ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR THE NEGATIVE CAPACITY AMPLIFIER Technical Report No. 33 Electronic Defense Group Department of Electrical Engineering By: L. C. Beavis Approved by: W. Welch,J. 4 L.W. Orr Project 2262 TASK ORDER NO. E1DG-4 CONTRACT NO. DA-36-O39 sc-63203 SIGNAL CORPS, DEPARTMENT OF THE ARMY DEPARTMEINT OF ARMY PROJECT NO. 3-99-04-042 SIGNAL CORPS PROJECT NO. 194B PLACED BY: SIGNAL CORPS ENGINEERING LABORATORY FORT MONMOUTH, NEW JERSEY August, 1954i

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iii ACKNOWLEDGEMENTS iv ABSTRACT v 1. INTRODUCTION 1 2. CIRCUIT CONSIDERATIONS 2 3. EXPERIMENTAL RESULTS 3.1 Actual Circuits 7 3.2 Explanation of Graphs 7 3.3 Summary of Results 13 3.4 Application to Dielectric Tuned Receivers 15 4, CONCLUSIONS 17 APPENDIX A 18 APPENDIX B 19 REFERENCES 23 DISTRTBUTION LIST 24 ii

LIST OF ILLUSTRATIONS Fig. No. Title Page 1 - Block Diagram of Negative Capacity Element 2 2 Thevenin Equivalent of Block Diagram of Negative Capacity Amplifier 3 3 Circuit Diagram of the Negative Capacity Element 4 4 Graph of Gi Vs. Frequency with Ck as a Parameter 9;5 Graph of Gi Vs. Frequency with C as a Parameter 10 6 Graph of C.i Vs. Frequency with C as a Parameter 11 I n 7 Oscillator Circuit Used in Conjunction with the Negative Capacity Element l1 8 Tuning Curves of a Dielectric Tuned Receiver 16 9 Block Diagram of Negative Capacity jAmplifier 19 10 Simplified Circuit of Negative Capacity Amplifier 21 11 Equivalent Current Generator Circuit of Figure 8 21 iii

ACKNOWLEDGEMENT The author wishes to thank Dr. L. W. Orr for his guiding influence in this investigation. The author also wishes to thank Dr. J. L. Stewart and Mr. H. Diamond for their assistance. iv

ABSTRACT The production of a negative-capacity by means of a two stage amplifier has been investigated with the hope that it would be helpful in extending the tuning range of existing ferroelectric capacitors. It is found that the negative capacity thus produced is limited in application because of its inability to handle input voltages above 3 or 4 volts rms, and to operate successfully at frequencies above 3 mc. Although the negative-capacity circuit may be effective in reducing the capacitance of an external circuit, its practical application is restricted to external circuits having a minimum positive capacitance; the actual value of this minimum positive capacitance is dependent upon the amount of negative capacitance to be added to the external circuit.

IEIf{INt.ICAL REPORT N0O 33 Page 5 Figue 3, CQ should be Ck Page 22 - Eqation 21 should read c 2tC -(Rfnc) + eCo"2 N+ o J( (.P.) Co "C. Page 23 Reference No. 4 (Po Eo Bell) should read (P. R. Bell)

ENGINEERING RESEARCH INSTITUTE. UNIVERSITY OF MICHIGAN THE NEGATIVE CAPACITY AMPLIFIER 1. INTRODUCTION The negative capacity amplifier is an active circuit having a negative capacitance input. It was investigated for possible incorporation in an electrictuned oscillator or rf amplifier circuit (Ref. l): to increase the tuning range available with existing ferroelectric capacitors. These capacitors have a capacitance which varies as a function of applied dc electric field, permitting electric tuning of rf oscillators and amplifiers. The maximum range of electric tuning is now limited by the ratio of the maximum to minimum capacitance of a particular capacitor. For instance, a ferroelectric capacitor may have an effective range of from 25 to 200 rlf with the use of a r~easonable bias field. In parallel with a fixed inductance, this will give a tuning range of about j20025 or 2.8. However, if some method could be found to increase this capacity ratio, the tuning range would be- correspondingly increased. Increasing the capacity ratio might be accomplished by subtracting capacity from the maximum and minimum ferroelectric values. For instance, if -20 Off was shunted with the 25-200 pgf variable dielectric capacitor, the new effective capacity range would be from 5-180,uquf, which more than doubles the original tuning range. Although these hypothetical conditions were not duplicated, the tuning range was increased from 2:1 to 2.7rl.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 2. CIRCUIT CONSIDERATIONS It might be well to define here exactly what a negative capacity is and how it may be produced. A negative capacity offers a reactive component to the circuit Xc = j/oC which differs from a positive capacitive reactance only in the sign preceeding the j operator. The methods for producing such a component are discussed by many authors (Refs. 2, 3, 4). The basic circuit used in this investigation (Fig. 3) is given by P. R. Bell in Vol. 19 of the MIT Radiation Series (Ref. 4). It is a simple two-stage RC coupled amplifier with a positive feedback from the output of the second tube to the input grid of the first tube, and a negative feedback loop from the output of tube two to the cathode of tube one. The reason for selecting the particular circuit used over others is that it appeared to be best suited to the desired frequency range. Only the shunt negative capacitive reactance amplifier will be discussed here. A much more complete study of negative impedance production by the means of feedback amplifiers is given in Ginzton's article (Ref. 2). For the sake of a simple explanation, imagine a two stage amplifier having zero phase shift, and a single positive feedback loop through the reactance Xn, as in Fig. 1. When a voltage el is applied to the input, the source supplies e, A O erA BLOCK DIAGRAM OF NEGATIVE CAPACITY ELEMENT FIG. I __ _ __ _ __ _ __ _ __ _ __ _ __ _ _,2

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN a current, i1. This current has the form it = el/Zi (1) where Zi is the input impedance with feedback, and the input impedance without feedback is considered infinite (see Appendix A). The equivalent circuit is shown in Fig. 2. X I + Zo eA THEVENIN EQUIVALENT OF BLOCK DIAGRAM OF NEGATIVE CAPACITY AMPLIFIER FIG. 2 Thevenin's theorem gives the relation el = il(Xn + Zo) + elA (2) where Z is the amplifier output impedance and A is the amplifier gain without feedback. Then by combining (1) and (2) we have el = Xn + Zo. (3) 1-A In this expression it can be seen that Zi is positive if A< 1 increasing A causes Zi to approach infinity, become negative, and have the value -(Xn + ZO) where A = 2. If an ideal amplifier could be produced, there is no reason why a simple two stage amplifier would not be good enough to produce a stable negative capacity over all frequencies, provided the negative resistance due to Zo were 3

ENGINEERING RESEARCH. INSTITUTE. — UNIVERSITY OF MICHIGAN balanced out by a positive resistance connected to: the input. But because an ideal amplifier does not exist, to improve the actual amplifier characteristics (i.e., stability and bandwidth), negative feedback is added to the basic amplifier as in Fig. 3. If the cathode resistors are considered unbypassed, degeneration due to this is included in the gain A. In addition, a feedback loop having a feedback fraction, I, is added from the output to the cathode of the first tube. This gives a new effective gain of the amplifierlf and substituting V for A in equation (1), the input impedance becomes Xn+Zo where Jf = A l-AP In an ideal amplifier Z0, A, and 4 are real quantities and frequency insensitive. In an actual amplifier all of these quantities are complex, and frequency dependent. In addition, a small compensating capacity Ck, is introduced (see Fig. 3). These factors lead to a very involved expression for Zi (see Appendix B). The compensating capacitor Ck is introduced to extend the frequency, response of the amplifier. It begins to reduce the cathode degeneration of the first stage at frequencies where the gain begins to fall off because of shunt capacitances. By a suitable adjustment, the upper frequency response of the amplifier may be increased with only slight variation in overall response. Criteria established for the negative capacity element were: (1) wide bandwidth (as it was to operate over a wide frequency range), (2) capability of handling high input voltages (because of the voltages it may be subjected to in the oscillator tank circuit), (3) good stability, and (4) moderate plate power requirements. Tubes chosen to satisfy (4) may not satisfy (1) and (2) since these criteria are mutually exclusive. 4

Cd ___ 5 N s Cn FIG. 3 CIRCUIT DIAGRAM OF THE NEGATIVE CAPACITY ELEMENT 5- -_=

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN If a parallel resonant circuit is placed at the input, oscillation takes place if the negative capacity element is able to overcame the external circuit power losses. This condition occurs when the input shunt conductance is negative and exceeds the external circuit shunt conductance in absolute magnitude. Two components go to make up this negative conductance. Since V > 2, the first negative component is present at all times, and is due to the resistance term, Ro, in the expression Xn +Xo + (5) where Ro + JXo = Zo, the output impedance. The second component is introduced as the frequency becomes higher. Lagging phase shift is introduced due to tube and stray shunt capacitances in the circuit. At these frequencies,% becomes complex, taking the form MY = ~r - J'i' At the point where iji becomes appreciable, X. and XO render a second negative resistive component. The resistive component of Zi is given in general by (1 - r)Ro - i(1 + ) (X) r' i Thus it is possible for the circuit to operate without oscillating at mid-band enough to cause oscillation. Overloading the input voltage will also cause the circuit to oscillate. The overload voltage is determined by the plate characteristics at a given grid bias, and the amount of negative feedback in the circuit. Negative feedback will allow the input voltage to be increased by a factor of o —) over overload voltage without negative feedback, within the normal operating frequency range. If this circuit happens to be left ungrounded or open, it behaves as an asymmetric multivibrator operating at about 1000 cps. This is to be expected because the two tubes are capacitively inter-coupled.' _ 2 - 6 -

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 3. EXPERIMENTAL RESULTS 3.1 Actual Circuits The circuit as given in Fig. 3 was built up using 6CL6 tubes. The transconductance is high (A 11,000 Wmho) in this type of tube. The values used in the circuit with this tube are given in Table I. Other types of tubes can be used in the circuit, provided the interelectrode capacities are low; such tubes are the 6AH6, 6AG5 or their octal equivalents. The circuit was built up using 6AG5's. The 6AG5 has the lowest gm (l 5000 imho) of the three tubes considered. The components used in the 6AG5 circuit are also given in Table I. The results derived using this type of tube were very similar to those found using 6CL6 tubes with two expected differences. First, the circuit does not operate to quite as high a frequency (maximum of 2.5 me as compared to somewhat over 3 mc for the 6CL6's). Second, the circuit is incapable of handling as high an input signal, primarily because of the lower bias on the 6AG5's. The type 6AH6 tube would probably give a circuit performance intermediate to that given by the 6AG5 and 6CL6 tube. The only advantage in using 6AG5 tubes was that the circuit required only 18 ma total plate current as compared to 70 ma with 6CL6's. 3.2 Explanation of Graphs Figures 4, 5, and 6 are plotted from data taken from the 6CL6 circuit. A Q-meter (Boonton 160A) was resonated at a given frequency with its internal capacitance. The Q was recorded. The negative capacity was placed in the circuit in parallel with the internal capacitance. The Q meter was re-resonated at the same frequency, and again the Q was recorded. There are now three cases to consider. Either the Q is (1) higher with __...... 7.....

ENGINEERING RESEARCH: INSTITUTE * UNIVERSITY OF MICHIGAN TABLE I Component Values Used in the Basic Circuit of Fig. 3 Element 6CL6 Circuit 6AG5 Circuit Cc.002 4uf.003,f Cd.01 luf.01 4 Cs1 *5 f 5 f CS2.5 5f 45 rf (1 - N)(Rk) 100. 180. (N)(Rk) 400oo. 680. Rk2 100. 180. Rf 1000. 3300. RL 1600. 1Ok R' 1600. 10k Rg1 1 meg 1 meg Rg2 1 meg 1 meg Rsl 22k 82k Rs2 22k 82k gm 11 klqmho 5 ktmho Cn 10-150PuLf 10-1501,mf mica trimmer mica' trimmer Ck Ck 10-150Uy f 10-150,u mica trimmer mica trimmer CO" Capacitance between the plate of tube 2 and ground C0' Capacitance between the plate of tube 1 and ground. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ 8__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

CIRCUIT FIG. 3 - - - CIRCUIT CONSTANTS TABLE I -~ N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~S 6C~ -CK - -~_~~~~~~~~~~~~~~~~~~~~- C 4*f ~ ~ ~ ~ ~ ~ ~ ~~M FREQUENCY~ GRAPHOF G VS.FREQENCQWTHCKASACARMEE

Vw-,&-u WUU tI.L7.-V g9ZZ CIRCUIT FIG. 3 - CIRCUIT CONSTANTS TABLE I - -E cK =44/4pf 20 CN IS A PARAMETER 15, F 10. 55 Z C —2MC 3MC 4 MC FREQUENCY FIG. 5 GRAPH OF Gi VS. FREQUENCY WITH N AS A PARAMETER 10

CIRCUIT FIG. 3 - CIRCUIT CONSTANTS TABLE I 60 = 1 CNA=T4PAf | UNSTABLE REGION Ct IS A PARAMETER, 50 20 ~O I MC 2 MCC 4MC FREQUENCY FIG. 6 GRAPH OF Cj VS. FREQUENCY WITH CN AS A PARAMETER

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN the negative capacity, (2) the same, or (3) it is lower. In case one, power is being supplied by the negative capacity to the Q-meter. The amount of negative conductance was determined by placing suitable resistance in shunt with negative capacity so that the value of Q for the Q-meter circuit was the same with and without the negative capacity. In case two, the negative capacity neither supplies, nor absorbs power. This means the input conductance is zero. In case three, power from the Q-meter is being supplied to the negative capacity. To determine this positive conductance, a resistor is shunted across the Q-meter without the negative capacity in the circuit. The above procedure was repeated for different frequencies from.3 me to the point where, depending upon the value of Cn and Ck, oscillation could not be stopped with the introduction of a reasonable amount of positive conductance ( 100 pmho). In Figs. 4 and 5 the data points were obtained from the nominal values of the shunt resistors used. The range of possible error, indicated by the vertical bars, was obtained from the resistor tolerance. The dashed lines on the graphs are estimates of the behavior of the conductance when no data were taken. Figure 6 shows a plot of negative capacitance as a function of frequency. The negative capacity oscillates in the region to the right of the diagonal dashed line. In Figures 4 and 5 it is noticed that the conductance starts out positive and quite low, increases to a maximum, and then goes negative very steeply as the frequency increases. With increasing Ck, or decreasing Cn, the positive conductance maximum increases in magnitude and occurs at higher frequencies. This is to be expected from the analytical derivation of Yi (see Appendix B). The shape of the Ci vs. frequency curves is also predicted by this derivation. l _ _ _ _ _ _ _ _ __ ~12 _

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 3.3 Summary of Results Satisfactory operation was obtained only when the circuit was not overloaded. Although extensive data were not taken, the overload voltage appeared to decrease as the frequency was increased. It also decreased as Cn was increased. Using the 6AG5 circuit, the overload voltage at 2 mc had decreased to 1.9 volts rms for Cn = 4j f, but to only 2.7 volts rms for Cn = 10fL'. This circuit was used in conjunction with a one tube oscillator (Fig. 7) to investigate the possible improvement in tuning range. So long as the oscillator tank voltage was below the overload point, an improvement in tuning range was obtained up to about 2.5 mc. Above this frequency, the negative capacity began to take control of the frequency of the tank circuit, raising it to a scmewhat higher frequency (- h mc). Near a region where the negative capacity controls the oscillation, increasing Cn first increases the frequency of oscillation (froms2 tofo4 mc and upward) then causes it to oscillate at a much lower frequency (la.9 mc). This indicates that as Cn is increased the negative capacity first increases very sharply (2 to 4 mc) and then continues to increase more slowly. With a further increase in Cn, the input capacity becomes positive. Limitations are imposed on the amount of negative capacity that can be added to the circuit. From Fig. 5 it is seen that increasing Ci negatively (e.g., Cn) lowers the frequency where negative conductance appears. For this reason the amount of negative capacity added must be such that the total capacity is large enough to resonate at a frequency below the negative conductance region. Examples of this are given in the following data:....__ _ __ __ _ __ __ __ __,13,

bS-LZ-8 0aa 911-.3-V z9s + T X cg 6J4 Rg NEGATIVE 1Rt Lt CAPACITY ELEMENT 1 FIG. 7 OSCILLATOR CIRCUIT USED IN CONJUNCTION WITH THE NEGATIVE CAPACITY ELEMENT 1Lt

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN C. C Measured 1 t Upper Frequency Limit Illf uL f (Megacycles) -20 44 1.l -24 64 1.5 -26 71 ~1.4 where Ct is the tank capacitance, including strays. When using Ci = -20p.Lif the tuning range can be extended from approximately 2:1 to 2.7.l as given in the following data:l C i C t Meaured Resonant Frequency Tuning Ramge | zLssf| Ad L~ f | (Megacycles) none 44 1.26 2:1 none 184.63 -2o 44 1.8 a1. 7:1 -20 184 67 The upper frequency limit for satisfactory operation could be raised by employing (1) cathode peaking in the second tube, (2) lower plate loads, or (3) shunt plate peaking. 3.4 Application to Dielectric Tuned Receivers An application of the negative capacity might be realized in a dielecric tuned receiver. Because the negative capacity's input voltage is limited it annot be used in the local oscillator. But in the rf and mixer stages, the negajive capacity could be used to advantage. Fig. 8 shows the tuning curves of a

4.0 3.6 OSCILLATOR [2.25:1.3 o 3.0 CWO~~~~~~~ / /~~RF AND MIXER WITH NEGATIVE CAPACITY 2.25 2.0 / / NEGATIVE CAPACITY [2.25:1] i6/ / /:Ao MAXIMUM ALLOWABLE BIASVOLTAGE ON FERROELECTRIC 1.0 FREQENCY CONTROLLING VOLTAGE FIG, 8 TUNING CURVES OF A DIELECTRIC TUNED RECEIVER 16

ENGINEERING- RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN dielectric tuned receiver. The local oscillator is designed to give a 600 kc intermediate frequency. In this example, the tuning range without negative capacity for the oscillator, rf and mixer stages is 2.25~1 for the maximum allowable ferroelectric bias field. The desired frequency range of the receiver is from 1 to 3 mc. The local oscillator can cover thiL range with no difficulty because it tracks the mixer tuning unit at 0.6 mc above, therefore the maximum range of the oscillator (1.6 to 3.6 mc.) is only 2.25:1. The rf and mixer stages can cover only the range 1 to 2.25 mc, however. If a negative capacity of the proper value is added to these stages, they will now tune from 1 to 3 mc giving the required increase in tuning range of the entire receiver. 4. CONCLUSION The negative capacity amplifier was found to operate satisfactorily in a restricted frequency range below 3 mc. The upper frequency limit can be raised somewhat with suitable circuit modifications. Because the negative capacity element is capable of handling very small input voltages it is limited to use in rf amplifiers and certain applications in rf oscillators where it is not subjected to more than 3 or 4 volts (rms) of alternating voltage. 17

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX A Approximation for Zi Zi the input impedance with feedback is (as shown in the Eq. 4) dependend upon the output inpedance, the circuit gain and Cn. However, if R is finite, Zi takes the form Zi R(Xn+Zb) (7) (1-U) (R+Xn + Zo) where Z0 is the output impedance of the amplifier and R, the dynamic input resistance in the absence of feedback through Xn, has the form R = g l( )N A(A (8) where N is the fraction from ground of the cathode resistor at the point of the Rg connection, and Rg, 4t and A are as previously defined. In the circuit used, R = 5 megohms and, therefore, at least two orders of magnitude larger than Xn or Zo. Therefore, Eq. 7 may be closely approximated by Xo + Zo 0~ 0.:. ~

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX B In studying the input conductance as shown in Figs. 4 and 5 it is more convenient to look at the input admittance rather than input impedance. The inin put admittance is given by l (e3 el) jCn (see Fig. 9) (9) i =e1 CN el AMPLIFIER e3 F(p) BLOCK DIAGRAM OF NEGATIVE CAPACITY AMPLIFIER FIG. 9 Yi= [(P)-i] PCn (10) where p = E and F(p) = 3 is a function of p to be found in the following e1 sections. The input admittance will be calculated on a somewhat simplified version (Fig. 9) of the circuit as given in Fig. 3. The tube transconductance, gi, is modified by cathode degeneration to gm given approximately by gm (11) gmRk + 1 where Rk is the cathode resistor, and gm is the effective transconductance of the tube in question assuming that the screen current is a small percentage of the ___________________________________ 19

ENGINEERING RESEARCH'INSTITUTE * UNIVERSITY OF MICHIGAN total cathode current. Replacing the loads and tubes of Fig.L1 by admittances and current generators we obtain Fig. 11, the equivalent current generator circuit. el is the input voltage to the first tube grid (no grid current is assumed'to flow in either tube). e2 is the voltage across Y2, which is the input to the second tube. The second tube is replaced by a current generator I2 = e2gm, and e3 is the output voltage. ek is the voltage across Yk, the cathode admittance. The nodal equations at A, B, and K are as follows el'mZ, (e2-e) + 2 2 (12) e2gm2 = Y3e3 + Gf(e3"ek) (13) elgml = Gf(e3-ek) + G.(e-ek)- Yk(ek) (14) -gmlGfy2 + gmlgm2(Gf+Yk) solving for = F(p) -fy3lGfY + 2m)2(Gf+Yk, GfY3(Gp' Y2)p+IY3+ G)Gp'Y2 + Yk(Y3+ -)(Gp'+Y2) P Substituting the components for the complex admittances Yk, Y3, Y2 and factoring powers of p we have i s RHTp2+ Up 1 PCn (16) where coefficients P, Q, R, S, T, and U are as follows: p l [gm,(Gf + Gk) - Gf,'L] (17) - tgm m2ck -GfCo] (18) R = fG3G2 + (G3+Gf)G IGL' + Gk(G3+Gf)G2 gm2GfGp (19) where G2 =p' + GL' and G3 = P" + G" S Gf(G3C + G2CO") + G' { CO' (G3+G) + c1o } (20) +ok(%3+G%)Co' + GkG2Co" + (G3+Gf)G2Ck 20

t,-L/.-8 00 LI.I-.L.1-V 9 Z ~ R L~ FIG. 10 SIMPLIFIED CIRCUIT OF NEGATIVE CAPACITY AMPLIFIER el gm, e2gmz e3 1 — T t 1 2 ( e2 f I 1~""Y 2 II G'plI i~ bc 6I, 4 I I eK FIG. II EQUIVALENT CURRENT GENERATOR CIRCUIT OF FIGURE 8 21

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN T = CO"C0 (Gf+Gp,) + GkCo"G2 + CkCo' (G3+Gf) + GkCO"CO' (21) U = CkCo= Co' (22) expanding F(p) in powers of p and substituting in Eq. 10 pn + R ({ -PS)S+PRT } p2 + higher (23) R 2 p terms in p [ (- 1) pCn is the negative capacity term [(QR) P pCn is a nega rtive resistive term which depends upon 2. The coefficient of p3 is another capacitive term and that of p4 another resistive term, etc. Plots of input conductance and capacitance based on'Eq. 23 give curves similar to Figs. 4, 5 and 6. 22

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN REFERENCES 1. Howard Diamond and L. W. Orr, "Interim Report on Ferroelectric Materials and Applications," EDG Tech. Rep. No. 31, July 1954. L. W. Orr, "Ferromagnetic and Ferroelectric Tuning," EDG Tech. Rep. No. 32, August 1954. 2. E. L. Ginzton, "Stabilized Negative Impedances Parts I and II," Electronics, July and August 1945. 3. Herbert J. Reich, "Theory and Application of Electron Tubes," McGraw-Hill, 1944, pp. 211-216. 4. Chance, Hughes, MacNickel, Sayre, Williams, "Waveforms," MIT Radiation Laboratory Series, Vol. 19, Appendix A (P. E. Bell), McGraw-Hill, 1948. 23.

DISTRIBUTION LIST 1 copy Director, Electronic Research Laboratory Stanford University Stanford, California Attn: Dean Fred Terman 1 copy Chief, Electronic Warfare Department Army Electronic Proving Ground Fort Huachuca, Arizona 1 copy Chief, Engineering and Technical Division Office of the Chief Signal Officer Department of the Army Washington 25, D. C. Attn.: SIGJM 1 copy Chief, Plans and Operations Division Office of the Chief Signal Officer Washington 25, D. C. Attn: SIGOP-5 1 copy Countermeasures Laboratory Gilfillan Brothers, Inc. 1815 Venice Blvd. Los Angeles 6, California 1 copy Commanding Officer White Sands Signal Corps Agency White Sands Proving Ground Las Cruces, New Mexico Attn:: SIGWS-CM 1 copy Commanding Officer Signal Corps Electronics Research Unit 9560th TSU Mountain View, California 75 copies Transportation Officer, SCEL Evans Signal Laboratory Building No. 42, Belmar, New Jersey FOR - SCEL Accountable Officer Inspect at Destination File No. 22824-PH-54-91(1701) 24

1 copy H. W. Welch, Jr. Engineering Research Institute University of Michigan Ann Arbor, Michigan 1 copy Document Room Willow Run Research Center University of Michigan Willow Run, Michigan 1 copy Engineering Research Institute Project File University of Michigan Ann Arbor, Michigan 11 copies Electronic Defense Group Project File University of Michigan Ann Arbor, Michigan 25

UNIVERSITY OF MICHIGAN 3 901111111115 0252 0111111197 3 9015 02523 0197