Adjoint network approach to sensitivity calculation for switched‐capacitor networks

Abstract

AbstractThis paper introduces a computer analytical technique for obtaining the element sensitivities of switched‐capacitor networks (SC networks) with good efficiency by using adjoint networks similar to those for conventional linear networks. The SC networks treated here consist of capacitors, ideal two‐mode switches and operational amplifiers represented by nullator‐norator models. The network equations for the SC networks with amount of charge movement and voltage as variables are so formulated that the network equations of the adjoint networks can be obtained by a simple transformation such as the transpose of their coefficient matrices and with minimum order in many cases. It is also shown that by using Tellegen's theorem in the SC networks, the element sensitivities for capacitors can be obtained as the product of the amount of charge movement in the original SC networks and the voltages in their adjoint networks. Therefore, the element sensitivities can be determined by network analysis of the SC networks and their adjoint networks and the analysis can be performed efficiently with the abovementioned formulation of network equations. Finally, an example of sensitivity analysis by implementing a computer program is shown and its effectiveness is confirmed.