Approximation methods for electronic filter design : with applications to passive, active, and digital networks

✍ Scribed by Richard W. Daniels

• Publisher: McGraw-Hill / The Kingsport Press
• Year: 1974
• Tongue: English
• Leaves: 414
• Category: Library

✦ Table of Contents

Front
Dust cover - Front
Dust cover - Flaps - About the Author
Title page
Copyright
Dedication
Contents
Preface
Symbols
Chapters
1. Introduction
1.1 Approximation theory
1.2 Filter jargon
1.3 Realizations
1.4 Types of approximations
REFERENCES
2. The Butterworth Approximation
2.1 Introduction
2.2 The characteristic function
2.3 The lowpass characteristic function
2.4 Butterworth polynomials
2.5 Butterworth lowpass filters
2.6 Determination of degree of Bn(w)
2.7 H(s) for the Butterworth approximation
2.8 Quality of Butterworth roots
2.9 Conclusions
REFERENCES
PROBLEMS
3. The Tschebycheff Approximation
3.1 Introduction
3.2 Equiripple approximations
3.3 The Tschebycheff lowpass approximation
3.4 Introduction to Tschebycheff polynomials
3.5 The Tschebycheff polynomial
3.6 The normalized Tschebycheff lowpass
3.7 Determination of degree of Tn(x)
3.8 A program for the loss of Tschebycheff lowpass filters
3.9 An optimum property of Tschebycheff filters
3.10 H(s) for the Tschebycheff approximation
3.11 Concluding remarks
REFERENCES
PROBLEMS
4. The Inverse Tschebycheff Filter
4.1 Introduction
4.2 Manipulation of Tschebycheff characteristics
4.3 Maximally flat property of the inverse Tschebycheff filter
4.4 Determination of inverse Tschebycheff loss
4.5 Determination of degree of the inverse Tschebycheff filter
4.6 A program for the loss of inverse Tschebycheff lowpass filters
4.7 Concluding remarks
5. Elliptic Filters
5.1 Introduction
5.2 Introduction to Tschebycheff rational functions
5.3 A basic form for Rn(x,L)
5.4 A differential equation for Rn(x,L)
5.5 The elliptic integral of the first kind
5.6 Elliptic functions
5.7 An alternative form for the elliptic integral
5.8 Elliptic functions and Rn(x,L)
5.9 The periodic rectangle for Rn(x,L)
5.10 Determination of degree of elliptic filters
5.11 Determination of L
5.12 A rational expression for Rn(x,L)
5.13 A program for elliptic lowpass filters
5.14 Concluding remarks
REFERENCFS
PROBLEMS
6. Frequency Transformations
6.1 Introduction
6.2 Normalized-lowpass-to-unnormalized-lowpass transformation
6.3 Lowpass-to-highpass transformation
6.4 Lowpass-to-bandpass transformation
6.5 Lowpass-to-bandstop transformation
6.6 Lowpass-to-multiple-bandpass transformation
6.7 Reactance transformations
6.8 Other frequency transformations
6.9 Conclusions
REFERENCES
PROBLEMS
7. The Transformed Variable
7.1 Introduction
7.2 The transformed variable
7.3 Functions in terms of the transformed variable
7.4 F(Z) and Q(Z) for lowpass filters
7.5 The inverse transformation
7.6 Conclusions
REFERENCES
PROBLEMS
8. Attenuation Poles for Equiripple Passband Filters
8.1 Introduction
8.2 Poles and zeros
8.3 The loss function L(Z)
8.4 The template method
8.5 Intuition development
8.6 A simple computer program
8.7 A computer template method
8.8 Terminology used for the general problem
8.9 Outline of solution
8.10 Determination of arc minimum
8.11 Determination of the minimum difference Dmin_i
8.12 Determination of new poles
8.13 Summary of pole-placer program
8.14 Examples for the pole-placer program
8.15 Modifications of the pole-placer program
8.16 Lowpass pole-placer program
8.17 Highpass pole-placer program
8.18 Conclusion
REFERENCES
PROBLEMS
9. The Characteristic Function for Equiripple Passband Filters
9.1 Introduction
9.2 The characteristic function and the transformed variable
9.3 Determination of Q^2(Z)
9.4 Determination of F^2(Z)
9.5 Determination of Q^2(Z) and F^2(Z) for lowpass filters
9.6 The loss function L(Z)
9.7 Stopband performance
9.8 Passband performance
PROBLEMS
10. Natural Modes for Equiripple Passband Filters
10.1 Introduction
10.2 H(s) and the transformed variable
10.3 Determination of E(Z)E*(Z)
10.4 Determination of e(s)
10.5 Determination of natural modes of equiripple lowpass filters
10.6 Conclusions
REFERENCE
PROBLEMS
11. Maximally Flat Passbands
11.1 Introduction
11.2 Determination of the characteristic function
11.3 Determination of Q^2(Z) and F^2(Z) for lowpass filters
11.4 Stopband and passband performance
11.5 Determination of attenuation poles for maximally flat filters
11.6 Natural modes for maximally flat passband filters
11.7 Comparison of maximally flat and equiripple filters
11.8 Conclusions
REFERENCES
PROBLEMS
12. Parametric Filters
12.1 Introduction
12.2 The basic trick
12.3 Addition of a pole at infinity
12.4 Addition of a pole at the origin
12.5 Stopband and passband performance
12.6 Determination of attenuation poles for parametric filters
12.7 Results from the pole-placer program
12.8 Parametric lowpass filters
12.9 Natural modes for parametric filters
12.10 Conclusions
REFERENCES
PROBLEMS
13. Optimization Techniques for Approximation Theory
13.1 Introduction
13.2 System response and error criteria
13.3 Initial parameters
13.4 Minimization techniques
13.5 Practical optimization programs for the approximation problem
13.6 Arbitrary passband, equiminimum stopband
REFERENCES
14. Delay and Related Subjects
14.1 Introduction
14.2 Definition of delay
14.3 Calculation of delay
14.4 A program for the calculation of delay
14.5 Relations between magnitude and delay
14.6 The Hubert transformations
14.7 The Bessel approximation
14.8 The Gaussian magnitude approximation
14.9 Transitional Butterworth-Thomson filters
14.10 Tschebycheff approximation of constant delay
14.11 Delay considerations for bandpass filters
14.12 Addition of attenuation poles
14.13 Amplitude equalizers
14.14 Allpass networks
14.15 Allpass networks derived from lowpass delay approximations
14.16 Conclusions
REFERENCES
PROBLEMS
15. Time-Domain Response
15.1 Introduction
15.2 Definition of terms
15.3 Transient response and the Laplace transformation
15.4 Partial fractions and the inverse Laplace transformation
15.5 Taylor series and the inverse Laplace transformation
15.6 Comparison of transient response
REFERENCES
PROBLEMS
16. Approximation Methods and Passive Network Synthesis
16.1 Introduction
16.2 Insertion loss
16.3 The transmission function H(s)
16.4 The reflection function T1(s)
16.5 The lossless coupling network
16.6 Synthesis of the lossless coupling network
16.7 The zero—shifting technique
16.8 Typical network configurations
16.9 Synthesis in terms of the transformed variable
16.10 Conclusions
REFERENCES
PROBLEMS
17. Approximation Methods and Active Filter Synthesis
17.1 Introduction
17.2 Negative-impedance-converter active filters
17.3 Gyrator active filters
17.4 Second-order transfer functions
17.5 Decomposition into second-order transfer functions
17.6 Some practical active circuits
17.7 Coupled active filters
17.8 Conclusions
REFERENCES
18. Approximation Methods and Digital Filter Synthesis
18.1 Introduction
18.2 The Z transformation
18.3 Design of digital filters from continuous filters
18.4 Nonrecursive digital filters
18.5 Impulse-invariant method
18.6 Matched Z-transform method
18.7 Bilinear digital filters
18.8 Realizations for digital filters
18.9 Conclusion
REFERENCES
Appendices
Appendix A Telcomp
Appendix B Filter Design by the “Cookbook” Approach
Answers to Selected Problems
Index
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