Contains reports on four research projects.National Aeronautics and Space Administration (Grant NGL-22-009-163)Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Mohlere, R. D. V.

Peterson, D. F.

Rosenkranz, P. W.

Webb, J. G., Jr.

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VI. SOLID-STATE MICROWAVE ELECTRONICSAcademic and Research StaffProf. R. P. RafuseDr. D. H. SteinbrecherGraduate StudentsBartholomayChenR. D. MohlereD. F. PetersonJ. E. RudzkiA. A. M. SalehJ. G. Webb, Jr.A. SMITH CHART PLOTTING CIRCUITFigure VI-1 shows a waveguide circuit that produces an oscilloscope display ofthe complex reflection coefficient of a load, at a single frequency, as a function of someinternal parameter such as diode bias.The waves reaching the two square-law detectors are superpositions of the incidentand reflected waves on the line. The voltages developed in the detectors are thereforethe following.Vhoriz. = const. {[ + Ay ej(-6)] - [comp. conj.]}= const. [1+ 2Ay cos (-6) + (Ay)vert. const. [e- (n3/4):+ A ej( 6+(n+ 3/4)] . [comp. conj.]= const. I + 2Ay cos (O ) + (Ay)2J= const. [1 + 2A sin (-6) + (A-) 2 ,where6gA = two-way amplitude attenuation coefficient through the load-side attenuatorF = y e j 6 = amplitude reflection coefficient of the load (time-varying).If Ay << 1, then the third term in each of the equations above is negligible, so thehorizontal and vertical inputs to the oscilloscope are proportional to the real and imag-inary parts of the reflection coefficient, rotated by an angle 8, plus a constant. TheThis work was supported by the National Aeronautics and Space Administration(Grant NGL-22-009-163); and in part by the Joint Services Electronics Programs(U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 94W. G.A. Y.LOAD F= yejeL2 +8=0 2 18TEEXgSLOTTEDLINE(POSITION TO BEADJUSTED EMPIRICALLY)SLIDING-SCREW TUNERO KLYSTRONFig. VI-1.OR VERTICALTO OSCILLOSCOPETOR HORI ZONTALCircuit.Fig. VI-2. Impedance locus of a parametric amplifier.QPR No. 94(VI. SOLID-STATE MICROWAVE ELECTRONICS)constant terms can be taken out with the position controls of the oscilloscope, and thegain controls can be used to counteract any asymmetry in the two halves of the circuit.The origin can be located by setting the load attenuator to maximum, and then with theprobe of the sliding-screw tuner run in to maximum VSWR, the load attenuator can beadjusted so that the unit circle of the F plane coincides with the edge of the oscilloscopeface.Reflections at the tee and the slotted-line probe have been neglected in this analysis,but since the reflection coefficients of these components are not variables, and multiplereflections from the load are diminished by the attenuator next to it, this is compensatedfor by adjusting the position of the slotted-line probe so that the unit circle in ther plane, as indicated by the sliding screw tuner, maps into a circle on the oscilloscopeface.It is also possible to use a "magic tee" instead of a slotted line in this circuit; inthis case, either the E-plane or the H-plane arm would be connected to the detector, andthe other arm would be terminated with an adjustable short.This circuit has proved to be useful in the construction of parametric amplifiers andvaractor doublers. In the case of an amplifier, the noise figure is determined by thereal axis intercept of the impedance locus as the diode bias is swept from forwardconduction to the breakdown point, and the maximum gain is related to the end points ofthis locus.1Figure VI-2 shows such a locus for a 22.2-GHz parametric amplifier. Here the loadattenuator is set at ~10 dB, for 10% accuracy.P. W. RosenkranzReferences1. K. Kurokawa, "On the Use of Passive Circuit Measurements for the Adjustment ofVariable Capacitance Amplifiers," Bell System Tech. J., Vol. XLI, No. 1, p. 361,January 1962.B. NONLINEAR CIRCUIT ELEMENTSA class of nonlinear electrical circuit elements was examined in order to determinewhich of them are passively realizable and which are not. The class of nonlinear ele-ments examined is defined as follows: Let v be the pth time integral of the voltageP thacross the element when p is positive, and the p time derivative of the voltage whenp is negative. Let i be the qth time integral of the current through the element whenq thq is positive, and the q time derivative when q is negative. Then each element in theclass under consideyation is defined either by the relationship v = f(i q), or the inverserelationship iq = g(v p), and the element can be identified by giving the values of theQPR No. 94(VI. SOLID-STATE MICROWAVE ELECTRONICS)ordered pair (p,q).Such elements can be divided for my purposes into reactances, for which p-q isodd, and dissipative elements, for which p-q is even. For each of these two groups,frequency-power formulas are derived relating the powers flowing in the element at var-ious frequencies. These formulas reduce to the Manley-Rowe equations for p + q = 1,and to Page's and Pantell' s inequalities for p = q = 0. In their general form they areuseful in showing that certain of the elements defined above are not passively realizable,by virtue of the fact that power is not conserved in the element. For nonlinear elements,I have shown that the following are not passively realizable:a. Elements for which p - q is odd and p * 1.b. Elements for which p - q = 2n, where n is odd, and p + q t 0.For linear elements of this class, the frequency-power formulas do not provide anyinformation about realizability. An analysis of the linear elements can be carried outin the time domain, however, and I have shown that the following linear elements arepassively unrealizable:All those linear elements for which I p-q > 1.J. G. Webb, Jr.C. INTERMODULATION DISTORTIONRecent work has been concerned with building equipment capable of extending thedynamic range of spectrum analyzers in the analysis of third-order intermodulation dis-tortion. The measurement of third-order products more than 70 dB below the level ofthe primary signals is usually meaningless, because of the limited dynamic range of thespectrum analyzer. The attack on this problem is based on cancellation of the primarysignals without altering the distortion products.Prior efforts in the construction of this nulling device have centered on the designand construction of the summing, power-dividing, isolating, and nulling hybrids,P-I-N diode attenuators, power supplies, and coaxial signal-directing switches.Recent tests have shown that the signal nulling ability is approximately 30 dB wide-band and up to 90 dB narrow-band. In the narrow-band case this instrument extends thedynamic range of the 70-dB spectrum analyzer to 160 dB. The intermodulation distortionproducts were measured on a P-I-N diode attenuator with two -1 3 dBm signals (at fre-quencies of 30. 000 MHz and 30. 001 MHz) applied. The intermod products were foundto be 110 below the primary signals.Improvements on the performance of the test set are planned to increasethe wideband cancellation to a minimum of 40 dB and improve the shieldingand isolation to values in excess of 150 dB. A slight modification of theQPR No. 94(VI. SOLID-STATE MICROWAVE ELECTRONICS)system's P-I-N diode attenuators has to be made to give them more range.R. D. MohlereD. AVALANCHE DIODE ANALYSISThe small-signal, or incremental, impedance of an avalanche diode junction hasbeen measured as a function of the direct avalanche current. These measurements weremade in the frequency range 4-12 GHz in increments of 1/2 GHz.At a given value of bias current, the frequency variation of the incremental imped-ance is very similar to that of the circuit shown in Fig. VI-3.IFig. VI-3. Avalanche diode junctionequivalent circuit.The frequency-independent circuit elements (R, L, G, C) are chosen so as to yielda minimum value for the error expressionNE = - I Y .-Y 2,N mi cii= 1where Ymi is the measured value of admittance at frequency fi, Y ci is the admittanceof the circuit at frequency fi, and the sum extends over the measuring frequencies.Following this procedure for several values of bias gives the dependence of the ele-ments on the direct current Io1L ccoGccIG cr IR cc const.C = Cmin = depletion layer capacitanceat avalanche breakdown.Further analysis will be directed toward a large-signal model for the diode.D. F. PetersonQPR No. 94

Solid-State Microwave Electronics

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Solid-State Microwave Electronics

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