Page 150 - Analog and Digital Filter Design

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CHAPTER

HIGHPASS FILTERS

This chapter describes how to design an analog active or passive highpass filter
having almost any desired specification. This chapter, like the previous one, uses
information from Chapters 1. 2. and 3. Examples for most types of highpass
filter are given. Formulae will be presented for the denormalization of cornpo-
nent values given in previously presented tables.

Passive Filters

Passive highpass filters are designed using the normalized lowpass model. The
model is normalized for a passband that extends from DC to lrad/s and is
terminated with a 1 R load resistance. The first part of the process is to carrj
out the conversion to a highpass model; this can then be scaled for the desired
load impedance and cutoff frequency. The highpass model has a passband that
extends from 1 rad/s to infinity (in theory, at least). In practice, parasitic com-
ponents exist to reduce the upper frequency response. These parasitic compo-
nents are, for example, capacitance between wires in an inductor’s windings
or inductance in the leads of a capacitor. More details on these are given in
Chapter 10

Converting the lowpass model into a highpass equivalent is not too demanding
in all-pole filters. like Butterworth or Chebyshev types. The process requires
replacing each inductor in the lowpass model by a capacitor. Similarly. each
capacitor in the lowpass model has to be replaced by an inductor.

In Cauer or Inverse Chebyshev filters there are series or parallel resonant LC
networks. For these components, replacing inductors in the lowpass rnodel bj
capacitors and replacing capacitors in the lowpass model by inductors would
appear to give no change. The net result is a series or parallel resonant circuit
as before. However, when each component is replaced by one with an opposite
reactance. the replacement will have a value that is the reciprocal of its value in
the lowpass model. Thus, the inductance value will be the reciprocal of the