Multiparameter time-domain sensitivity computation

In this paper, a novel approach for the computation of multiparameter time-domain sensitivity during circuit simulation is presented. The computation of the sensitivity values of one or more circuit variables (e.g., node voltages or branch currents) with respect to both design parameters (e.g., R, C, MOS length, MOS width...) and process parameters (e.g., tox, nsub, u0...) is addressed by introducing a rigorous mathematical derivation of the proposed direct differentiation modified algorithm (DDMA). First, the circuit interpretation of the analytical formulas as well as their theoretical derivation from the Tellegen´s theorem is discussed. Then, DDMA is compared with the direct method and the adjoint technique to emphasize the cost difference in terms of CPU operations. The accuracy of the new algorithm is also evaluated, by estimating the numerical error involved in the solution of discretized sensitivity equations. Finally, a set of circuit examples is presented to demonstrate the effectiveness of DDMA together with the implementation details needed to include the present sensitivity analysis in a circuit simulator such as Spice3F5