Analysis of communication circuits based on multidimensional Fourier transformation

There are many communication circuits driven by multitone signals such as modulators and mixers, and so on. In this case, if frequency components of the modulators are largely different, the brute force numerical integration will take an enormous computation time to get the steady-state responses, because the step size must be chosen depending on the highest frequency input. The same situation happens to mixer circuits which generate very low frequency output. In this paper, an efficient algorithm is shown to solve the communication circuits driven by multitone signals which is based on the frequency-domain relaxation method and the multi-dimensional Fourier transformation. Attenuation of the transient phenomena mainly depends on the reactive elements such as capacitors and inductors, so that we partition the circuit into two groups of the nonlinear resistive subnetworks and the reactive elements using the substitution sources. The steady-state response can he calculated in such a manner that the responses at each partitioning point have the same waveform. We have developed a simple simulator carrying out our algorithm that only uses the transient, dc-analysis and ac-analysis of SPICE. It can be easily applied to relatively large scale integrated circuits, efficiently, We found from many simulation results that the convergence ratio at the iteration of our relaxation method is sufficiently large, and can be applied to wide class of the communication circuits.