Why Don't Back-to-Back Abrupt Junction Frequency Triplers Work?

The recent interest in direct frequency tripling. i.e., tripling without idler circuits, is due primarily to advances in the fabrication of planar, two-terminal nonlinear circuit elements having a symmetrical capacitance-voltage characteristic. Over the past few years, several research groups have put considerable effort into the development of triplers based on uniformly doped (abrupt-junction) back-to-back varactors only to measure little if any power conversion despite an apparently reasonable Cmair,,,, ratio, the common figure of merit. Although a symmetrical capacitance-voltage function is desirable for efficient direct tripling, the dynamics of direct tripling using symmetrical varactors is more complex than first expected. We describe the nonlinear circuit behavior of back-to-back varactors using the elastance-charge function, and discuss the phenomenon of self-biasing. We conclude by showing that it is physically impossible for a back-to-back uniformly doped varactor circuit to convert power from the pump frequency to any harmonic.