Active Filters

Theory and Design

S.A. Pactitis

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351835237
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Using an accessible yet rigorous approach, Active Filters: Theory and Design highlights the essential role of filters, especially analog active filters, in applications for seismology, brainwave research, speech and hearing studies, and other medical electronics. The book demonstrates how to design filters capable of meeting a given set of specifications. Recognizing that circuit simulation by computer has become an indispensable verification tool both in analysis and in design, the author emphasizes the use of MicroCap for rapid test of the filter. He uses three basic filter types throughout the book: Butterworth, Chenyshev, and Bessel. These three types of filters are implemented with the Sallen-Key, infinite gain multiple feedback, state-variable, and biquad circuits that yield low-pass, high-pass, band-pass, and band-reject circuits. The book illustrates many examples of low-pass, high-pass, band-pass, and notch active filters in complete detail, including frequency normalizing and denormalizing techniques. Design equations in each chapter provide students with a thorough grounding in how to implement designs. This detailed theoretical treatment gives you the tools to teach your students how to master filter design and analysis.

1	Introduction

1.1 FILTERS AND SIGNALS

A filter is a circuit that is designed to pass a specified band of frequencies while attenuating all signals outside this band. Filter networks may be either active or passive. Passive filter networks contain only resistors, inductors, and capacitors. Active filters, which are the only type covered in this text, employ operational amplifiers (op-amps) as well as resistors and capacitors.

The output from most biological measuring systems is generally separable into signal and noise. The signal is that part of the data in which the observer is interested; the rest may be considered noise. This noise includes unwanted biological data and nonbiological interference picked up by or generated in the measuring equipment. Ideally, we would like to remove it while retaining the signal, and often this is possible by suitable filtration.

If the spectra of signal and noise occupy completely separate frequency ranges, then a filter may be used to suppress the noise (Figure 1.1).

As filters are defined by their frequency-domain effects on signals, it makes sense that the most useful analytical and graphical descriptions of filters also fall under the frequency domain. Thus, curves of gain versus frequency and phase versus frequency are commonly used to illustrate filter characteristics, and most widely used mathematical tools are based on the frequency domain.

The frequency-domain behavior of a filter is described mathematically in terms of its transfer function or network function. This is the ratio of the Laplace transforms of its output and input signals. The voltage transfer function of a filter can therefore be written as

$\begin{array}{l}H\left(s\right)=\frac{V_0\left(s\right)}{V_i\left(s\right)}\hfill \end{array}$

(1.1)

where s is the complex frequency variable.

The Laplace transform approach to the filter analysis allows the designer to work with algebraic equations in the frequency domain. These are relatively easy to interpret by observation. In contrast, a time-domain approach to filter mathematics results in complex differential equations that are usually far more difficult to manipulate and interpret.

The transfer function defines the filter’s response to any arbitrary input signals, but we are most often concerned with its effect on continuous sine waves, especially the magnitude of the transfer function to signals at various frequencies. Knowing the transf...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Chapter 1 Introduction
• Chapter 2 Sallen–Key Filters
• Chapter 3 MultiFeedback Filters
• Chapter 4 Filters with Three Op-Amps
• Chapter 5 Sensitivity
• Chapter 6 Filters with GIC
• Chapter 7 OTA Filters
• Chapter 8 Switched Capacitor Filters
• Appendix A Node Voltage Network Analysis
• Appendix B Filter Design Nomograph
• Appendix C First- and Second-Order Factors of Denominator Polynomial
• Appendix D Formulas of Normalized Filters
• Appendix E Element Values for Low-Pass LC Filters
• Appendix F Coefficients of Denominator Polynomial
• Bibliography
• Index