On the Passivity of Wave Digital Networks

Abstract

With inventing the wave digital (WD) filters almost fifty years ago, Alfred Fettweis laid the foundation to a completely new approach for the digital modeling of passive analog filter circuits. Soon it became clear that not only classical filter structures could be modeled by the WD concept, but also other linear and nonlinear electrical circuits and, moreover, even general physical systems, including those being described by partial differential equations. Of particular significance is the fact that this approach makes it possible to transfer the important physical concepts of passivity and losslessness from the analog to the digital domain. As a result, properly designed passive WD filters exhibit a very low coefficient sensitivity which considerably reduces the hardware requirements. This is clearly one important issue of the WD concept. However, even more important are the excellent stability properties which can be achieved by applying the concepts of passivity and incremental passivity. In this paper a review of these latter properties and its consequences will be presented. It will in particular be discussed how the passivity can be preserved even under finite arithmetic conditions.