Idler Circuits in Varactor Frequency Multipliers

This paper presents a general large-signal analysis for frequency multiplication with "lossy" abrupt-junction varactors. A Fourier-series representation of the current, the nonlinear elastance and the voltage is used to obtain exact closed-form solutions. Lossless coupling networks are considered in the theory so that the performance limits obtained will be fundamental to the varactor itself. Additional circuit losses can be added quite simply to find the expected performance in a practical case. Idler currents (currents flowing at frequencies other than the input and output frequencies) are shown to be necessary for multiplication by integers greater than two with abrupt-junction varactors. The effects of these currents are included in the general theory and a particular case, the tripler, is completely solved to demonstrate the procedures involved and to show the performance limits set by varactor and idler losses. Graphs which show the comparative theoretical performance of several multipliers are presented.