A symbolic approach for the efficient computation of transfer functions in two-ports

Abstract

We present in this paper a number of formulae to compute all four transfer functions of a two-port in a uniform and efficient manner. Our approach improves on previous results by substantially reducing the order of the matrices involved in the computations. We handle circuit elements which may not have an admittance description: not only devices described in impedance terms, but also for instance the ones arising in the small-signal equivalents of operational amplifiers. In greater generality, we may accommodate devices without specifying a priori any control variables for their characteristics. Our framework avoids the need to use ad-hoc techniques depending on the form of the devices' characteristics, with all four transfer functions addressed in the same manner. Classical and generalized cofactors formulae are derived as particular cases. We apply the results to the analysis of active filters: in this context, both ideal and nonideal op-amps can be treated in a uniform manner, and the computation of certain sensitivities turns out to be possible because of the availability of explicit analytical expressions for the transfer functions.