Passive Network Synthesis: An Approach to Classification

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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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