Theory, Design and Performance of Maximum-Efficiency Variable-Reactance Frequency Multipliers

Although the Manley and Rowe relations indicate that complete conversion of fundamental power to any specific harmonic with a nonlinear-reactance element is not impossible theoretically, many factors contribute to lowering the efficiency of real multipliers. Analysis, based on a Taylor series expansion of the nonlinear-reactance characteristic and Fourier expansion of the voltage and charge, with the introduction of suitable parameters and quiescent conditions, permits the exact determination of the various effects. Given the characteristics of a nonlinear element and the inevitable circuit losses, maximum obtainable efficiency can be predicted from the analysis. Significant increases in efficiency are obtained in various circuit configurations where selected intermediate harmonic currents are permitted to flow and where harmonics which cannot contribute to useful output at the desired harmonic frequency are suppressed. The characteristic of nonlinear reactance is shown to have a calculable effect on the multiplier efficiency, so that the most desirable characteristic can be specified. Experimental nonlinear capacitance multipliers designed according to the developed theory have provided an efficiency of 50 per cent for a quintupler and 70 per cent for a tripler, very close to the predicted values.