Preface |
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1 General Properties of Linear Circuits and Systems |
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1 | (22) |
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1.1 Operator Representation |
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1 | (2) |
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1.2 Linear Time Invariant Systems and Operators |
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3 | (3) |
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6 | (2) |
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1.4 Power, Energy, and Passivity |
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8 | (9) |
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1.5 Passivity, Linearity and Causality |
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17 | (6) |
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2 LTI System Response to Exponential Eigenfunctions |
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23 | (82) |
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2.1 Solution of Operator Equations |
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23 | (4) |
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2.2 LTI Operator Eigenfunctions |
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27 | (4) |
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2.3 Homogeneous Solution of LTI Operator Equations |
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31 | (6) |
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2.4 The Particular Solution under Exponential Excitation |
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37 | (3) |
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2.5 Conditions for Pure Eigenfunction Response |
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40 | (4) |
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2.6 Phasors and A.C. Analysis |
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44 | (2) |
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46 | (7) |
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2.8 Topology and Kirchhoff's Laws |
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53 | (5) |
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58 | (8) |
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2.10 Mesh and Loop Analysis |
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66 | (8) |
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74 | (4) |
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2.12 Transfer Functions and n-Ports |
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78 | (11) |
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2.13 Incidence Matrices and Network Equations |
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89 | (6) |
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2.14 Tellegen's Theorem, Reciprocity, and Power |
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95 | (10) |
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3 Impulses, Convolution, and Integral Transforms |
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105 | (66) |
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105 | (5) |
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3.2 The Fourier Integral Theorem |
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110 | (11) |
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3.3 Impulse Response and Convolution |
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121 | (5) |
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3.4 Real-Imaginary Part Relations; The Hilbert Transform |
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126 | (6) |
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3.5 Causal Fourier Transforms |
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132 | (8) |
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3.6 Minimum Immittance Functions |
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140 | (3) |
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3.7 Amplitude-Phase Relations |
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143 | (5) |
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3.8 Numerical Evaluation of Hilbert Transforms |
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148 | (4) |
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3.9 Operational Rules and Generalized Fourier Transforms |
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152 | (7) |
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3.10 Laplace Transforms and Eigenfunction Response |
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159 | (12) |
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4 The Scattering Matrix and Realizability Theory |
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171 | (42) |
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4.1 Physical Properties of n-Ports |
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171 | (2) |
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4.2 General Representations of n-Ports |
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173 | (6) |
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4.3 The Scattering Matrix Normalized to Positive Resistors |
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179 | (7) |
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4.4 Scattering Relations for Energy and Power |
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186 | (2) |
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4.5 Bounded Real Scattering Matrices |
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188 | (12) |
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4.6 Positive Real Immittance Matrices |
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200 | (10) |
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4.7 The Degree of a One-Port |
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210 | (3) |
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213 | (70) |
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213 | (1) |
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5.2 Lossless One-Port Synthesis |
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214 | (13) |
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5.3 RC and RL One-Port Synthesis |
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227 | (4) |
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5.4 The Scattering Matrix of a Lossless Two-Port |
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231 | (7) |
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5.5 The Immittance Matrices of a Lossless Two-Port |
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238 | (2) |
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240 | (2) |
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5.7 Darlington's Procedure of Synthesis |
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242 | (7) |
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249 | (3) |
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5.9 Cascade Synthesis: Type A and B Sections |
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252 | (2) |
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5.10 Cascade Synthesis: Brune's Section |
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254 | (8) |
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5.11 Cascade Synthesis: Darlington's C-Section |
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262 | (5) |
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5.12 Cascade Synthesis: Darlington's D-Section |
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267 | (7) |
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5.13 Ladder Synthesis: Fujisawa's Theorem |
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274 | (5) |
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5.14 Transmission Zeros All Lying at Infinity and or the Origin |
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279 | (4) |
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283 | (54) |
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6.1 The Concept of a Filter and the Approximation Problem |
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283 | (3) |
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6.2 Synthesis of doubly terminated filters |
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286 | (3) |
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6.3 Impedance Scaling, Frequency Transformations |
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289 | (7) |
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6.4 Specifications for Amplitude Approximation |
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296 | (3) |
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6.5 Butterworth Approximation |
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299 | (5) |
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6.6 Chebyshev Approximation |
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304 | (8) |
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6.7 Elliptic Approximation |
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312 | (9) |
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321 | (2) |
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6.9 Allpass C-Section Phase Equalizers |
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323 | (3) |
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6.10 Allpass D-Section Phase Equalizers |
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326 | (3) |
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6.11 Bessel Approximation |
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329 | (3) |
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6.12 Synthesis of Single-Terminated Filters |
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332 | (5) |
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337 | (46) |
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337 | (4) |
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7.2 The Unit Element (UE); Richards' Transformation |
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341 | (9) |
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7.3 Richards' Theorem: UE Reactance Functions |
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350 | (2) |
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7.4 Doubly Terminated UE Cascade |
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352 | (4) |
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7.5 Stepped Line Gain Approximations |
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356 | (9) |
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7.6 Transfer Functions for Stepped Lines and Stubs |
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365 | (8) |
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7.7 Coupled UE Structures |
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373 | (10) |
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8 Broadband Matching I: Analytic Theory |
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383 | (32) |
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8.1 The Broadbanding Problem |
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383 | (2) |
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8.2 The Chain Matrix of a Lossless Two-Port |
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385 | (1) |
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8.3 Complex Normalization |
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386 | (5) |
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8.4 The Gain-Bandwidth Restrictions |
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391 | (10) |
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8.5 The Gain-Bandwidth Restrictions in Integral Form |
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401 | (5) |
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8.6 Example: Double Zero of Transmission |
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406 | (2) |
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408 | (7) |
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9 Broadband Matching II: Real Frequency Technique |
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415 | (24) |
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415 | (4) |
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419 | (6) |
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9.3 Transmission Line Equalizers |
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425 | (4) |
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429 | (4) |
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9.5 Double Matching of Active Devices |
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433 | (6) |
Appendices |
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439 | (1) |
A Analytic Functions |
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439 | (26) |
A.1 General Concepts |
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439 | (3) |
A.2 Integration of Analytic Functions |
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442 | (2) |
A.3 The Cauchy Integral Formula |
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444 | (1) |
A.4 Laurent and Taylor Expansions |
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445 | (3) |
A.5 The Theorem of Residues |
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448 | (1) |
A.6 Zeros, Poles and Essential Singularities |
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449 | (2) |
A.7 Some Theorems on Analytic Functions |
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451 | (1) |
A.8 Classification of Analytic Functions |
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452 | (1) |
A.9 Multivalued Functions |
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453 | (2) |
A.10 The Logarithmic Derivative |
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455 | (1) |
A.11 Functions with a Finite Number of Singularities |
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456 | (1) |
A.12 Analytic Continuation |
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457 | (2) |
A.13 Calculus of Definite Integrals by the Residue Method |
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459 | (6) |
B Linear Algebra |
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465 | (18) |
B.1 General Concepts |
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465 | (2) |
B.2 Geometrical Interpretation |
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467 | (4) |
B.3 Linear Simultaneous Equations |
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471 | (6) |
B.4 Eigenvalues and Eigenvectors |
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477 | (6) |
Index |
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483 | |