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## Über dieses Buch

Analog filters are commonly used in areas such as electronics, communications, controls and signal processing. It is desirable for engineers and students in these areas to have a sound understanding of basic filter theory. This book is intended to be an intermediate level treatise of this subject. It can be used either as a textbook in a course at either the undergraduate or graduate level, or as a reference for engineers who find it useful to have an introductory knowlege or a general overview of analog filters. It introduces the theory behind filter development and the design techniques commonly used in practice, including the application of standard software packages. Extensive use is made of MATLAB for examples and problem sets, allowing readers to acquire familiarity with the methods for designing filters with a modern software tool.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
This chapter describes the roles and basic concepts of analog filters, their applications in electrical engineering, and certain fundamental ideas and terminology associated with them.
The term filter is used in many different ways in electrical engineering. An algorithm in a computer program that makes a decision on which commands and how certain commands are executed performs a filtering function. A decision technique that estimates the input signal from a set of signals and noise is known as optimal filtering. In analog and digital signal processing, filters eliminate or greatly attenuate the unwanted portion of an input signal. These analog and digital filtering processes may be performed in real-time or in off-line situations.
Kendall L. Su

### Chapter 2. The approximation

Abstract
As was mentioned in Chapter 1, the first step in the design of a normalized filter is to find a magnitude characteristic, ǀH(jω)ǀ, such that the set of specifications of an application is satisfied. Usually it is more convenient to deal with ǀH(jω)ǀ2 instead. As should be well known to the reader, a network function, H(s) must be a real rational function in s (the ratio of two polynomials with real coefficients), ǀH(jω)ǀ2 can be obtained by
$$\mathop {\left. {\mathop {\left| {H(jw)} \right|}\nolimits^2 = H(s)H( - s)} \right|}\nolimits_{s = jw} = H(jw)H( - jw) = H(jw)H^*(jw){\rm} (2.1)$$
Kendall L. Su

### Chapter 3. Network functions

Abstract
Once a magnitude characteristic has been chosen for a particular filter application, the next step is to determine a network function that not only has this magnitude characteristic, but is also realizable. By realizable, we mean that the function must be such that a workable network at least exists in theory, can be implemented with real-world components, and, barring unrealistic assumptions on these components, can be constructed and expected to perform the task accordingly. For example, the network function must be such that it has no pole in the right half of thes plane. If it does, the network will not be stable. The constructed network will either become nonlinear and function improperly or self destruct.
Kendall L. Su

### Chapter 4. Frequency transformation

Abstract
Thus far, we have placed our major emphasis on the lowpass filters. One justification for this approach is that other types of filters can be generated from lowpass ones. We shall now develop these procedures to show how other types of filters can be obtained from lowpass ones. The procedures we are going to use are the frequency transformations. In developing each of these procedures, we will be addressing the following issues: (1) the effects on the magnitude characteristic, (2) the effects on the network function, (3) the effects on the poles and zeros, and (4) the effects on the network elements.
Kendall L. Su

### Chapter 5. Properties and synthesis of passive networks

Abstract
We are now at a point where we can assume that a network function H(s) or, in some cases, its magnitude function ǀH(ω)ǀ has been determined. Our next task is to find one or more networks that will realize the given function. We will cover two broad categories of networks. One of them is networks using lossless elements. The other is networks containing resistors, capacitors, and op amps.
Before we embark on the development of various techniques to realize filters, we shall state without proof certain properties of some lossless networks and synthesis techniques that are relevant to filter realizations using lossless elements.
Kendall L. Su

### Chapter 6. Singly-terminated LC ladders

Abstract
We are now in a position to realize a very useful configuration, one of the simplest arrangements in filter applications. We shall deal with the situation where the source is an ideal one - either a voltage or a current source. The filter itself is an LC ladder. The load is a pure resistance.
Kendall L. Su

### Chapter 7. Doubly-terminated LC ladders

Abstract
The filter configurations dealt with in Chapter 6 assume that one of the ports of the lossless twoport is restricted to one of the idealized conditions - open circuit, short circuit, ideal voltage source, or ideal current source. Another situation that is often encountered in filter applications is when finite impedances exists at both ports. This filter arrangement is often referred to as the doubly-terminated lossless network. The lossless twoport is often referred to as the insertion network or insertion filter. The theoretical basis and design technique for this configuration is quite different from the singly-terminated configuration.
Kendall L. Su

### Chapter 8. Sensitivity

Abstract
The problem of finding a network to realize a certain network function is an open-ended one. There is no limit to how many networks one may be able to find to realize a given network function. This feature is especially true when active networks are used as we shall study in the upcoming chapters. In selecting a particular network from a number of available ones, different criteria may be used to make the final decision. Usually, the selection is based on the economics of the construction of the filter circuit. For example, in passive filters, the determining factor may be the number of inductors or the total inductance necessary. This is because inductors are usually the most expensive type of components, they deviate most from the idealized model, and they are most difficult to calibrate.
Kendall L. Su

### Chapter 9. Basics of active filters

Abstract
Chapters 5, 6, and 7 deal with the theory and basic methods of realizing filters that use passive elements - chiefly inductors and capacitors. These filters were the mainstay for filtering applications from the 1920’s through the 1940’s. Since the 1940’s, another type of filters - the active filters - have emerged and the technology has improved to the point that they are now in very common use and have attained a great deal of success. Originally motivated mainly by the low-frequency applications of filters in which inductors are too costly or too bulky and heavy, engineers began to search for alternative approaches using active devices. In the early stages of the development of active filters, some successes were achieved even when vacuum tubes were used. However, those filters were only feasible for very low frequency applications. When low-cost, light-weight, low-voltage solid-state devices became available, active filters became much more attractive and are applicable over much wider frequency ranges. As integrated-circuit devices - chiefly the op amp - became more and more economical and their applicable frequency range became wider and wider, so active filters became quite competitive with passive ones. Nowadays, both types of filters have their appropriate places in filtering applications.
Kendall L. Su

### Chapter 10. Biquad circuits

Abstract
In this chapter we shall present several widely used and well-established biquad circuits. The reader will find that the analysis and synthesis of these circuits are rather simple. Usually, given a circuit, it’s a matter of writing a few node equations and obtaining the voltage transfer function. Then the coefficients of the desired transfer function are matched with the transfer function coefficients in terms of the circuit element values. Various related concepts and other basic techniques and formulas used here were developed and explained in Chapter 9. Sensitivities may be an issue; we already have developed the basic methods of evaluating them in Chapter 8.
Kendall L. Su

### Chapter 11. High-order active filters

Abstract
In Chapters 9 and 10, we laid the foundation for general, high-order active filters. In Chapter 9, several basic principles and useful tools were developed. In Chapter 10, we concentrated on the various second-order filter sections - the biquads. We considered several design criteria and formulas for obtaining element values of some better-known biquad circuits.
Kendall L. Su

### Chapter 12. Active simulation of passive filters

Abstract
In addition to the methods presented in Chapter 11 for realizing high-order active filters, there is another entirely different approach to the same end. This other approach is to take a passive filter and simulate it by means of active devices and circuits. We shall devote this chapter to techniques in and examples of this approach.
Kendall L. Su

### Chapter 13. Switched-capacitor filters

Abstract
The filters we have studied in the two previous chapters are primarily based on the assumption that they are to be implemented in discrete or hybrid forms - thick-film or thin-film. Although the op amp may be fabricated in integrated-circuit (IC) form (sometimes in groups), it is actually treated as a separate entity for our purposes. Although some of the circuits we have studied can be fabricated in IC form, this is not a routine matter. There are many attendant problems and special details that need to be addressed and overcome.
Kendall L. Su

### Backmatter

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