Chapter 7 - Highpass Filters

Abstract

This chapter describes how to design an analog active or passive highpass filter with almost any desired specification. Passive highpass filters are designed using the normalized lowpass model. The model is normalized for a passband that extends from DC to 1 rad/s and is terminated with a 1Ω load resistance. The first part of the process is to carry 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 practice, parasitic components exist to reduce the upper frequency response. These parasitic components are capacitance between wires in an inductor's windings or inductance in the leads of a capacitor. 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. Denormalization of the highpass model for higher-load impedance requires component values to be scaled to have higher impedance. This is an identical process to that of denormalizing a lowpass filter. The impedance of an inductor is proportional to its inductance, but the impedance of a capacitor is inversely proportional to its capacitance.