Adjoint time-domain sensitivity of retarded peec using the numerical inversion of laplace transform

In this work, we present a method for the adjoint time-domain sensitivity analysis of delayed Partial Element Equivalent Circuit models using the Numerical Inversion of Laplace Transform technique. The proposed approach uses the Laplace-domain adjoint representation of delayed differential equations. The time-domain solution is obtained using an efficient Numerical Inversion of Laplace Transform method. Consequently, an impulse source can be directly included in the adjoint equations without the need to approximate it as in the case of marching-on-in-time techniques. In addition, since the analysis is done in the Laplace domain, time-domain numerical stability issues are avoided. The proposed method is compared with the perturbation approach and direct sensitivity computed by marching-on-time techniques demonstrating good accuracy.