Filter Theory

Abstract

The main categories of filters are defined in terms of the general response types of lowpass, bandpass, highpass, and bandstop. The basic concepts of filters including transfer function, insertion loss, return loss, phase delay and group delay, are described. Filter characteristics such as maximally flat or Butterworth, equally ripple or Chebyshev, elliptic function, generalized Chebyshev or pseudoelliptic, and maximally flat time delay are discussed in terms of the poles of transfer function. Two‐port lumped‐element lowpass prototype networks and their element values and filter transformations are given. Richards’ transformation and Kuroda's transformations (or identities), impedance, and admittance inverters are also investigated, which are required for transforming lumped elements to transmission‐line sections, for separating physically filter elements and changing impractical elements into more realizable elements in a filter network.