I 7956-5-T Air Force Avionics Laboratory Research and Technology Division Air Force Systems Command Wright-Patrson Air Force Base, Ohio TRANSMITTER IMPEDANCE CHARACTERISTICS FOR AIRBORNE SPECTRUM SIGNATURE Interim Technical Report No. 5 1 April - 30 June 1967 J. E. Ferris, W. R. DeHart and W. B. Henry 15 July 1967 Contract AF-33(615)-3454 Contract Monitor: K. W. Tomlinson AVWE 7956-5-T = RL-2170 THE JNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING Radiation Laboratory Administered through: OFFICE OF RESEARCH ADMINISTRATION. ANN ARBOR

THE UNIVERSITY OF MICHIGAN 7956-5-T TABLE OF CONTENTS Page ABSTRACT ii I. INTRODUCTION 1 II. SOURCE IMPEDANCE MEASUREMENT 3 m. SPECTRUM SIGNATURE ANALYSIS OF A CLASS C AMPLIFIER 7 3.1 Theoretical Analysis 7 3.2 The Classical Model 8 3.3 An Improved Model 10 3.4 A Comparison of the Models 14 3.5 Amplifier Design and Construction 15 3. 6 Design of a Class C Amplifier 15 3.7 Specific Design Details 26 3.8 Construction Details 26 IV. EXPERIMENTAL INVESTIGATION OF TRANSMITTER NON-LINEARITIES 37 V. CONCLUSIONS 42 APPENDIX 43 REFERENCES 44 i

THE UNIVERSITY OF MICHIGAN 7956-5-T ABSTRACT A more general method for making source impedance measurements has been investigated during this reporting period. Previous methods for determining the impedance of a transmitter required varying the phase angle of the load impedance by at least 90 electrical degrees. Employing this more general technique, it is necessary to change the phase of the impedance a few degrees only; after performing an analysis of the data, one can then determinethe transmitter im-. pedance. In addition to this technique, an analytical analysis of a class C amplifier has been performed to determine the spectrum signature of such an amplifier. Included in this report is a discussion of the construction of the class C amplifier and its theory of operation. A third aspect of the program fduring this reporting period has been the collection of additional harmonic Rieke diagrams for an ARC-27 and ARC-34 transmitter. ii

THE UNIVERSITY OF MICHIGAN 7956-5-T I. INTRODUCTION The statement of problem as set forth in the contract which provides for the present investigation is as follows: 1) A determination of the power delivered to the antenna for "spectrum signature" purposes will require a measurement of the antenna impedance, transmission line characteristics, transmitter maximum power output, and transmitter output impedance at the fundamental, spurious and harmonic frequencies. The transmitter output impedance at the spurious and harmonic frequencies is not well understood and therefore, requires further study. The prime payoff in this study will be better "spectrum signatures" for more accurate predictions of interference between systems. 2) There is a requirement to verify the results of the earlier successful program, Contract AF 33(615)-2606 "Simplified Modeling Techniques for Avionic Antenna Pattern Signatures", with a mock-up of an aircraft transmitter system. 3) The stated objective of the contract is: To conclude the development of "simplified" techniques for determining the RF spectrum signatures of flight vehicle electronics systems. To establish the validity of the techniques by comparing the results of data obtained by the "simplified" techniques with data obtained from tests employing a typical transmitter system in a mock-up. 1

THE UNIVERSITY OF MICHIGAN 7956-5-T 4) The present phase of the contract is concerned with developing a technique for the accurate prediction of the power output of a typical transmitter. The realization of such a technique requires a thorough knowledge of a transmitterts output as a function of the parameters most likely to vary in a practical situation at not only the fundamental frequency but the harmonic and spurious frequencies as well. 2

THE UNIVERSITY OF MICHIGAN 7956-5-T II. SOURCE IMPEDANCE MEASUREMENT Techniques for measuring the impedance of a source (i. e., a transmitter) have been discussed in previous interim reports. This discussion presents a more general method for making such measurements. The two previously proposed measurement schemes are specific applications of this more general technique. The methods previously described for determining the impedance of a transmitter included varying the phase angle of the load impedance by at least 90 electrical degrees. This technique, while adequate for laboratory measurements on transmitters whose parameters do not vary as a function of the load impedance, is unsatisfactory for a wide range of sources. The basis for a scheme which minimizes the change of load impedance necessary for transmitter impedance measurements is described below. One concept for measuring the transmitter impedance is shown schematically in Fig. 2-1. iiiiI ll-' — ' ^''' ~...I. It (t)i Y t M Y E FIG. 2-1: Transmitter Equivalent Circuit and Variable Load 3

THE UNIVERSITY OF MICHIGAN 7956-5-T The transmitter is modeled by its equivalent current source I = I sin wt, and t,t internal admittance Yt; the load is YL. The voltage E is measured for two values of Yt, Y and Y2. The following equations apply. It E1 (Yt + Y1) (2.1) ItE2 (Yt+Y2) (2.2) Combining equations (2. 1) and (2. 2), E1 (Y + Y1) E2 (Yt + ) (2.3) From which, E2 EY1-E Y Y-Y 11 22 1 E 2 Y E_ _ 2 (2.4a,b) t E -E 1 E 2 1 2 E It must be remembered that Yt, Y1, Y2, E1, and E2 are in general complex quantitives, hence t Gt + j Bt (2. 5a) Y1 G1 + j B (2.5b) Y2 G2 +j B2 (2. 5c) E1 'El e l 1 (2. 5d) E2 1E 2 e 02 (2. 5e) 4

THE UNIVERSITY OF MICHIGAN 7956-5-T The ratio E2/E1 becomes, E E j02 EE2 (2 01 (2. 6a) E E E Substituting equations (2. 5a, b, c) and (2. 6b) into (2.4) and setting - cos (02 - 0) = a; 1 E sin (0 - 01) b for convenience we continue 2 Gl(a-1)+Bl(b)+G2(-a2 +a-b2)+B2 (-b) Gt....... (2 8a) t (a - 1)2 + b2 1 (-b)+ B (a- 1)+G2 (b)+B2 (-a2 + a - b2) B 2 (2. 8b) t 22 (a - 1)2 + b 2 Equations (2. 8a, b) and Fig. 2-1 describe a very general method for determining a transmitter's output admittance. One specific variation of Fig 2-1 is shown in Fig. 2-2. It is interesting to note parenthetically that the methods previously 5

THE UNIVERSITY OF MICHIGAN 7956-5-T described for determining the transmitter impedance are simply special cases of!! (2. 8a,b) where (0 - 0) and Z is transformed to the point where Zt R 2 1t2 1 t t? T implying that Yt Gt. I (t)( ) Y Y Y3 FIG. 2-2: A Variable Load Method for Transmitter Impedance Measurement In Fig. 2-2, Y is a small admittance which can be switched into the circuit. Thus Y1 and Y2 (equations. 4a,b) would become Y1 and Y + Y respectively. In practice, when dealing with a transmitter whose output parameters vary with load admittance, one could choose Y1 equal to the actual load admittance which would be placed on the transmitter terminals in actual service. Y could then be chosen sufficiently small (commensurate with measurement equipment accuracy) to effectively preclude variations of the transmitter parameters. 6

THE UNIVERSITY OF MICHIGAN 7 956-5-T m. SPECTRUM SIGNATURE ANALYSIS OF A CLASS C AMPLIFIER Much work has been done in the past few months to develop methods for determining the spectrum signature of a transmitter. The analysis at present includes an assumption that the transmitter output voltage varies linearly with the load impedance at each frequency for which there is an output present. The output of such a linear device may then be calculated as a function of load impedance once, a) the device internal impedance, and b) power output into a known load have been determined at each frequency of interest. Large deviations in power output and degree of linearity are experienced from unit to unit, necessitating a complete series of measurements for each transmitter and load in question. This is obviously a very time consuming procedure. The purpose of this study is to determine feasible methods to calculate the spectrum signature of that class of transmitters as a function of the tube bias and load conditions. The transmitters to be considered utilize a c w or plate modulated vacuum tube class C final amplifying stage. The experiment includes developing a model for predicting the spectrum signature of a class C amplifier and comparing these results with the actual output of a laboratory amplifier, designed and constructed especially for this purpose. 3. 1 Theoretical Analysis This section will be concerned with developing a large signal model of a vacuum tube and calculating the Fourier components of the model output (the notation used is standard as listed in the Appendix). The classical model is discussed 7

THE UNIVERSITY OF MICHIGAN 7956-5-T along with a modified version designed to yield more accurate results. 3.2 The Classical Model The classical approach to class C amplifier spectrum signature analysis includes modeling the tube and its output circuitry by a current source and shunt admittance (Cheng, 1959) as shown in Fig. 3-1. For this type of analysis, it is usually assumed that the plate current is a linear function of the grid voltage for those values of grid voltage above the tube cut-off value. ec(t) <~)-^ — O1 >i_0 (t) YL FIG. 3-1: Classical Model: ib (t)= K1 e (t) + K2 co flows. From (3.1), it is evident that if the grid voltage is a sinusoid of agrument 8

THE UNIVERSITY OF MICHIGAN 7956-5-T wt, the plate voltage will be a truncated and rectified sinusoid of the same argument. Let e gE 1 C g 1 sin wt + E cc (3.2) then Kl I E I sin ut + E +K2 b K1 g I 1 CC, 2 t! for ( E \ sin wt + E > e 1 cl co (3.3) ib OC for E 1 sin wt + E < e g 1 cc co Once K1 is specified, the Fourier components of ib can be calculated. ib b + Ip n sin (n wt+ ) n 1/2 A +- A cos n t+b sin n wt o n n n (3.4) where 1 r A = / n 7rJ0 1 b - i n 7rTO 0 27r ib (t) cos n dwt bn ib (t) sin wt dwt n (3.5) 9

THE UNIVERSITY OF MICHIGAN 7956-5-T The power output of the device is given by 2 p = P - R (3. 6) out - n 2 pi n e i n 3 n n where R Z is the real part of the load impedance at the angular frequency (nw). e n 3.3 An Improved Model The approximation for ib given by (3. 3), while sufficient for many applications, is not difficult to improve. Figure 3-2 is the static characteristic curves of a dual tetrode (Amperex 6252). In the classical approach just discussed, it describes constant current curves which are linearly spaced, horizontal straight lines. It is evident from these characteristics that the constant current contours are not horizontal, especially for low values of plate voltage and are not linearly spaced. (The constant current contours of a triode have in fact a much steeper slope than those in Fig. 3-2). To account for the non-zero slope and slope variations with plate voltage, the curves can be accurately represented by piece-wise linear approximations as given by (3.7) (see Fig. 3-3). ibA e + B eb +C for e (r-1)>e > e r c s r c c- c (r) and b ( l)eb eb (s) (3.7) ib 0 e < e D c- co 10

THE UNIVERSITY OF MCIA MICHlGAN 7 956-5-T 62521X~991 +40 r S 1 i, 4 6 1 1 1 i 6 i AmdgmF; — 1 i 4 4 i # f i f 4 0 0. T -4 f i f ft 'It.......... .. 0 # # 0 i i F —knlbow 300 -IITII -100 0 I.. a.... I..10 t,.Ema0 I I I I I I! I t. m II!0 -40. -.. - 4............ A. I. a A a 1........................ MPAEREX dI5f/AX9P/O CONSTANT CURRENT CHARATERISTICS, SCREEN VOLTMGEuSO VOLTS 1 i i i -60. IJZ 11111.1 i I I tPLATE CURRENT -MILLIAMPERES ~ SCRkEN GRID CURRIENT -MILLIAMIPRERESso nTRO 6110r.JI ADRTMLUAM PER&S - I I. IA f 0 i 100 200 300 400 S00 600 PLATE VOLTS FIG. 3-2: Static Characteristic Curves for 6252 'I1

THE UNIVERSITY OF MICHIGAN 7956-5-T where Ar, B, and C are appropriately chosen constants over the region r e (r-l) to ecer) and eb (s,) to e b(. In general, any desired accuracy can be c (r-1) c(r) b (s-i) b(s) attained simply by increasing the number of piece-wise linear approximations of the form (3.7) to the experimental characteristics. eb (t) e (t) FIG. 3-3: Improved Model: ib (t) Ar ec t) + B eb (t) + er Including the second variable, eb, in the equation for ib (3.7) has, however, introduced some additional complications. Consider (3.7) together with the constant, E = i Z (3.8) pn p n n Moving the dependent variable eb to the left hand side of the equation and solving for ib, 12

THE UNIVERSITY OF MICHIGAN 7956-5-T 00 ib-B e=Ib(l-B )+ I sin(ntt+p )+ (1-B Z )=A e +C (3.9) b s nb s p n s n r c r for e > e C CO where Zn Z (rt) Zn os + j sin y (3.10) A casual inspection suggests setting e = Eg, sin At + E as in (3.2) and integrating C g CC over the period ut = 2?r to obtain an expression relating the constant terms on each side of (3. 9). It must be noted, however, that (3.9) is valid only for e > e C- CO prohibiting this approach. Assuming that e is of the form (3.2) or any other c completely specified form) we are able to solve (3. 9) for ib (t) by a series of successive approximations. The method is as follows: 1) Assume e -=E - E, sin t and eb Ebb Eb cos t (this is equivalent to stipulating Z1 = R1 Z = 0 n 1). 2) Calculate ib (b) from (3.7). 3) Determine the Fourier components of ib 00 4) Solve eb(t)T R + I nsin (nwt+ ). Z where Z is bi0 nn 1 n given by 10. 13

THE UNIVBRSITY OF MICHIGAN 7956-5-T 5) Substitute this expression for eb (t) into (3.7) and calculate a new value of ib(t). 6) Repeat the sequence 2) - 5) until ib(t) has been obtained to the desired accuracy. The power output as a function of frequency is then the same as given by (3. 6). Clearly this type of solution requires many calculations for each new set of parameters that are investigated. However, it lends itself well to techniques utilizing a digital computer. 3.4 A Comparison of the Models To evaluate the improvement afforded by the piece-wise linear model described above, an input (e ) and plate load impedance were selected for the tube c and the resulting first three Fourier components of the plate current waveform calculated from: 1) the actual tube characteristics, 2) the classical model, 3) a four-region piece-wise linear model, and 4) a six-region piece-wise linear model. The procedure was as follows. Assuming the grid and plate voltages to be sinusoids of period ut and 1800 out of phase e = E + E,sinwt c cc g eb =Ebb + E cos t (3.11) b b Ep, 14

THE UNIVERSITY OF MICHIGAN 7956-5-T a value of plate current is specified for each value of wt. These values were tabulated and plotted for - < wt <. The Fourier components are then given by (3.4) and (3. 5). In order to evaluate the coefficients A and b, it is necessary n n only to plot ib(t) cos (aont), ib(t) sin (wnt). The integral of ib(t) cos (Ont) is then the area under the curve grounded by the ut axis, (Skilling, 1957). For this example, the symmetries present (even function and quarter wave symmetry) assuming a symmetric dual tube (see Fig. 3-4), require only odd harmonics of even functions. The curves appear in Figs. 3-5 through 3-8, the model in Table 3-1, and the results in Table 3-2. Notice that the results of the third model represent about a 10 per cent improvement over the classical model. 3.5 Amplifier Design and Construction Since the purpose of the experiment is to determine the spectrum signature of a class C amplifier as a function of its operating characteristics, it is imperative that the design be kept as flexible as possible to allow the desired changes to be readily made. The first part of this section discusses the general problem of the design of a class C amplifer, and the second details of the procedure followed for the unit which has been constructed. Finally, the third portion deals with the hardware realizations of the required circuit elements and describes the completed unit. 3. 6 Design of a Class C Amplifier A class C amplifier is an amplifier for which the grid bias is so large that plate current flows for less than one half the cycle. A sketch of ib versus ec 15

THE UNIVERSITY OF MIC1HIGTAN 7956-5-T $4. 0.J co 1-4 16

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THE UNIVERSITY OF 79563-5-T MICHIGAN I.: I... I.. I... I - - - - t I. - - - I... I I - - - -, I -.. --.- I --.1 - I - I..- I 1 i t.. I I. I.. I i — l- - -- I I. i. I. 1. I I I j I I f - - 11 i - - f.. I I I i:,, t -T I i i i II i i~. -. i - - I I - I I i..,. 4 -. 4 1 1.. I.. t - i.. i 1 t I i I I i I I ~ —. —1-~ - * t. *i. -V -.4 - 7 II I I I. I. I. t - I ib(t) =K e (t) + K tI " — i411.1 e (t) = 1yocosLt - 8 KW 7. 5 K2 1601, 4 I I 1 4 -., I,, t. i 't 14 1 1 1 —. -.-. I FIG. 3-6: lb(t) Calculated From Classical Model 18

THlE UNIVERSITY OFMIIGA MICHIG AN 7 956-5-T 1. * I — rI I. I I I I I.. I I 4 4 - i t * 1 I t - -- t, i.. I f - I!.. I. I, - ---. I r- - I. i i i. t I I. II: 1 I i 4 — 1 1 i t I t i I i - I -4- -- I I e x 100cos wt - 80O -C t i i I II t e. '350Osin wtL+ 5O i I v I f *1, -1. i. A. t - I I -. I i I I I t - I I I FIG. 3-7: ibD(t) Calculated From Linear Model No. 2. Piece-Wise 19

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THE UNIVERSITY OF MICHIGAN 7956-5-T Model I ib 7.5 e + 160 bc TABLE 3-1 Three Piece-wise Linear Models Model II e < 150 2 e + 0.04 e +58 ib 7.1e +0.14eb + 135 b c b e <- 15 c e > - 15 C eb > 150 b-~ ib 2 e + 0.013 eb + 58 i+ 48eb +135 i b7.1e +0.048e +135 D c b e <- 15 c e >-15 C eb < 210 b i 2.33 e +.025 eb + 71 ib 4 e +.076 e + 98 ib 5.6e +1.O06eb +111 b = 7.78 + 0. 148 eb + 123 Model m e c -80 < e <-19 - c -19 < e <-9 c - 9 <e < -1 - c - 1 <e -=23 - c 210 <e <400 i = 2.33 e + 0.012 e + 71 ib 4 e + 0.02 e + 98 c b ib =5.6e +0.29eb +111 ib 7.78 e +0.04 e +123 L1U 77e+c b 21

THE UNIVERSITY OF MICHIGAN 7956-5-T TABLE 3-2 Results of Model Analysis Tube Quant. Curves Model 1 Model 2 Model 3 109 118(+7.4/) 113(+4. 1 ) 114 (+4. 2) ----— ~..._.._, __~. ~ ~ __ --- —------— __ I' 1 199 220 (+10. 5) 207 (+ 4 % ) 204 (2.5 %) p 3 87.6 102(+16.4%) 92(+5 ) 85.6 (-2.5%) 22

THE UNIVERSITY OF MICHIGAN 7956-5-T appears in Fig. 3-9. Assuming that the plate voltage is a sinusoid of period wt, the following equations apply (Cruft Laboratory, 1957). D.C. plate input = Pbb Ebb Ibb Eb (3.12a) ^ 2 Power delivered to the plate load = P = = E-P —R (3. 12b) Plate dissipation P = Pbb - P (3. 12c) p bb 1 Plate circuit efficiency = N P1/Pbb (3. 12d) 1' b Dirving power P - E I (3. 12e) Power supplied to the grid bias source = P E I (3. 12f) cc cc c Grid dissipation a P = P - P (3.12f) g d cc Power amplification = A =P P1/P (3. 12h) All of the parameters listed above can be determined direct by the D. C. currents and voltages and A. C. voltages except Pd which includes an A. C. current. However, assuming a sinusoidial input, T T P e i dt= E coswti dt (3.13) d T c T c 0 0 If we assume that i flows only when cos t = 1, c Tt P i dt= E I (3.14) d T c g c 23

e (t) O '-4 -4 tril ~-i i-eL 4E cn l t -IL 0-4 2: FIG. 3-9: Plate Current and Grid Voltage v. s. Time for a Push-Pull Class C Amplifier.

THE UNIVERSITY OF MICHIGAN 7956-5-T All of the necessary parameters are now in a form which allows them to be determined from easily measured quantities. The selection of Ebb, - E, Eg and R (the load impedance at the fundabb cc g 1 mental frequency) is accomplished with the aid of the tube constant current characteristics. Fig. 3-4 is the constant current characteristics of an Amperex 6252 dual tetrode. Assuming that the grid and plate voltages are sinusoids of period wt and 180 out of phase, the points corresponding to values of e and eb for ttl.. wt2 c b 1.. 2 will form a straight line from the maximum to the minimum values of plate voltage. Let these points be Q and P respectively. The coordinates of Q are Ebb, -E. Those of P are - (E, -E + E. The selection of Q and P cc bb pcc g (and thus Ebb, E -E E are accomplished by a trial-ar~i-error process as bb p cc g follows: 1) Select arbitrarily the points P and Q. (The tube manufacturer will usually specify normal operating supply voltages which are a good starting point). 2) Draw the line PQ. 3) Lay off from Q the following fractions of the length QP along the line: 1, 0. 966, 0. 866, 0. 707, 0. 500, and 0. 259. 4) Determine, by inspection, the values of instantaneous currents at these points: ia, ib, i..... if. 25

THE UNIVERSITY OF MICHIGAN 7956-5-T 5) The average and fundamental components of the current are given by the formulas '1 I a i l - +ib+i +id+ i +if (3.15) 12 2 b c d e i = i +1.93ib+1.73i +1.41id+i +0.52if (3.16) i- 12 L a ' ' c ' e E Ebb (3.17) (EbL = Ebb -eb. (3.18) (The details of this analysis are given in Cruft Labs, 1957, pp. 255-259, and pp. 443-445). The constants in (3.15) and (3.16) are based on the assumption of a sinusodial excitation. Once the fundamental and D. C. components have been found, it is possible to calculate the parameters listed in (3.12a-h). The points P and Q may now be shifted and the process repeated until the desired results are obtained. 3.7 Specific Design Details The procedure described above was used in the design of the experimental transmitter. Figure 3-10 shows three possible operating paths. The results are tabulated in Table 3-3. These values are for one (half) tube only. Path two was tentatively selected as the operating path. 3.8 Construction Details Figures 3-11 and 3-12 are schematics of the experimental unit which was 26

THE UNIVERSITY OF 71956-5-T MICHIGAN.40 PlP 2 * to 0 ~- i t! ll - T!!! ill!!. I 1 4 0 6. — + 4 f - -4.; + 4 4 - 4 4. - -t -r - -+ - —* bw I i i I - a -4 L 6-4 iA a- 4 — I,. 1! I - 7 1 , I I -- -I: I I 1-1 4-,,20~ 300 250 200. i00 -so'-~ 5Ot I.1 0 0 I. I i O -20 I -040 - 60 I I 4 tt-4 f, 1 -4.4 -4 0 100 200 300 400 500 800 PLATE VOLTS FIG. 3~-10: Three Sample Operating Paths 27

THE UNIVERSITY OF MICHIGAN 7956-5~-T II Parameter CCS. ABs. Max. Path No. 1 Path No. 2 Path No. 3 _______ 6 8 m a (c ath ode) 51 ma 53.5 ma 72. 3 ma E bb 500 V 500 V 400 V 500 V I 98 ma 97. 5 ma 128 ma E 1450 V 350 V 450 V bb 30w 27 w 21.4 W 36.2 w ______22.2 w 17.1 w 28. 8w P 6. 7w 4183w 4.3 w 7.4 w N 82 per cent 80 per cent 80 per cent P 14500 Q 3600Q0 3500 Q Screen 300 V 250 V 250 V 250 V I2 ma 2.4 ma 2 ma 4.25 ma F -200V -80V -8V.I 1 4.2 ma 3.9 ma _ _ _ _ _ _ E 100 V 100 V 1O cc 5 w 0.2 w 0. 16 w P 0. 04 w 0. 04 w P d __ _ _ _ __ _. 24 w 0. 2 w 4. 68 w A n92. 5 85. 5__ _ _ _ _ _ _ TABLE 3-3 t. Results from the Three Paths Shown in Fig. 3-10. 28

C1, C2, C7, C8.OOlpf lOOO L1 - L5 24 ph i * 2 2 CC - 3 - 30 f, L5!0 1 2 C7 'See Text "See Text I w+ Ebb + Screen bb FIG. 3-11: Schematic of Experimental Amplifier

THE UNIVERSITY OF MICHIGAN 7956-5-T 110 Gnd.> White Gnd. ---- 6.3V v Blue AC, -150 OV >Green DC )______. 200-300 V O DC > --- — 0-500 V Red DC > --- — F- a Rly 1 >2 --- 3> ---E — > 0- 5 Ma. 4> - Nc. 5> l 6 -— Nc. 0-100 Ma. 125 Ma. 8' -- Nc. n Fil. Grid Scrn. Plate FIG. 3-12: D. C. Meters and Cables for Experimental Amplifier 30

THE UNIVERSITY OF MICHIGAN 7956-5-T constructed. The layout of the R. F. section is shown in Fig. 3-13 and a sketch of the complete unit in Fig. 3-14. The construction is quite typical except for the use of coaxial tuned circuits. The baluns are 15" broadband coaxial baluns (Duncan and Minerva, 1960). The transformer T, is a quarter wave transformer with an impedance transformation ratio of 10:1 and the tune circuits are shorted lengths of coaxial transmission line. It is well known that resonant circuits composed of lumped circuit elements can be constructed for use at 300 MHz. However, the primary purpose of this study is to evaluate transmitter performance at the harmonics of 300 MHz as a function of the circuit parameters. The behavior of conventional coils and capacitors is not well understood at microwave frequencies. The design of the output circuitry was accomplished in the following manner. Knowing that an impedance of R = 3600 0 at the fundamental frequency was necessary at each plate of the 6252 in order to provide operation along path 2 described above, the impedance transfer function of the balun was measured using a slotted line and a known balanced load. Tbalun Zunbal. / Zbal (0. 18 + jO. 35), thus in order to see Zb R 3600, balun unbal. / bba Z must equal (648 + j 1260) which is Z /Z = 13 + j25.2 or a VSWR of 62. A sketch of the tank circuit appears in Fig. 3-14. Choosing a design Q of about 10 and recalling Q W C I R where C 1.78 pr/ in for 50 / air line lV-/43001 R must be-' 300 Q. Referring to Fig. 3-15, the admittance of a short circuit is located at point A. Transforming this through 1, adding the load (Y = 1.0 + jO) 31

THE UNIVERSITY OF MICHIGAN 79563-5-T -. v cc Q I I I'd, 04 x LO) - - C\1 IC) (.0 " —4 C?) '-4 -C? r I ---. -1-2 T!IT Wi-Ti C? C~zJ I' 0 ~ 01 ' —4 0 0l i - 32 f I

Cooling Fan ~.8 Grid Current Plate Current LD I 01l I Ul -4 Cr? )-4 10 -4 -4 C) z 0 0 FIG. 3-14: Sketch of the Completed Transmitter

THE UNIVERSITY OF MICHIGAN 795(6-5-T {a.! ~In 4 30 4 3 t 0: 4, of as 11 (P Oj at as~Y w dM C. j 7:74 '9i 1, /. [7 - I -4 - 01 I 0 —t 0 -s w-T9-ie-i FIG. 3-15: Design of the Resonant Output Circuit 34

THE UNIVERSITY OF:MICHIGAN 7956-5-T and transforming through 2 we have that t1 2.88", 2 7. 40. It is now necessary to transform the R/Z x 6 seen at the end of the tuned circuit to the Z/Z 13 + j25.2 needed at the balun. A two section quarter wave transformer was constructed as follows. The impedance transformation afforded by each section is given by Z. Z =Z (3.19) in out o Thus for two sections in series, Z01 ZZ2 02 723 (3.20) or Z3/Z1 02 2/01 Since we need a Z3/Z1 10, Z02/Z01 10 =3.36. The values selected were Z01 35 n, Z02 1250 The input resonant circuit was constructed similar to the output, and the transmitter was excited by an ARC-27. The output spectrum measurement scheme is given in Fig. 3-16. 35

Circuit Low Pass Filter Variable Attenuator T14 ft~i ICI) Load — I 'I1 CJl c. 1-3 Coupler Power - Meter Wavemeter Meter C)I C)zr Tuned Circuit Transformer FIG. 3-16: Schematic of Spectrum Signature Measurement Test

THE UNIVERSITY OF MICHIGAN 7956-5-T IV. EXPERIMENTAL INVESTIGATION OF TRANSMITTER NON-LINEARITIES During this portion of the investigation, consideration has been given to load impedance variations at the fundamental frequency and their effects on the power output at the harmonic frequencies. During this investigation both ARC-27 and ARC-34 transmitters have been evaluated. Typical harmonic Rieke diagrams are shown in Figs. 4-1 and 4-2. These diagrams were measured employing the test setup shown in Fig. 4-3. It is apparent from the harmonic Rieke diagram of Fig. 4-1 that the transmitter is not pseudo-linear, e. g., power variations are greater than 3db. This unit was an ARC-27 that was not properly tuned and as a consequence this may have contributed to the non-linear effects. This supposition is further substantiated from the data that is presented in Fig. 4-2 where the power variations are less than 3db such that the unit has been designated as pseudo-linear. It will be observed that the power level recorded was measured at the second harmonic frequency (600 MHz.) as a function of the load impedance at the fundamental frequency (300 MHz). The data was collected by terminating the transmitter in a matched load with respect to the transmission line at 600 MHz and a mis-match (VSWR's of 1. 2, 1. 5, 2. 0, 3. 0, and 5. 0) at 300 MHz. The power level was monitored at the harmonic frequency as the load impedance angle at the fundamental frequency was varied through 180. 37

THE UNIVERSITY OF MICHIGAN 7956-5-~T VOL. W Ite I LOS$ ~4O II ~* 7la \,.3I ' to 1la I 0 'A. OL II SI 7 -Nj 6 Of 0t O *> *s mi 0ARC-27 S TX-i fl00Mt ON 01 0n FI.4iwamnioikoigamfrS-01 38

THE UNIVERSITY OF MICHIGAN 795(3-5 -T At — < u3 3 *. 10 I.t F 4 01 [ 4- - I" Il.., -,e N - 00-zAC-7 N f 60 MJrn FIG 4-: Hrmoic iek Digra fo SN161 39

Adjustable Stub (open) I - - - - -- -* I, ' Slotted Lir I ARC-27 I I.I. Shielded Enclosure / le Directional Coupler Line Stretcher 5 LoadI 500 Load = I-'l Adjustable Attenuator — t Wavemeter z Wavemeter Bolometer | L Power Meter VSWR Meter, ] > C) FIG. 4-3: Experimental "Harmonic Rieke Diagramn" Equipment Arrangement

THE UNIVERSITY OF MICHIGAN 7956-5-T Additional harmonic Rieke diagrams have been collected for two ARC-34 transmitters, however, contour plots have not been plotted. It has been observed that in general it is not appropriate for the ARC-34 to be termed a pseudo-linear device. Power transfer data has been collected for a constant VSWR load at the fundamental frequency with the load varying at the harmonics; this has not yet been plotted. The data appears to be in good agreement with the theoretical curves that have been presented in previous reports (Ferris, et al, 1967). 41

THE UNIVERSITY OF MICHIGAN 7956-5-T V. CONCLUSIONS The class C amplifier has recently been completed and the sole experimental result is, that given bias voltages and an input signal, there exists an output. Similarly, the transmitter analytical model has only been solved for sinusodial inputs and outputs. One interesting result not included here was the selection of a load with a reactive component providing a relative phase shift between the input and output voltages. A graphical analysis was done for such a case using a phase shift of 100. The results showed no appreciable change in the waveform of Lb from that given in Fig. 3-5. A more realistic model would, of course, include the tube input, output, and plate grid coupling capacitances. In addition, the 6252 has a neutralizing capacitance from the grid of unit 1 to the plate of unit 2 and vice versa. This must also be included in a detailed analysis. With the experimental data obtained to date and the analysis that has-been accomplished, it is not yet possible to-say to what extent the characteristics of either the ARIC-27 or the ARC-24 can be determined by linear prediction techniques. 42

b i ~I pn % Eb Ebb E pn e c E c E cc E gn i c I c I g n bb p! P 1 P Up p N p P cc p cc THE UNIVERSITY OF MICHIGAN 7956-5-T APPENDIX total instantaneous plate current average (DC) plate current magnitude of the n'th component of plate current total instantaneous plate voltage average (DC) plate voltage plate supply voltage magnitude of the n'th component of plate voltage total instantaneous grid voltage average (DC) grid voltage grid supply voltage magnitude of the n'th component of grid voltage total instantaneous grid current average (DC) grid current magnitude of the n'th component of grid voltage DC plate, input power power delivered to the plate load plate dissipation plate circuit efficiency input driving power P grid dissipation power supplied to the grid bias source Ap power amplification power supplied to the grid bias source A power amplification 43

THE UNIVERSITY OF- MICHIGAN 7956-5-T REFERENCES Cheng, David K. Analysis of Linear Systems, Addison-Wesley, Reading, Mass., 1959, Chapter V. Cruft Laboratory, Electronic Circuits and Tubes, McGraw-Hill, New York, N. Y., 1947, pp. 423-462. Duncan, J. W. and V. P. Minerva, "100:1 Bandwidth Balun Transformer", Proc. IRE, Vol. 48, No. 2, February, 1960, pp. 156-164. Ferris, J. E., W. R. DeHart and W. B. Henry, "Transmitter Impedance Characteristics for Airborne Spectrum Signature", Interim Technical Report No. 3, January, 1967, University of Michigan Radiation Laboratory Report 7956-3-T, 14 pages. Skilling, H. H., Electrical Engineering Circuits, John Wiley and Sons, New York, N.Y., 1957, pp. 439-442. 44