secondary emission from the grids forming the walls of the interaction gap. These secondary electrons can make multiple transits of the interaction gap, and by this means can attain higher energy than primary electrons emitted directly from the cathode. In Eig, 4.5 a plot of repeller current against incident power is shown for a TH2220 klystron (from reference No. 9, Eig, 31, page 143). The effects of secondary emission electrons can be taken into account i f the curve of repeller current Versus incident power i s extended to a range of incident power much 60 1.25 o u I u co H H co CO PA 1,00 -0,75 0.5 -0*25 25 50 Incident Power - mW Pig. 4°5° Repeller Current vs Incident Power (Reference No. 9, Pig. 31, Page 143) higher than the value required to produce the i n i t i a l indication. As shown in Pig, 4.5? the curve exhibits break points where the slope changes abruptly. The breakpoints (5), (3) and (l) correspond to the interception of electrons which have made 5, 3, and 1 transit of the interaction gap. Let and be the 61 power absorbed in the cavity corresponding to the instant when single transit and f i f t h transit electrons are intercepted at ( 9 ) the repeller. Musson-G-enon has calculated a value of ¥^~ TT- = 2 d for a TH2220 klystron. In view of the above result 5 i t can be seen that the procedure used to determine the instant of electron interception w i l l result in a low value for ¥ , a Since K i s inversely proportional to ¥ , the calculated value of K w i l l be high. 4.3 Pulse Detection The most effective nanosecond pulse detector makes ( ? ) use of a heterodyne technique ' where both phase and amplitude information is obtained. The development of a heterodyne system was beyond the scope of this work. Instead,a semiconductor diode detector was used for pulse detection. A diode detector, although very much simpler than a heterodyne detector,, sacrifies sensitivity and phase information,, 4.3»1 Detector Output Voltage Response Since the input resistance of the sampling oscilloscope is 50 ohms and the nominal output resistance of a crystal detector is several kilohms, terminating the deteotor with the sampling oscilloscope introduces a large attenuation factor which reduces the overall sensitivity of the system. 62 Consider the equivalent circuit of the detector-display system shown in Fig. 4.6. This circuit applies only during steady-state conditions when transients have decayed. E = BP O Transmission, Termination detector I i •Q-Line I I O l out l F i g 0 4*6. Equivalent Circuit of Detector System Under Steady-State Conditions The voltage attenuation factor is given hy E , R0 where E = open .circuit voltage from the detector R^  = output resistance of the detector and R2 = input resistance of the sampling oscilloscope. 63 For the particular case of the H-P 423A detector (one of two types used in the tests) R^  = 15K. Therefore, a = 3.32 x 10 . If the detector had a square-law response over the entire operating range, the ahove attenuation factor would correspond to a 24.8 dB decrease in system sensitivity compared to the case where the detector is terminated in a high impedance. Output voltage from the H-P 423A detector was approxi-mately 50 mV for an input power of + 15 dBm. A 1N23C semiconductor diode in a tuned mount produced approximately three times the output voltage under identical conditions. The detector system was adequate for direct measure-ment of the peak pulsed output power. Lack of sensitivity, however, would render the system unsuitable for viewing low-power reflected pulses in a transmission-line testing system. 4.3.2 Transient Response The observed envelope risetime when using a H-P 423A detector was 10 ns. The envelope risetime was 15 ns when using a 1N23C diode placed in a tuned mount. In view of this, 40 ns modulating pulses were applied to the switching klystron when performing the tests. In order to evaluate the test results,-let us consider the transient response of the individual components contained in the modulating system. -The time required for Y^ to reach a new equilibrium hi value after application of a modulating pulse is at least one (5) 1 electron transit time. ' For the 5T switching mode this time 64 delay equals 0.584 ns at 9000 MHz. As a f i r s t approximation, the transition time is considered to he proportional to the mode number m and inversely proportional to frequency. The time constants for the transition of klystron parameters such as due to an instantaneous change in 7^ are not predictable because of the nonlinear dependence of Y-g on 7 and also the phase (5 6) dependence of the bunched beam current on V . D' 1 If the pulse envelope i s to be reproduced faithfully, the detector and its associated circuitry should'have bandwidths of the same order as the spectral bandwidth of the modulated carrier.(12,14) The detector may be viewed as two coupled systems consisting of the RF section terminated by the diode and the video section. The RF section should be matched to the transmission line so that maximum power i s coupled to the diode. W h i t f o r d h a s shown that the bandwidth of thE RF section furnishes a lower bound for overall detector risetime. The transient response of the video output circuit i s determined by i t s RC time constant. In a typical detector the output resistance i s several kilohms shunted by a capacitanoe of a few picofarads. Since the output is to be displayed on a sampling scope (nominally 50-fl input resistance), the risetime of the video network w i l l reduce to the product of the input resistance of the sampling oscilloscope (15) and the shunt by-pass capacitance. As an example, consider the H-P 423A broadband detector. RF response is f l a t from 0.5 to 12 GHz, but the risetime of a practical system containing this detector is of the order of 10 ns. The risetime of the modulating pulse as measured at the repeller electrode was less than one ns (Appendix II). If a maximum klystron transition time of one ns is allowed, i t can "be seen that the syst risetime is determined hy the detector. 66 5. CONCLUSIONS A modulator which can he used for high-speed switching of microwave power has heen investigated. The modulator i s a .-reflection-type'switch, the operation of which depends on! the properties of hoth the T-junction and the switching klystron. The performance of the modulator was found to he c r i t i c a l l y dependent on the incident power level and the switching mode that was used. The switching characteristics within a certain mode were found to he relatively independent of the direction of change of repeller voltage. The ohserved minimum output power was virtually the same when either end of the switching mode was chosen as the OFF position. For the particular klystron used i t was found that the switching range was greatly reduced for the higher modes. In order to obtain optimum switching at a certain level of RF power, a switching klystron which is capable of produoing higher power when operated as an oscillator should be used. The switching mode to be used should be a- compromise between the power—handling capacity of lower modes and the switching' rate of higher modes. The increase in bunching parameter X toward the boundary of the passive region (for fixed incident power), although unexpected, can only explain partially why the minimum output power under optimum phasing conditions increased so rapidly after a certain c r i t i c a l value of input power was applied to the modulator. 67 Under the above conditions, the passive reflex klystron pulse modulator can become a useful source of nanosecond-width pulses at relatively high power levels. 68 APPEMDIX..I. . ' SCATTERING MATRIX ANALYSIS OE A T-JUNOTION 1 - 0 Scattering Matrix Representation of a Junction Consider the n-port junction shown in E£g. 1 -1 . Fig. 1 - 1 . N-Port Junction Let the fi e l d components he normalized with respect to the characteristic impedance Z^ "^  of the i ^ * 1 transmission line. ' o a*^ , ^ 2' ».., ^ n the normalized components of the incident waves at ports. 1 , 2 , n respectively and h^, hg, ...» h^ are those for the reflected waves at ports 1 , 2 , n respectively. Using the principle of linear superposition the total outgoing wave at any port of the junction i s related to the incident waves hy the following matrix equation:^''"^ 69 where S l l S12 * *' S l n • = S21 S22 ''' S2n t • Sn2 • •» S nn s.. 1 1 s . . n ( I - D the reflection coefficient looking into the th i port; with a l l other ports terminated in their reference impedances and the emergent wave at the i ^ * 1 port due to a th wave of unit amplitude incident at the j port with a l l other ports terminated in their reference impedances. I- 1 Scattering Matrix of an E^Plane T-Junction A typical waveguide E-plane T-junction with the side arm perpendicular to the wide dimension is shown in Pig. 2.6. Considering the junction to he lossless and reciprocal, i t may he descrihed hy a matrix having nine scattering coef-ficients of which six are independent. S l l S12 S13 S12 S22 S23 S13 S23 S33 (1-2) The normalized input and output f i e l d components at the ports of the junction are related as follows: 70 S l l S 1 2 S 1 3 S 1 2 S 2 2 S 2 3 q q q 13 23 33 a. ( 1 - 3 ) Referring to Fig. 2.6, let port 1 be fed by a matched generator. Let port 2 be terminated in a matched load, Port 3 is terminated in a load with a reflection coefficient of = [2 . J - 0 bg has not been determined yet, and b^ is a, equal to - r r . Eq. (1-3) may be expanded to give 13 ' 1 R S l l a l + S l 3 a 3 S 1 2 a l + S 2 3 a 3 S 1 3 a l + S 3 3 a 3 (1-4) From Eq. (1-4) the following may be deduced: The reflection coefficent, f^, at port 1 is a, ~ ' l " j2 13 1 1 T 1 - s 53 R 5 J (1-5) and the normalized output f i e l d component at port 2 is hg = a^ S S 1 3 S 2 3 _ f ^ _ 33 ["i 12 1 •— S (1-6) Eqs. (1-5) and (1-6) provide relationships which are functions of the complex reflection coefficient on the side arm. 71 If the junction is structurally symmetrical, ^11 = ^ 2 2 ° ^ symmetry conditions for an Emplane T, = -S-^' Therefore, the junction scattering matrix hecomes S l l 3 1 2 S 1 3 S 1 2 S 1 1 ~ S 1 3 ^ 1 3 " ^ 1 3 S 3 3 Eq, (1-6) may he rewritten in the form 2 h 2 = & 1 '12 1 - S The power output from port 2 is given hy a n J12 1 - S 35 r, (1-7) (1-8) (1-90'' I - 2 Measurement of Scattering Coefficients and Junction Isolation Scattering coefficients; were calculated hy use of (19 2 0 ) a graphical procedure based on Deschamps' Method. ^' ' These are shown in Table 3 . 2 . The data required were obtained (fl 1 ? ) by means of input VSWR measurements on the. junction. v f 1 One arm.of the junction was terminated with a matched load while the other arm was terminated with a moveable plunger. Characteristic reference planes were located in the' input arm by a method described by Allanson (18) and then input VSWR was 72 measured for a series of positions of the plunger. A second set of measurements were carried out with the positions of the plunger and the matched load reversed. An important characteristic of the T-junction is the degree of isolation between arms 1 and 2. When a shorting plunger i s located at a characteristic plane in the side arm W of the junction, the isolation, defined as 10 log^Q y0""1 , can he measured. The measurement was carried out by use of a (12) substitution technique. ' The junction isolation curve is shown in Fig. 3.6. Measurement errors and graphical construction errors limit the accuracy of the scattering coefficients. The effects of flanged joints were considered small and were not taken into account in these measurements. Isolation measurements by substitution methods are also subject to error but to a lesser degree. The scattering matrix was checked by comparing the measured input reflection coefficient and junction isolation with those calculated by use of Eq. (1-5) and Eq. (1-9). For calculation purposes an ideal plunger was assumed to be located at the characteristic reference plane in the side arm (i.e. I"^ 1 = -1). Results are shown in Table 1-1. Table 1-1. Calcaulated and Measured T-Junction Parameters Measured Calculated Isolation in dB 36.6 37.5 Input Reflection Coefficient 0.972 0.970 73 It was concluded from the agreement shown hy the above figures that the junction measurements were valid. 1-3 Application of the Junction Scattering Matrix - Eq. (1-9) has been tested hy using the klystron input admittance data shown in Eig. 3.3b (for the 5^ mode) to plot a theoretical switching, curve showing the power variation with repeller voltage. This i s shown below in Fig. (1-2). a Ti CD o PM -P a -p +10 +5 0 ^5 -10 -15 -20 -25 2204 240 260 280 300 Win = + 10 dBm Fig. 1-2.. Theoretical Switching Curve 74 APPENDIX II II-O Pulse Coupling Network The switching klystron is modulated hy applying the desired pulse to the repeller electrode. At low frequencies the modulation waveform i s capacitively coupled to the repeller, thereby isolating the source from the high repeller voltage. However, i f nanosecond pulses with very short risetimes are to xbe coupled into the repeller circuit, special precautions must be taken to reduce reflections and pulse distortion. I I - l Network Function The pulse coupling network must perform two functions simultaneously. Pulses must be coupled to the repeller of the switching klystron with a minimum of reflection or distortion, and the pulse generator must be isolated from the klystron circuit. II-2 Network Configuration The pulse coupling network i s shown in Fig. I I - l Pulse Generator Pulse - In _ 20,000 pF 2 Q E J X Y In Repeller An'odp W - ' - ' - D -Figure I I - l . Pulse Coupling Network 75 This network was housed in a small metallic container, lead lengths were kept as short as possible to reduce reflections and ringing. The output from the pulse generator was fed into the network through a cable section terminated by a 50 ohm resistor. Since the capacitance between repeller and anode is approximately 10 pF, the pulse could be efficiently coupled to the repeller hy a 20,000 pP coupling capacitor. This capacitor also provided dc isolation to the pulse generator. II-3 Measurements While the network was being assembled, the pulse shape was monitored at various points by use of a Tektronix Type P6032 high-impedance cathode-follower probe connected to a sampling oscilloscope. Negligible deterioration of the pulse shape was observed within the network. The major source of distortion was the short cable section connecting the network to the repeller electrode. The waveform measured between the repeller and anode exhibited rise and f a l l times of less than 1 ns. However, the waveform had a 50$ overshoot with a ringing frequency of 250 MHz. A series RC compensation network connected between repeller and anode reduced the overshoot to 20$. In Pig. II-2 an oscilloscope trace of the modulating waveform is shown. The horizontal scale i s 10 ns per major division and the vertical scale is 100 mV per major division. Pick-up at the sampling scope which terminated the microwave pulse detector was a problem at the beginning but 76 this was reduced hy wrapping the coupling network and the switching klystron with an aluminum-foil shield. Fig. I I - 2 . Modulating Pulse Measured between Repeller Electrode and Anode 77 REFERENCES 1 . Beck, A.C, and Mandeville, CD,, "Microwave Travelling Wave Tube Millimicrosecond Pulse Generators", I.R.E. Transactions on Microwave Theory and  Techniques. Vol. MTT-3, No. 6 , pp. 4 8 - 5 5 , December, 1 9 5 5 . 2 . Miyauchi, K., "Observation of Nanosecond Carrier Pulses", I.E.E.E. Transactions of Microwave Theory and • Techniques.- Vol. MTT-12, No. 2 , pp. 2 2 1 - 2 3 0 , March, 1 9 6 4 . 3 . Ito, M., "Dispersion of Very Short Microwave Pulses"in Waveguide", I.E.E.E. Transactions on Microwave  Theory and Techniques. Vol. MTT-13, No. 3 , PP. 3 5 7 - 3 6 4 , - May, 1 9 6 5 . 4 . Metivier, R., and Audoin, P., "Modulation en Amplitude a l TAide d'un Klystron-Reflex de l'Energie Hyperfrequence Transmise Sur un Guide d'Onde", L'Onde Electriaue. Vol. 3 9 , pp. 250 -253, 1 9 5 9 . 5 . Whitford, B.G., "Reflex Klystron as a High Speed Microwave Switch", Rev. Sci. Instrum.. Vol. 3 2 . No. 8 , pp. 9 1 9 - 9 2 1 , August, 1 9 6 1 . 6 . Hamilton, D.R., Knipp, JiK. t and Horner Kuper, J.B., Klystrons and Microwave Triodes. M.I.T. Rad. Lab. Series No. 7 , McGraw H i l l Book Company Inc., New York and London, 1 9 4 8 . 7 . Gvozdover, S.D., Theory of Microwave Valves. Pergamon Press, New York and London, 1 9 6 1 , 8 . Ginzton, E.L., Microwave Measurements. McGraw H i l l Book Company Inc., New York and London, 1 9 5 7 . 9 . Musson-Genon, R., "Verification Expl'rimentale de l a The'orie ' des" Klystrons-Reflex" , La Revue Tech. CF.T.H., No. 2 2 , April, 1 9 5 6 . 1 0 . Quate, CF., Kompfner, R., and Chisholm, D.A., "The Reflex Klystron as a Negative Resistance Type Amplifier", I.R.E. Transaction on Electron Devices. Vol. E.D.-5 , No. 3 , pp. 1 7 3 - 1 7 9 , July, 1 9 5 8 , 1 1 . Montgomery, CG». Technique of Microwave Measurements. M.I.T. Rad. Lab. Series No. 1 1 , McGraw H i l l Book Company Inc., New York and London, 1 9 4 7 . 78 1 2 . Sucher, M,, and Fox, J., Handbook of Microwave Measurements. Polytechnic Press, 1 9 6 3 . 1 3 . Pierce, J.R., and Shepherd, W.G., "Reflex Oscillators", B.S^T.J.. Vol. 26, No. 3 , pp. 460-681, July, 1 9 4 7 . 1 4 . Whitford, B.G., "Frequency Response of Nanosecond Radio Frequency Pulse Detectors", Rev. Sci. Instrum.. Vol. 3 9 , pp. 303-304, April 1961T 1 5 . Whitford, B.G., "The Video Resistance Concept in Nonlinear A.M. Detectors", Microwave Journal. Vol. 7 , No. 4 , pp. 54-61, April, 1 9 6 4 . 16. Ghose, R.N., Microwave Circuit Theory and Analysis. McGraw H i l l Book Company Inc., New York and London, 1 9 6 3 . 17. Montgomery, C.G., Dicke, R.H., and Purcell, E.M., Principles of Microwave Circuits. MvI.T,, Rad; Lab. Series No. 8 , McGraw H i l l Book Company Inc., New York and London, 1 9 4 8 . 18. Allanson, J.T., Cowling, T.G., and Cooper, R., "The,Theory and Experimental Behavior of Right Angled Junctions in Rectangular Section Waveguides", Proc. I.E.E.. Vol. 9 3 , Ft. 3 , pp. 177-187, May,- 1 9 4 6 . 1 9 . Storer, J.E., Sheingold, L.S., and Stein, S., "A Simple Graphical Analysis of a Two-Port Waveguide Junction", Proc. I.R.E.. Vol. 4 1 , pp. 1004-1013, August, 1 9 6 3 . 2 0 . Stein, S., "Graphical Analysis of Measurements on Multi-Port Waveguide Junctions ", Proc. I.R.E.. Vol. 4 2 , p. 5 9 9 , March, 1 9 5 4 . 

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