Broadband matching : theory and implementations

Description

Contents Preface to the 3rd Edition Preface to the 2nd Edition Preface to the 1st Edition Chapter 1. Foundations of Network Theory 1. Basic network postulates 1.1. Real-time function postulate 1.2. Time-invariance postulate 1.3. Linearity postulate 1.4. Passivity postulate 1.5. Causality postulate 1.6. Reciprocity postulate 2. Matrix characterizations of n-port networks 2.1. The impedance matrix 2.2. The admittance matrix 2.3. The hybrid matrix 2.4. The indefinite-admittance matrix 3. Power gains 4. Hermitian forms 5. The positive-real matrix 6. Frequency-domain conditions for passivity 7. Conclusions Problems References Chapter 2. The Scattering Matrix 1. A brief review of the transmission-line theory 2. The scattering parameters of a one-port network 2.1. Basis-dependent reflection coefficients 2.2. Basis-independent reflection coefficient 2.3. The factorization of the para-hermitian part of z(s) 2.4. Alternative representation of the basis-independent reflection coefficient 2.5. The normalized reflection coefficient and passivity 3. The scattering matrix of an n-port network 3.1. Basis-dependent scattering matrices 3.2. Basis-independent scattering matrix 3.3. The scattering matrices and the augmented n-port networks 3.4. Alternative representation of the basis-independent scattering matrix 3.5. Physical interpretation of the normalized scattering parameters 3.6. The normalized scattering matrix and passivity 3.7. The normalized scattering parameters of a lossless two-port network 4. The bounded-real scattering matrix 5. Interconnection of multi-port networks 6. Conclusions Problems References Chapter 3. Approximation and Ladder Realization 1. The Butterworth response 1.1. Poles of the Butterworth function 1.2. Coefficients of the Butterworth polynomials 1.3. Butterworth networks 1.4. Butterworth LC ladder networks 2. The Chebyshev response 2.1. Chebyshev polynomials 2.2. Equiripple characteristic 2.3. Poles of the Chebyshev function 2.4. Coefficients of the polynomial p(y) 2.5. Chebyshev networks 2.6. Chebyshev LC ladder networks 3. Elliptic functions 3.1. Jacobian elliptic functions 3.2. Jacobi’s imaginary transformations 3.3. Periods of elliptic functions 3.3.1. The real periods 3.3.2. The imaginary periods 3.4. Poles and zeros of the Jacobian elliptic functions 3.5. Addition theorems and complex arguments 4. The elliptic response 4.1. The characteristic function Fn(ω) 4.2. Equiripple characteristic in passband and stopband A. Maxima and minima in the passband B. Maxima and minima in the stopband C. Transitional band 4.3. Poles and zeros of elliptic response 4.4. Elliptic networks 5. Frequency transformations 5.1. Transformation to high-pass 5.2. Transformation to band-pass 5.3. Transformation to band-elimination 6. Conclusions Problems References Chapter 4. Theory of Broadband Matching: The Passive Load 1. The Bode–Fano–Youla broadband matching problem 2. Youla’s theory of broadband matching: preliminary considerations 3. Basic constraints on ρ(s) 4. Bode’s parallel RC load 4.1. Butterworth transducer power-gain characteristic 4.2. Chebyshev transducer power-gain characteristic 4.3. Elliptic transducer power-gain characteristic 4.4. Equalizer back-end impedance 5. Proof of necessity of the basic constraints on ρ(s) 6. Proof of sufficiency of the basic constraints on ρ(s) 7. Design procedure for the equalizers 8. Darlington type-C load 8.1. Butterworth transducer power-gain characteristic 8.2. Chebyshev transducer power-gain characteristic 8.3. Elliptic transducer power-gain characteristic 8.4. Equalizer back-end impedance 9. Constant transducer power gain 10. Conclusions Problems References Chapter 5. Theory of Broadband Matching: The Active Load 1. Special class of active impedances 2. General configuration of the negative-resistance amplifiers 3. Nonreciprocal amplifiers 3.1. Design considerations for Nα 3.2. Design considerations for Nβ 3.3. Design considerations for Nc 3.4. Illustrative examples A. Realization of Nα B. Realization of Nβ C. Realization of Nc 3.4.1. The tunnel diode amplifier: maximally-flat transducer power gain A. Realization of Nα B. Realization of Nβ 3.4.2. The tunnel diode amplifier: equiripple transducer power gain A. Realization of Nα B. Realization of Nβ 3.5. Extension and stability 4. Transmission-power amplifiers 4.1. Tunnel diode in shunt with the load 4.1.1. Transducer power gain: R2 > R A. Maximally-flat low-pass amplifiers B. Equiripple low-pass amplifiers 4.1.2. Transducer power gain: R2 R 4.2.2. Transducer power gain: R1 < R 4.3. Stability 4.4. Sensitivity 4.4.1. Tunnel diode in shunt with the load 4.4.2. Tunnel diode in shunt with the generator 5. Reciprocal amplifiers 5.1. General gain-bandwidth limitations 5.2. Cascade connection 6. Amplifiers using more than one active impedance 6.1. Nonreciprocal amplifiers 6.2. Reciprocal amplifiers 7. Conclusions Problems References Chapter 6. Explicit Design Formulas for Broadband Matching Networks 1. Low-pass Butterworth networks 1.1. Basic constraints for low-pass Butterworth response 1.2. Explicit design formulas for low-pass Butterworth response 1.3. General explicit formulas for low-pass Butterworth networks 1.3.1. Explicit formulas for the Darlington type-C section 1.3.2. lllustrative examples 2. Low-pass Chebyshev Networks 2.1. Basic constraints for low-pass Chebyshev response 2.2. Explicit formulas for low-pass Chebyshev response 2.3. General Explicit Formulas for Low-pass Chebyshev Networks 2.3.1. Explicit formulas for the Darlington type-C section 2.3.2. Illustrative examples 3. Band-pass Butterworth networks 3.1. Basic constraints for band-pass Butterworth response 3.2. Explicit formulas for band-pass Butterworth response 4. Band-pass Chebyshev networks 4.1. Basic constraints for band-pass Chebyshev response 4.2. Explicit formulas for band-pass Chebyshev response 5. Conclusions References Chapter 7. Broadband Matching of Frequency-Dependent Source and Load 1. The problem of compatible impedances 1.1. Wohlers’ compatibility theorem 1.2. Equivalency of conditions 2. Broadband matching of frequency-dependent source and load 2.1. Method of synthesis 2.2. Illustrative examples 3. Coefficient realizability conditions of a scattering matrix 3.1. Basic coefficient constraints 3.2. Coefficient realizability conditions 3.3. Illustrative example 3.4. Realization of the matching networks 4. General scattering matrix realizability 5. Conclusions References Chapter 8. Real-Frequency Solutions of the Broadband Matching Problem 1. Direct real-frequency approach 2. Piecewise linear approximation 3. Piecewise linear Hilbert transforms 4. Gain objective function 5. Rational representation of R22(ω) 6. Rational least-squared-error approximation of R22(ω) 7. Calculation of the network function from a given real part 7.1. Bode method 7.2. Brune-Gewertz method 8. Double matching problems 8.1. Basic equations 8.2. Computational algorithm 8.3. Realizability of R20(ω) 8.4. Illustrative examples 9. The complex-normalized reflection coefficients 9.1. Main theorem 9.2. Illustrative examples 10. Analytic solution of the matching problem of Fig. 8.12. 10.1. Coefficient constraints imposed by z1(s) 10.2. Coefficient constraints imposed by z2(s) 10.3. Equalizer back-end impedance 10.4. Realization of the Darlington type-C section 10.5. Verification of design 11. Conclusions References Chapter 9. The Maximally-Flat Time DelayApproximation: The Bessel–Thomson Response 1. The Bessel–Thomson response 2. Maximally-flat group delay characteristic 3. Poles of the Bessel–Thomson function 4. Synthesis of the Bessel–Thomson filters with prescribed RLC load 4.1. Basic constraints for the Bessel–Thomson response 4.2. Design procedure for the Bessel–Thomson response 5. Synthesis of the Bessel–Thomson filters with general loads 5.1. Scattering representation with indeterminate coefficients 5.2. The system transmission function 5.3. Realizability conditions 5.4. Illustrative examples 5.5. Appendix References Chapter 10. Diplexer and Multiplexer Design 1. Diplexer having Butterworth characteristic 2. Symmetrical diplexer having Butterworth characteristic 3. Real-frequency approach to the design of a reactance-ladder diplexer 3.1. Real-frequency approach to the design of a low-pass high-pass reactance-ladder diplexer 3.2. Optimization procedure 3.3. Butterworth diplexer 3.4. Elliptic response diplexer 3.5. Appendix: Derivatives required in the formation of Jacobian matrix 4. Design of a multiplexer with a common junction 4.1. Formulas for the scattering parameters 4.2. Derivations of formulas 4.3. Design method 4.4. Illustrative examples 5. Design of a singly-matched multiplexer with a common junction 5.1. Design formulas 5.2. Design approach 5.3. Illustrative example References Appendices Appendix A. The Butterworth Response Appendix B. The Chebyshev Response Appendix C. The Elliptic Response Symbol Index Subject Index