Contains reports on four research projects.Lincoln Laboratory (Purchase Order DDL B-00368)United States Air Force (Contract AF19(604)-7400)United States ArmyUnited States Nav

Penfield, Paul L., Jr.

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XX. CIRCUIT THEORY AND DESIGNProf. P. Penfield, Jr. Prof. R. P. RafuseProf. C. L. Searle Prof. R. D. ThorntonA. PRIME-NUMBER MULTIPLIER CHAINSHigh-order frequency multipliers often consist of a chain, or cascade, of lower-order multipliers, usually doublers or triplers. Thus, for example, a X 24 circuitcould be made as a cascade of three doublers and a tripler. But what if the desiredharmonic number is a prime? An ordinary cascade cannot be used. We show in thisreport how the concept of multiplier chains can be extended slightly to allow generationof all high harmonics (prime and nonprime) by cascading individual stages.Let us examine in a fundamental way the generation of the harmonic. An input atfrequency wo is used to excite the nonlinear device. The nonlinearities force this signalto mix with itself and power is generated at the sum frequency w0 + wo = 20 . Thissecond harmonic, if allowed to exist, mixes again with the fundamental to form thefrequency wo + Zw0 = 30 , or with itself to form 4w . The process is one of mixing asignal either with itself or with another signal.Now suppose that instead we introduce two input frequencies (each a harmonic ofsome fundamental) and let them mix with each other. The output is taken at the sum(or difference) frequency, which can be a prime multiple of the fundamental. Approxi-mately as much power can be generated at this output frequency as could be deliveredby a multiplier with the same nonlinear element. What we have described is a "powerupconverter" ( or "power downconverter"). To generate a large prime number, we canuse two multipliers or multiplier chains to generate two nonprime harmonics whosesum is the desired prime, and then mix the outputs from these two chains in a powerupconverter.For example, consider the generation of the fifth harmonic. This can be generatedat high efficiency with idlers at 200 and 3 0 , or with idlers at 2w0 and 4w . It can alsobe generated, however, by mixing the outputs from a tripler and a doubler, or bymixing the output from a chain of two doublers with the fundamental, or even by mixingthe output from a chain of a doubler and a tripler with the fundamental. Thus, the quin-tupler (and other multipliers) can be built either with idlers or as a cascade of simplermultipliers and power upconverters.1Power upconverters made from abrupt-junction varactors can have efficienciesand power outputs that are comparable to those of varactor multipliers, and they aredesigned by using very similar techniques.This research was supported in part by Purchase Order DDL B-00368 withLincoln Laboratory, a center for research operated by Massachusetts Institute ofTechnology with the joint support of the U. S. Army, Navy, and Air Force under AirForce Contract AF19(604)-7400.QPR No. 67 273(XX. CIRCUIT THEORY AND DESIGN)Power upconverters (and downconverters) should be considered possible componentsin multiplier chains. With this slight extension of the concept of "multiplier chain,"chains can be built to generate any harmonic, prime or nonprime, and the designer ofmultipliers is somewhat less restricted in his choice of frequencies.P. Penfield, Jr.References1. P. Penfield, Jr. and R. P. Rafuse, Varactor Applications (The M.I.T. Press,Cambridge, Mass., 1962), Chapter 10.QPR No. 67 274

Circuit Theory and Design

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Circuit Theory and Design

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