Passive Network Synthesis: An Approach to Classification

Front cover
Title page
Copyright
Contents
1 Introduction
1.1 Outline
1.2 Acknowledgments
2 Classical results of network synthesis
2.1 Preliminaries of electrical networks
2.2 Foster and Cauer canonical forms
2.3 Positive-real functions and passivity
2.4 The Foster preamble and Brune cycle
2.5 The Bott–Duffin construction and its simplifications
2.6 Darlington synthesis
2.7 Reactance extraction
3 Modern developments of network synthesis
3.1 Regular positive-real functions and the Ladenheim catalogue
3.2 Reichert’s theorem
3.3 Algebraic criteria for circuit realizations
3.4 The behavioral approach to passivity
4 Mechanical networks
4.1 Network analogies and the inerter
4.2 Applications of mechanical network synthesis
5 The enumerative approach to network synthesis
5.1 Definition and derivation of the Ladenheim catalogue
5.2 Approach to classification
5.3 Classical equivalences
6 Structure of the Ladenheim catalogue
6.1 Catalogue subfamily structure with orbits and equivalences
6.2 One-, two-, and three-element networks
6.3 Four-element networks
6.4 Five-element networks
6.5 Summary of realizability conditions
6.6 Realizability regions for five-element networks
7 Main results and discussion
7.1 Cauer–Foster transformation
7.2 Formal results on the Ladenheim catalogue
7.3 Smallest generating set of the catalogue
7.4 Remarks on Kalman’s 2011 Berkeley seminar
7.5 A note on d-invariance of RLC networks
7.6 Six-element networks with four resistors
8 Conclusions
Appendix A Realization theorems
A.1 Equivalence class IV-1B
A.2 Equivalence class V-1A
A.3 Equivalence class V-1B
A.4 Equivalence class V-1C
A.5 Equivalence class V-1D
A.6 Equivalence class V-1E
A.7 Equivalence class V-1F
A.8 Equivalence class V-1G
A.9 Equivalence class V-1H
A.10 Equivalence class VI
Appendix B Basic graphs
Appendix C The Ladenheim networks (numerical order)
Appendix D The Ladenheim networks (subfamily order)
Bibliography
Index
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