Modern Filter Design: Active RC and Switched Capacitor

Chapter 1: Filter Transmission and Related Topics

1.1 INTRODUCTION

An electrical wave filter can be defined as an interconnected network of electrical components, such as resistors, capacitors, inductors, and transistors, which operates on or processes applied electrical signals. The applied electrical signal is referred to as the input signal or excitation. The product of the processing performed by the network on the excitation is referred to as the output signal or response. The excitation and response will differ according to the processing or filtering performed by the network. As we shall see shortly, there are several means by which we can represent and specify this filtering operation. In this book we are concerned with the analysis, specification, design, and realization of electrical filters for the frequency range f ? 500 kHz, with emphasis on audio-frequency ( f ? 20 kHz) applications. It is in this frequency range where the greatest benefits are derived from the use of active components in electrical filter networks.

Filtering in the general sense is a selection process. The output of a filter is then a selected subset of the input. In electrical filtering the object is to perform frequency-selective transmission. We know from elementary signal theory that any periodic wave of period 2 ?/ ? R can be represented by its Fourier series expansion

(1-1)

where the coefficients a k and b k define the harmonic content of the wave s( t). The frequency-independent term a 0 is...

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