Wideband Circuit Design

1. General Properties of Linear Circuits and Systems Operator Representation Linear Time Invariant Systems Operators Causality Power, Energy, and Passivity Passivity, Linearity, and Causality 2. LTI System Response to Exponential Eigenfunctions Solution of Operator Equations LTI Operator Eigenfunctions Homogeneous Solution of LTI Operator Equations The Particular Solution under Exponential Excitation Conditions for Pure Eigenfunction Response Phasors and A.C. Analysis Network Geometry Topology and Kirchhoff's Laws Nodal Analysis Mesh and Loop Analysis Cut Set Analysis Transfer Functions and n-Ports Incidence Matrices and Network Equations Tellegen's Theorem, Reciprocity, and Power 3. Impulses, Convolution, and Integral Transforms The Impulse Function The Fourier Integral Theorem Impulse Response and Convolution Real-Imaginary Part Relations; The Hilbert Transform Causal Fourier Transforms Minimum Immittance Functions Amplitude-Phase Relations Numerical Evaluation of Hilbert Transforms Operational Rules and Generalized Fourier Transforms Laplace Transforms and Eigenfunction Response 4. The Scattering Matrix and Realizability Theory Physical Properties of n-Ports General Representations of n-Ports The Scattering Matrix Normalized to Positive Resistors Scattering Relations for Energy and Power Bounded Real Scattering Matrices Positive Real Immitance Matrices The Degree of a One-Port 5. One-Port Synthesis Introduction Lossless One-Port Synthesis RC and RL One-Port Synthesis The Scattering Matrix of a Lossless Two-Port The Immittance Matrices of a Lossless Two-Port Transmission Zeros Darlington's Procedure of Synthesis An Example Cascade Synthesis: Type A and B Sections Cascade Synthesis: Brune's Section Cascade Synthesis: Darlington's C-Section Cascade Synthesis: Darlington's D-Section Ladder Synthesis; Fujisawa's Theorem Transmission Zeros All Lying at Infinity and/or the Origin 6. Insertion Loss Filters The Concept of a Filter and the Approximation Problem Synthesis of Doubly Terminated Filters Impedance Scaling, Frequency Transformations Specifications for Amplitude Approximation Butterworth Approximation Chebyshev Approximation Elliptic Approximation Phase Equalization Allpass C-Section Phase Equalizers Allpass D-Section Phase Equalizers Bessel Approximation Synthesis of Singly Terminated Filters 7. Transmission Lines The TEM Line The Unit Element (UE); Richard's Transformation Richard's Theorem; UE Reactance Functions Doubly Terminated UE Cascade Stepped Line Gain Approximations Transfer Functions for Stepped Lines and Stubs Coupled UE Structures 8. Broadband Matching I: Analytic Theory The Broadbanding Problem The Chain Matrix of a Lossless Two-Port Complex Normalization The Gain-Bandwidth Restrictions The Gain-Bandwidth Restrictions in Integral Form Example: Double Zero of Transmission Double Matching 9. Broadband Matching II: Real Frequency Technique Introduction Single Matching Transmission Line Equalizers Double Matching Double Matching of Active Devices A. Analytic Functions General Concepts Integration of Analytic Functions The Cauchy Integral Formula Laurent and Taylor Expansions The Theorem of Residues Zeros, Poles, and Essential Singularities Some Theorems on Analytic Functions Classification of Analytic Functions Multivalued Functions The Logarithmic Derivative Functions with a Finite Number of Singularities Analytic Continuation Calculus of Definite Integrals by the Residue Method B. Linear Algebra General Concepts Geometrical Interpretation Linear Simultaneous Equations Eigenvalues and Eigenvectors Index

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