Asymptotic analysis of nonlinear electronic circuits

It is very important to analyze mixers and modulators for designing communication circuits. They are driven by multiple frequencies, one of which is usually very high carrier frequency compared to the other. To know the transient behaviors, we need to calculate many carrier waveforms, so that the transient analysis is very time-consuming. Hence, we propose an efficient envelope analysis for calculating the asymptotic behaviors of the amplitudes, which is based on the harmonic balance (HB) method with the slowly varying coefficients. In order to develop the Spice-oriented simulators, the Fourier expansions of nonlinear devices such as bipolar transistors are executed with MATLAB, and the Fourier modules should be stored in our computer library. Thus, we can easily formulate the determining equations of HB method called sine-cosine circuit. We found from many examples that the envelope method is several ten times faster than the transient analysis.