Multi-resolution based sensitivity analysis of complex non-linear circuits

This study addresses the sensitivity analysis of non-linear circuits in their transient and periodic behaviour. The circuits here considered are built of connections of N-ports with frequency-dependent parameters whose input and output quantities are expanded in the wavelet domain. The use of wavelet instead of the Fourier analysis allows a significant increase in the sparsity of the matrices with a comparable accuracy and convergence rate. In addition, by using the proper wavelet basis, it is possible to analyse both the steady state and the transient behaviour. The adjoint system method is used to obtain the sensitivities of the response of the circuit with respect to the design parameters. The multiport connection is described in terms of scattering parameters and the hierarchical approach is extended to the adjoint system. Computational aspects are discussed and examples of application of the proposed technique are reported. The results are compared with those obtained by the use of other techniques.