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E-raamat: Broadband Matching: Theory And Implementations (3rd Edition)

(Univ Of Illinois, Chicago, Usa)
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The third edition presents a unified, up-to-date and detailed account of broadband matching theory and its applications to the design of broadband matching networks and amplifiers. A special feature is the addition of results that are of direct practical value. They are design curves, tables and explicit formulas for designing networks having Butterworth, Chebyshev or elliptic, Bessel or maximally flat group-delay response. These results are extremely useful as the design procedures can be reduced to simple arithmetic. Two case studies towards the end of the book are intended to demonstrate the applications to the practical design of modern filter circuits.
Preface to the 3rd Edition xvii
Preface to the 2nd Edition xix
Preface to the 1st Edition xxi
Chapter 1 Foundations of Network Theory 1(47)
1 Basic network postulates
2(9)
1.1 Real-time function postulate
3(1)
1.2 Time-invariance postulate
4(1)
1.3 Linearity postulate
5(1)
1.4 Passivity postulate
6(3)
1.5 Causality postulate
9(1)
1.6 Reciprocity postulate
10(1)
2 Matrix characterizations of n-port networks
11(10)
2.1 The impedance matrix
12(1)
2.2 The admittance matrix
13(1)
2.3 The hybrid matrix
14(1)
2.4 The indefinite-admittance matrix
15(6)
3 Power gains
21(2)
4 Hermitian forms
23(5)
5 The positive-real matrix
28(11)
6 Frequency-domain conditions for passivity
39(4)
7 Conclusions
43(2)
Problems
45(2)
References
47(1)
Chapter 2 The Scattering Matrix 48(68)
1 A brief review of the transmission-line theory
49(1)
2 The scattering parameters of a one-port network
50(16)
2.1 Basis-dependent reflection coefficients
52(2)
2.2 Basis-independent reflection coefficient
54(3)
2.3 The factorization of the para-hermitian part of z(s)
57(5)
2.4 Alternative representation of the basis-independent reflection coefficient
62(2)
2.5 The normalized reflection coefficient and passivity
64(2)
3 The scattering matrix of an n-port network
66(25)
3.1 Basis-dependent scattering matrices
70(4)
3.2 Basis-independent scattering matrix
74(3)
3.3 The scattering matrices and the augmented n-port networks
77(3)
3.4 Alternative representation of the basis-independent scattering matrix
80(2)
3.5 Physical interpretation of the normalized scattering parameters
82(6)
3.6 The normalized scattering matrix and passivity
88(2)
3.7 The normalized scattering parameters of a lossless two-port network
90(1)
4 The bounded-real scattering matrix
91(7)
5 Interconnection of multi-port networks
98(9)
6 Conclusions
107(1)
Problems
108(6)
References
114(2)
Chapter 3 Approximation and Ladder Realization 116(104)
1 The Butterworth response
117(16)
1.1 Poles of the Butterworth function
119(2)
1.2 Coefficients of the Butterworth polynomials
121(3)
1.3 Butterworth networks
124(2)
1.4 Butterworth LC ladder networks
126(7)
2 The Chebyshev response
133(19)
2.1 Chebyshev polynomials
133(2)
2.2 Equiripple characteristic
135(4)
2.3 Poles of the Chebyshev function
139(3)
2.4 Coefficients of the polynomial p(y)
142(2)
2.5 Chebyshev networks
144(2)
2.6 Chebyshev LC ladder networks
146(6)
3 Elliptic functions
152(14)
3.1 Jacobian elliptic functions
152(2)
3.2 Jacobi's imaginary transformations
154(1)
3.3 Periods of elliptic functions
155(4)
3.3.1 The real periods
157(1)
3.3.2 The imaginary periods
158(1)
3.4 Poles and zeros of the Jacobian elliptic functions
159(3)
3.5 Addition theorems and complex arguments
162(4)
4 The elliptic response
166(32)
4.1 The characteristic function Fn(ω)
167(7)
4.2 Equiripple characteristic in passband and stopband
174(10)
A Maxima and minima in the passband
177(1)
B Maxima and minima in the stopband
178(1)
C Transitional band
179(5)
4.3 Poles and zeros of elliptic response
184(7)
4.4 Elliptic networks
191(7)
5 Frequency transformations
198(9)
5.1 Transformation to high-pass
199(3)
5.2 Transformation to band-pass
202(3)
5.3 Transformation to band-elimination
205(2)
6 Conclusions
207(2)
Problems
209(8)
References
217(3)
Chapter 4 Theory of Broadband Matching: The Passive Load 220(100)
1 The Bode—Fano—Youla broadband matching problem
221(1)
2 Youla's theory of broadband matching: preliminary considerations
222(3)
3 Basic constraints on ρ(s)
225(2)
4 Bode's parallel RC load
227(38)
4.1 Butterworth transducer power-gain characteristic
228(11)
4.2 Chebyshev transducer power-gain characteristic
239(13)
4.3 Elliptic transducer power-gain characteristic
252(10)
4.4 Equalizer back-end impedance
262(3)
5 Proof of necessity of the basic constraints on ρ(s)
265(4)
6 Proof of sufficiency of the basic constraints on ρ(s)
269(3)
7 Design procedure for the equalizers
272(7)
8 Darlington type-C load
279(19)
8.1 Butterworth transducer power-gain characteristic
279(8)
8.2 Chebyshev transducer power-gain characteristic
287(6)
8.3 Elliptic transducer power-gain characteristic
293(3)
8.4 Equalizer back-end impedance
296(2)
9 Constant transducer power gain
298(14)
10 Conclusions
312(1)
Problems
313(4)
References
317(3)
Chapter 5 Theory of Broadband Matching: The Active Load 320(96)
1 Special class of active impedances
321(2)
2 General configuration of the negative-resistance amplifiers
323(2)
3 Nonreciprocal amplifiers
325(38)
3.1 Design considerations for Nα
328(2)
3.2 Design considerations for Nβ
330(1)
3.3 Design considerations for Nc
330(3)
3.4 Illustrative examples
333(28)
A Realization of Nα
336(5)
B Realization of Nβ
341(1)
C Realization of Nc
342(2)
3.4.1 The tunnel diode amplifier: maximally-flat transducer power gain
344(8)
A Realization of Nα
346(2)
B Realization of Nβ
348(4)
3.4.2 The tunnel diode amplifier: equiripple transducer power gain
352(12)
A Realization of Nα
353(4)
B Realization of Nβ
357(4)
3.5 Extension and stability
361(2)
4 Transmission-power amplifiers
363(21)
4.1 Tunnel diode in shunt with the load
364(12)
4.1.1 Transducer power gain: R2 > R
365(9)
A Maximally-flat low-pass amplifiers
367(3)
B Equiripple low-pass amplifiers
370(4)
4.1.2 Transducer power gain: R2 < R
374(2)
4.2 Tunnel diode in shunt with the generator
376(3)
4.2.1 Transducer power gain: R1 > R
378(1)
4.2.2 Transducer power gain: R1 < R
378(1)
4.3 Stability
379(1)
4.4 Sensitivity
380(4)
4.4.1 Tunnel diode in shunt with the load
381(2)
4.4.2 Tunnel diode in shunt with the generator
383(1)
5 Reciprocal amplifiers
384(9)
5.1 General gain-bandwidth limitations
385(3)
5.2 Cascade connection
388(5)
6 Amplifiers using more than one active impedance
393(8)
6.1 Nonreciprocal amplifiers
396(3)
6.2 Reciprocal amplifiers
399(2)
7 Conclusions
401(2)
Problems
403(11)
References
414(2)
Chapter 6 Explicit Design Formulas for Broadband Matching Networks 416(86)
1 Low-pass Butterworth networks
417(31)
1.1 Basic constraints for low-pass Butterworth response
417(8)
1.2 Explicit design formulas for low-pass Butterworth response
425(8)
1.3 General explicit formulas for low-pass Butterworth networks
433(15)
1.3.1 Explicit formulas for the Darlington type-C section
439(3)
1.3.2 Illustrative examples
442(6)
2 Low-pass Chebyshev Networks
448(22)
2.1 Basic constraints for low-pass Chebyshev response
448(5)
2.2 Explicit formulas for low-pass Chebyshev response
453(6)
2.3 General Explicit Formulas for Low-pass Chebyshev Networks
459(11)
2.3.1 Explicit formulas for the Darlington type-C section
461(3)
2.3.2 Illustrative examples
464(6)
3 Band-pass Butterworth networks
470(18)
3.1 Basic constraints for band-pass Butterworth response
470(8)
3.2 Explicit formulas for band-pass Butterworth response
478(10)
4 Band-pass Chebyshev networks
488(12)
4.1 Basic constraints for band-pass Chebyshev response
488(6)
4.2 Explicit formulas for band-pass Chebyshev response
494(6)
5 Conclusions
500(1)
References
500(2)
Chapter 7 Broadband Matching of Frequency-Dependent Source and Load 502(90)
1 The problem of compatible impedances
503(28)
1.1 Wohlers' compatibility theorem
506(11)
1.2 Equivalency of conditions
517(14)
2 Broadband matching of frequency-dependent source and load
531(17)
2.1 Method of synthesis
537(1)
2.2 Illustrative examples
538(10)
3 Coefficient realizability conditions of a scattering matrix
548(31)
3.1 Basic coefficient constraints
551(2)
3.2 Coefficient realizability conditions
553(11)
3.3 Illustrative example
564(11)
3.4 Realization of the matching networks
575(4)
4 General scattering matrix realizability
579(11)
5 Conclusions
590(1)
References
590(2)
Chapter 8 Real-Frequency Solutions of the Broadband Matching Problem 592(101)
1 Direct real-frequency approach
593(3)
2 Piecewise linear approximation
596(3)
3 Piecewise linear Hilbert transforms
599(11)
4 Gain objective function
610(7)
5 Rational representation of R22(ω)
617(5)
6 Rational least-squared-error approximation of R22(ω)
622(12)
7 Calculation of the network function from a given real part
634(9)
7.1 Bode method
635(1)
7.2 Brune-Gewertz method
636(7)
8 Double matching problems
643(14)
8.1 Basic equations
643(4)
8.2 Computational algorithm
647(3)
8.3 Realizability of R20(ω)
650(2)
8.4 Illustrative examples
652(5)
9 The complex-normalized reflection coefficients
657(16)
9.1 Main theorem
658(5)
9.2 Illustrative examples
663(10)
10 Analytic solution of the matching problem of Fig. 8.12
673(16)
10.1 Coefficient constraints imposed by z1(s)
675(2)
10.2 Coefficient constraints imposed by z2(s)
677(4)
10.3 Equalizer back-end impedance
681(1)
10.4 Realization of the Darlington type-C section
682(4)
10.5 Verification of design
686(3)
11 Conclusions
689(2)
References
691(2)
Chapter 9 The Maximally-Flat Time Delay Approximation: The Bessel—Thomson Response 693(50)
1 The Bessel—Thomson response
693(1)
2 Maximally-flat group delay characteristic
694(7)
3 Poles of the Bessel—Thomson function
701(2)
4 Synthesis of the Bessel—Thomson filters with prescribed RLC load
703(14)
4.1 Basic constraints for the Bessel—Thomson response
703(9)
4.2 Design procedure for the Bessel—Thomson response
712(5)
5 Synthesis of the Bessel—Thomson filters with general loads
717(25)
5.1 Scattering representation with indeterminate coefficients
718(3)
5.2 The system transmission function
721(4)
5.3 Realizability conditions
725(3)
5.4 Illustrative examples
728(10)
5.5 Appendix
738(4)
References
742(1)
Chapter 10 Diplexer and Multiplexer Design 743(92)
1 Diplexer having Butterworth characteristic
743(9)
2 Symmetrical diplexer having Butterworth characteristic
752(15)
3 Real-frequency approach to the design of a reactance-ladder diplexer
767(27)
3.1 Real-frequency approach to the design of a low-pass high-pass reactance-ladder diplexer
769(7)
3.2 Optimization procedure
776(3)
3.3 Butterworth diplexer
779(8)
3.4 Elliptic response diplexer
787(6)
3.5 Appendix: Derivatives required in the formation of Jacobian matrix
793(1)
4 Design of a multiplexer with a common junction
794(24)
4.1 Formulas for the scattering parameters
795(6)
4.2 Derivations of formulas
801(4)
4.3 Design method
805(3)
4.4 Illustrative examples
808(10)
5 Design of a singly-matched multiplexer with a common junction
818(14)
5.1 Design formulas
821(3)
5.2 Design approach
824(2)
5.3 Illustrative example
826(6)
References
832(3)
Appendices 835(10)
Appendix A The Butterworth Response
835(2)
Appendix B The Chebyshev Response
837(3)
Appendix C The Elliptic Response
840(5)
Symbol Index 845(3)
Subject Index 848
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