《NETWORK THEORY:AN INTRODUCTION TO RECIPROCAL AND NONERCIPROCAL CIRCUITS》

Introduction1

Basic Network Postulates1

Notation7

Further Readings10

Chapter One—Relation between Matrix Algebra and Network Topology11

1．1Introduction11

1．2 The Kirchhoff Current Equations;Topology of Trees12

1．3 Determinants17

1．4 Matrix Algebra and Linear Dependence20

1．5 Solution of the Current Junction Equations;Branch-Node Incidence Matrix32

1．6 Relation between Branch and Mesh Currents;Branch-Mesh Incidence Matrix35

1．7 The Kirchhoff Voltage Equations;Duality43

1．8 Multiply Connected Networks46

Problems 1．1-1．3547

Further Readings55

Chapter Two—Mesh and Nodal Analysis of Networks56

2．1Branch Current-Voltage Relations;Branch Impedance Matrix56

2．2Mesh Analysis63

Mesh Excitation63

Mesh Impedance Matrix64

2．3Solution of the Mesh Equations69

Solution for Nonsingular ZM69

Solution for Singular ZM72

2．4Nodal Analysis75

Nodal Admittance Matrix75

Nodal Admittance Parameters by Inspection81

2．5 Solution of Nodal Equations85

2．6 Equivalent Circuits without Transformers87

2．7 Measurement of the Elements of ZM and Z？89

2．8 Measurement of the Elements of YJ and Y？94

Problems 2．1-2．2397

Further Readings106

Chapter Three—Network Transformations and Equivalences107

3．1Change of Variables107

3．2 General Node-Pair Analysis109

3．3 The Application of Cut-Sets to Network Analysis113

3．4 Accessible Terminal Pairs or Ports116

3．5 Network Interconnections120

3．6Further Generalization of the Interconnection Equations130

General Series Interconnection130

Series Ring Circuits136

3．7Elimination of Meshes and Node Pairs138

Matrix Reduction Equations138

Campbell＇s Reduction Formula139

3．8 Generalized Form of Thèvenin＇s Theorem for an n-port144

3．9 Elimination of Variables in Interconnected Networks146

3．10Equivalences for Symmetrical 2-Port Networks148

The 2-Ports:T,П,Lattice,and Bridged-T,148

Measurement of Immittance Parameters156

3．11 Properties of the Symmetric Lattice157

3．12 Bartlett Bisection Theorem161

3．13 Equivalent 1-Port Networks167

3．14Analysis of Ideal Transformer Networks172

The 2-Winding Ideal Transformer172

Interconnection with 2-Winding Ideal Transformers176

Multi-winding Ideal Transformers179

3．15 Mesh Analysis of General Ideal Transformer Networks182

3．16Network Transformations with Ideal Transformers190

Impedance Matrix Diagonalization and Synthesis190

Energy Relations in an n-Port199

Problems 3．1-3．48207

Further Readings221

Chapter Four—The Scattering Matrix222

4．1Application of Scattering Parameters222

4．2Scattering Relations for a 1-Port224

Definition of Scattering Variables224

Physical Interpretation of Scattering Variables227

Generation of Incident and Reflected Voltages230

4．3Power Relations in a 1-Port232

Power Transfer and Return Loss232

Constant Power,Variable Phase 1-Port;Low-Pass Filter234

4．4Scattering Representation of n-Ports237

Derivation of the Scattering Matrix237

Scattering-Impedance Relations241

Nonnormalized Scattering Matrix243

4．5Examples of Scattering Matrix Calculations244

Series Element 2-Port244

Ideal Transformer 2-Port245

Hybrid Coil Circuit246

Scattering Immittance Relations for a 2-Port249

4．6Scattering Computations in Match-Terminated Networks250

All-Pass Symmetrical Lattice254

Image Impedance Parameters255

4．7Scattering Computations with General Terminations257

Balanced Bridge Circuit258

Broad-Band Matching Transformer261

4．8Scattering Formulation of Power Transfer in Passive n-Ports269

Unitary Scattering Matrix273

Gain-Bandwidth in a Matched Constant Resistance 2-Port274

4．9Scattering Properties of Lossless n-Ports275

Lossless 2-Port275

Lossless 3-Port Networks277

Lossless Matched 4-Ports;Biconjugate Networks281

4．10Linear Transformation of the Scattering Matrix283

Orthogonal Transformations and Matrices283

Eigenvalues and Eigenvectors288

Frequency-Invariant,Lossless Scattering Matrices291

Direct Realization of a Unitary,Symmetric Scattering Matrix295

Matched Lossless,Frequency Invariant n-Ports298

4．11Transfer Scattering Coefficients300

Impedance Transfer Coefficients,(ABCD)300

Transfer Scattering Matrix302

Transfer Formalism for a 2n-Port305

Cascaded 2-Ports308

Resistive Attenuator311

4．12Networks Cascaded on an Image and Iterative Basis313

Use of Image Parameters313

Periodic Structures(Iterative Cascade)319

4．13Complex Normalization326

Properties of the Normalized Scattering Matrix326

Power Transfer from Complex Generator to Complex Load331

Conjugate Image Impedances—Intrinsic Loss335

General Form of Tunnel Diode Amplifiers338

Problems 4．1-4．32344

Further Readings349

Chapter Five—Nonreciprocal Networks350

5．1Circuit Properties of the Gyrator350

Lorentz Reciprocity and the Gyrator350

Mesh Analysis with Gyrators355

5．2Representation of a Nonreciprocal Impedance Matrix359

Properties of the Impedance Matrix of a Passive Network359

Synthesis of a Nonreciprocal Impedance Matrix362

Complex Ideal Transformers367

Equivalent Circuit for General Passive Nonreciprocal 2-Port370

5．3 Lossless Nonreciprocal Impedance Matrices373

5．4Scattering Properties of Nonreciprocal Networks377

Nonreciprocal Lossless 2-Port378

Matched Lossless 3-Port(The Circulator)379

Nonreciprocal Lossless 4-Port;4-Port Matched Power Divider380

5．5Some Typical Applications of Nonreciprocal Isolating Networks384

Lossless Duplexer Utilizing a Circulator385

Duplexer with Loss389

One-Way Line391

Frequency Selector Network391

Band-Pass Filter with Interactions Suppressed392

Hall Plate Nonreciprocal Devices:Gyrator,Isolator393

Hall Plate Networks:Gyrator,Isolator,Circulator399

5．6Equivalent Circuits for Nonreciprocal Isolating Networks404

Equivalent Circuit for One-Way Line404

Equivalent Circuit for 3-Port Circulator406

4-Port Circulator407

5．7Representation of Nonreciprocal Scattering Matrices411

Removal of Degeneracy by Gyrator Extraction412

4-Port Circulator Without Z or Y416

5．8 Removal of Degeneracy by Complex Transformer Interconnections418

5．9Direct Synthesis of a Non symmetric Orthogonal Scattering Matrix429

Minimum Number of Gyrators for n-Port Circulator436

Direct Synthesis of 3-Port Circulator438

5．10Direct Realization of a Complex Scattering Matrix440

Synthesis of Nonsingular S440

Synthesis when S is Singular445

5．11Invariants of a Nonreciprocal Network Under Lossless Reciprocal Imbedding446

Invariants of a Nonreciprocal 2-Port446

Invariants of a Nonreciprocal n-Port451

Problems 5．1-5．42455

Further Readings463

Index465