Time-domain Sensitivity Computation for Networks Containing Transmission Lines

The key to the efficient automated design and optimization of nonlinear networks is the sensitivity vector. The sensitivity vector is a measure of the performance of the network with respect to the changes of the design parameters. A derivation of the sensitivity vector for nonlinear networks containing transmission lines is presented. If the transmission lines are either lossless or dispersionless, the network can be characterized by a set of differential-difference equations. Variational techniques are used to derive a set of equations which is adjoint to the original set. Solving both sets of equations only once suffices to obtain the desired sensitivity vector for all possible design parameters. The adjoint network approach is then considered. It is shown that transmission lines are self-adjoint and that the initial waves stored on the transmission lines in the adjoint network are always identically zero. For purpose of evaluation, an experimental program based on the preceding methods was written and the results were compared to the (less efficient) method of direct parameter partubation for a problem involving a switching circuit containing transmission lines. Good agreement was observed.