Contains reports on one research project.Joint Services Electronics Program (Contract DAAB07-71-C-0300

Brodsky, Wesley G.

Freund, Robert W.

Kyhl, Robert L.

Penfield, Paul L., Jr.

Staelin, David H.

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V. MICROWAVE AND MILLIMETER WAVE TECHNIQUESAcademic and Research StaffProf. Richard B. Adler Prof. Robert L. Kyhl Dr. Joerg SanderProf. Bernard F. Burke Prof. Paul L. Penfield, Jr. Dr. Mikail TyukhtinProf. Madhu S. Gupta Prof. R. Marcus Price D. Cosmo PapaProf. David H. StaelinGraduate StudentsWesley G. Brodsky Wojciech K. Gwarek Bosco SunRobert W. Freund Robert V. McGahan Robert C. WalkerA. LOW-TEMPERATURE MILLIMETER WAVE RECEIVERSJoint Services Electronics Program (Contract DAAB07-71-C-0300)1. FREQUENCY-POWER FORMULAS FOR JOSEPHSON JUNCTIONSPaul L. Penfield, Jr.Russer and Thompson2 have derived (correctly) frequency-power formulas for loss-less models of Josephson junctions. Each of these authors stated that his formulas aresimilar to the Manley-Rowe relations, but have additional terms for dc power.It has previously been shown3 that the Manley-Rowe equations apply in similar caseswith dc power. My original motivation for this proof was to allow for power transmittedthrough rotating shafts, especially on synchronous and induction motors, but the deriva-tion was general enough to include the present Josephson models. Recent results, there-fore, should be regarded as a special case of the Manley-Rowe equations, rather than anew set of equations. Thompson stated explicitly his interpretation that the Josephsonjunction does not obey the Manley-Rowe equations; it is my belief that a more fruitfulviewpoint is that with the dc power interpreted properly, the Josephson junction doesobey the Manley-Rowe equations. This viewpoint makes it unnecessary to rederive otherforms for the equations, such as would be necessary for subharmonic generation, or forexcitation with more independent frequencies.My early result 3 may be stated as follows. Consider a device with one or more portsthrough which power can pass. Each port has a pair of covariables. In this case thereis only one port and the covariables are voltage and current. The Manley-Rowe equa-tions are obeyed by any such device with an energy state function that (i) is a functionof the integrals of one of the covariables from each port, and (ii) has as partial deriva-tives the other covariables. In this case the energy is a function of \, the integral ofvoltage:W(k) = f i dX,whereQPR No. 113(V. MICROWAVE AND MILLIMETER WAVE TECHNIQUES)2ewith c the superconducting phase, anddk-= v.dtIt is perfectly valid for the covariables to have nonzero average values, in which casethe variables upon which the energy depends may be unbounded.The resulting Manley-Rowe equations depend on the number of independent frequen-cies and the relationship of these to all frequencies at which power is exchanged. Thegeneral form is known, but the specific equations are different; for example, dependingon whether subharmonics are present or there is synchronization. The equations arenot altered by the presence of dc power, but the dc terms enter as if that power wereexchanged at an ac frequency dictated by the unbounded variable on which the energydepends. In the case of a rotating machine, it is the angular frequency of the shaft, andin the case of the Josephson junction, the autonomous frequency.Thompson also shows an equivalent circuit that has a parasitic loss element denotedG(v) to represent, among other things, tunneling electron current. A somewhat moreaccurate model 4 for this loss is a resistor whose value depends not upon the voltage butrather upon the superconducting phase, i. e., upon the integral of the voltage. Chua 5has discussed this model, and given it the name "memristor." In particular, Chua hasgiven the form of the frequency-power formulas for memristors, and they are differentfrom the Manley-Rowe equations, and from the formulas for nonlinear resistors.References1. P. Russer, "General Energy Relations for Josephson Junctions," Proc. IEEE 59,282-283 (1971).2. F. D. Thompson, "Power Flow for Josephson Elements," IEEE Trans., Vol. ED-20,No. 8, pp. 680-683, August 1973.3. Paul L. Penfield, Jr., Frequency-Power Formulas (The Technology Press of Mas-sachusetts Institute of Technology, Cambridge, Mass., 1960), see Secs. 3. 2 and4.6.4. B. T. Ulrich, Private communication, 1973.5. L. O. Chua, "Memristor - The Missing Circuit Element," IEEE Trans., Vol. CT-18,No. 5, pp. 507-519, September 1971.QPR No. 113(V. MICROWAVE AND MILLIMETER WAVE TECHNIQUES)2. K-BAND GaAs SCHOTTKY-BARRIER DIODE MIXERRobert W. Freund, Robert L. KyhlExperimental determinations of the mixing properties of a Schottky-barrier GaAsdiode at K-band (~20 GHz), described in Quarterly Progress Report No. 112 (page 35),continue. The diode used in the K-band waveguide mixer assembly is a GaAs Schottky-barrier device obtained from the M. I. T. Lincoln Laboratory. Figure V-1 is a micro-scope photograph that clearly indicates the numerous "dot" sizes available on the250 pm X 250 pm X 80 pm semiconductor chip. Each "dot" is a gold layer 500 A thickimmediately above each platinum-gallium arsenide Schottky-barrier diode. Electricalcontact is made by soldering the chip into the circuit and contacting one of the diode"dots" by means of an etched tungsten whisker as shown in Fig. V-2.A ridged rectangular waveguide is used for the millimeter-wave circuitry. A por-tion of the ridge guide is shown in Fig. V-3. The semiconductor chip is soldered to theFig. V-1. Various sizes of diode "dots"on a semiconductor chip.Fig. V-2. An etch whisker about to con-tact a 6 pm diode "dot."Fig. V-3. Bottom portion of the taperedsection of the ridged wave-guide mixer mount.QPR No. 113(V. MICROWAVE AND MILLIMETER WAVE TECHNIQUES)ridge approximately 8 mm (X~ /4 at these frequencies) from the front end (as viewed inthe picture) and contacted by a whisker-post combination. The post passes through theIF choke section in the top portion of the mount.Theoretical and experimental data are used to relate the different millimeter-waveproperties to the actual waveguide mount. Measurement data of 1-MHz capacitance vsvoltage permits the de-embedding of the diode from the rest of the waveguide structure.It has been assumed that the diode capacitance follows the familiar c /i 1 - v/, law forabrupt junctions. The current-voltage measurements indicate a zero-bias capacitanceof 24 fF (= 1015 farad) and a barrier potential D of .86 volt. Current-voltagedata for the forward conduction region indicate a consistent value of D and a dcspreading resistance R s of 16 0. Millimeter wave measurements are continuing on thissystem at room temperature and will soon be undertaken at cryogenic temperatures.3. 118-GHz MIXER DEVELOPMENTWesley G. Brodsky, David H. StaelinThe machined block for a mixer designed for use from 108 GHz to 128 GHz has beenreceived and has been gold plated. In this block a "chip" consisting of many Schottky-barrier diodes must be mounted and a small wire positioned across the waveguide andcontacted to a diode. Techniques for accomplishing this are now being perfected.QPR No. 113

Microwave and Millimeter Wave Techniques

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Microwave and Millimeter Wave Techniques

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