TABLE OF CONTENTS In the following we discuss briefly some selected topics in passive-network properties. The reader is referred to [B1] and [B2] at the end of this appendix for a detailed treatment of these topics.
In the design of active- RC networks, active devices and passive RC networks are employed. It is helpful to the designer to be familiar with some of the basic properties of RC networks. Before we consider passive- RC networks, it is useful to know some basic properties of passive networks in general.
In Chapter 1 we discussed driving-point functions. A driving-point function is a subclass of a network function where the response and excitation are considered at the same port. The driving-point impedance function Z( s) is the reciprocal of the driving-point admittance function Y( s). It can be shown [B1] that the necessary and sufficient conditions for a driving-point immittance [1] function H( s) to be a passive- RLC network is that H( s) is a positive real (p-r) function. A p-r function is defined as follows:
A function H( s) is p-r if and only if:
H( s) is real for real s.
Re H( s) ? 0 for Re s ? 0 where Re stands for the real part of.
A convenient testing criterion for p-r functions is as follows:
H( s
