Simple numerical and multiple scales solution for the steady-state response of non-linear balanced modulators and mixers

Abstract

A simple and straightforward numerical steady-state solution of the strongly non-linear differential equations governing the differential-pair amplitude modulator is presented. It is shown that under normal biasing conditions and input signal levels exponential terms that give rise to coupling of the governing equations are very small in practice and may be dropped from the equations without influencing the circuit behaviour. The simplified equations lend themselves to a simple numerical solution by the brute force method. The results thus obtained are in excellent agreement with the harmonic balance results of Chua and Ushida (1981). The operation of the circuit in mixing an AM signal with an LO signal as well as the small signal modulator case are also treated. In the former case, four input frequencies are involved. In the latter, a multiple scales analysis is used to find the steady-state response analytically and it is found to be in excellent agreement with the numerical solution and other approximate methods of analysis.