Jacobian calculation using the multidimensional fast Fourier transform in the harmonic balance analysis of nonlinear circuits

A technique which allows the gradient of frequency-domain simulation variables to be analytically determined using time-domain derivative information and the multidimensional fast Fourier transform is discussed. It is shown that this technique can be efficiently implemented when a circuit is driven by any number of incommensurate input frequencies. A harmonic balance simulator that uses this technique to determine the entries of the Jacobian matrix needed in a quasi-Newton iteration scheme is constructed. A significant reduction of simulation time is observed when compared with a harmonic balance simulator that uses transforms based on matrix multiplication