A derivation of the switched-capacitor adjoint network based on a modified Tellegen´s theorem

A method of generating an adjoint network for switchedcapacitor (SC) circuits with periodic switching and piecewise-constant inputs is derived in a general manner using a modified form of Tellegen´s theorem. The derivation is independent of the method used to formulate the network equations. It is shown that under certain conditions the adjoint network may be described by the transposed system equations of the original switched capacitor circuit. The SC adjoint network is applied to the problem of determining the transfer functions from many input ports to a single output port.