Transient sensitivity computation for MOSFET circuits

This paper discusses the algorithms and implementation necessary for computing time domain sensitivities during circuit simulation. The adjoint approach and the direct approach have been studied, and it was concluded that the direct approach is the best for implementation. The direct approach allows the transient sensitivities to be computed concurrently in time with the normal simulation, and it has been demonstrated that accurate sensitivity computations can be obtained, by simply allowing the sensitivity circuits to use the same time steps as the original circuit. This implementation also incorporates the charge based model for the MOSFET's and those sensitivity derivations are shown. It has been found that the responses of the sensitivity circuits can be discontinuous, and that this is due to discontinuities in the derivatives of the charge with respect to voltage. Derivations for various performance function sensitivities in terms of the response sensitivities are also given.