Geared toward upper-level undergraduates and graduate students, this book offers a comprehensive look at linear network analysis and synthesis. It explores state-space synthesis as well as analysis, employing modern systems theory to unite the classical concepts of network theory.

Preface to the Dover Edition,

vii

Preface,

ix

Part I INTRODUCTION

1

(8)

1 Introduction,

3

(6)

1.1 Analysis and Synthesis,

3

(1)

1.2 Classical and Modern Approaches,

4

(2)

1.3 Outline of the Book,

6

(3)

Part II BACKGROUND INFORMATION—NETWORKS AND STATE-SPACE EQUATIONS

9

(132)

2 m-Port Networks and their Port Descriptions,

11

(52)

2.1 Introduction,

11

(1)

2.2 m-Port Networks and Circuit Elements,

12

(9)

2.3 Tellegen's Theorem; Passive and Lossless Networks,

21

(7)

2.4 Impedance, Admittance, Hybrid and Scattering Descriptions of a Network,

28

(5)

2.5 Network Interconnections,

33

(9)

2.6 The Bounded Real Property,

42

(9)

2.7 The Positive Real Property,

51

(7)

2.8 Reciprocal m-Ports,

58

(5)

3 State-Space Equations and Transfer Function Matrices,

63

(78)

3.1 Descriptions of Lumped Systems,

63

(5)

3.2 Solving the State-Space Equations,

68

(13)

3.3 Properties of State-Space Realizations,

81

(16)

3.4 Minimal Realizations,

97

(7)

3.5 Construction of State-Space Equations from a Transfer Function Matrix,

104

(12)

3.6 Degree of a Rational Transfer Function Matrix,

116

(11)

3.7 Stability,

127

(14)

Part III NETWORK ANALYSIS

141

(72)

4 Network Analysis via State-Space Equations,

143

(70)

4.1 Introduction,

143

(2)

4.2 State-Space Equations for Simple Networks,

145

(11)

4.3 State-Space Equations via Reactance Extraction—Simple Version,

156

(14)

4.4 State-Space Equations via Reactance Extraction—The General Case,

170

(30)

4.5 State-Space Equations for Active Networks,

200

(13)

Part IV THE STATE-SPACE DESCRIPTION OF PASSIVITY AND RECIPROCITY

213

(114)

5 Positive Real Matrices and the Positive Real Lemma,

215

(52)

5.1 Introduction,

215

(3)

5.2 Statement and Sufficiency Proof of the Positive Real Lemma,

218

(5)

5.3 Positive Real Lemma: Necessity Proof Based on Network Theory Results,

223

(6)

5.4 Positive Real Lemma: Necessity Proof Based on a Variational Problem,

229

(14)

5.5 Positive Real Lemma: Necessity Proof Based on Spectral Factorization,

243

(15)

5.6 The Positive Real Lemma: Other Proofs, and Applications,

258

(9)

6 Computation of Solutions of the Positive Real Lemma Equations,

267

(40)

6.1 Introduction,

267

(3)

6.2 Solution Computation via Riccati Equations and Quadratic Matrix Equations,

270

(3)

6.3 Solving the Riccati Equation,

273

(3)

6.4 Solving the Quadratic Matrix Equation,

276

(7)

6.5 Solution Computation via Spectral Factorization,

283

(9)

6.6 Finding All Solutions of the Positive Real Lemma Equations,

292

(15)

7 Bounded Real Matrices and the Bounded Real Lemma; The State-Space Description of Reciprocity,

307

(20)

7.1 Introduction,

307

(1)

7.2 The Bounded Real Lemma,

308

(6)

7.3 Solution of the Bounded Real Lemma Equations,

314

(6)

7.4 Reciprocity in State-Space Terms,

320

(7)

Part V NETWORK SYNTHESIS

327

(182)

8 Formulation of State-Space Synthesis Problems,

329

(40)

8.1 An Introduction to Synthesis Problems,

329

(1)

8.2 The Basic Impedance Synthesis Problem,

330

(9)

8.3 The Basic Scattering Matrix Synthesis Problem,

339

(8)

8.4 Preliminary Simplification by Lossless Extractions,

347

(22)

9 Impedance Synthesis,

369

(36)

9.1 Introduction,

369

(3)

9.2 Reactance Extraction Synthesis,

372

(14)

9.3 Resistance Extraction Synthesis,

386

(7)

9.4 A Reciprocal (Nonminimal Resistive and Reactive) Impedance Synthesis,

393

(12)

10 Reciprocal Impedance Synthesis,

405

(37)

10.1 Introduction,

405

(1)

10.2 Reciprocal Lossless Synthesis,

406

(2)

10.3 Reciprocal Synthesis via Reactance Extraction,

408

(10)

10.4 Reciprocal Synthesis via Resistance Extraction,

418

(9)

10.5 A State-Space Bayard Synthesis,

427

(15)

11 Scattering Matrix Synthesis,

442

(32)

11.1 Introduction,

442

(2)

11.2 Reactance Extraction Synthesis of Nonreciprocal Networks,

444

(10)

11.3 Reactance Extraction Synthesis of Reciprocal Networks,

454

(9)

11.4 Resistance Extraction Scattering Matrix Synthesis,

463

(11)

12 Transfer Function Synthesis,

474

(35)

12.1 Introduction,

474

(5)

12.2 Nonreciprocal Transfer Function Synthesis,

479

(11)

12.3 Reciprocal Transfer Function Synthesis,

490

(7)

12.4 Transfer Function Synthesis with Prescribed Loading,

497

(12)

Part VI ACTIVE RC NETWORKS

509

(28)

13 Active State-Space Synthesis,

511

(26)

13.1 Introduction to Active RC Synthesis,

511

(2)

13.2 Operational Amplifiers as Circuit Elements,

513

(6)

13.3 Transfer Function Synthesis Using Summers and Integrators,

519

(7)

13.4 The Biquad,

526

(4)

13.5 Other Approaches to Active RC Synthesis,

530

(7)

Epilogue: What of the Future?

537

(2)

Subject Index,

539

(7)

Author Index,

546

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Network Analysis and Synthesis A Modern Systems Theory Approach

9780486453576

048645357X

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