Comparison of harmonic balance to boundary constraint within autonomous and nonautonomous circuits

This paper examines two methods of solving circuits with stationary periodic responses presented by truncated harmonic series. The first is the standard implementation of harmonic balance, which includes DFT for calculating amplitudes of signals. The second is the boundary constraints approach, which matches signals at chosen points within a period. To compare the effectiveness of the two methods, the circuit is divided into reactive and resistive parts. Exploiting the standard Newton numeric procedure, it is shown that the Jacobian of the former method requires more basic arithmetical operations. The convergence ratio is observed using a simple example.