Preface ........................................................ ix
1 Auxiliary results ............................................ 1
1.1 Introduction ............................................ 1
1.2 The rank of a matrix product ............................ 1
1.3 Compound matrices and Jacobi's theorem .................. 2
1.4 Singular value decomposition ............................ 4
1.5 Joint diagonalization of hermitian matrices ............. 5
1.6 Sylvester's law of inertia .............................. 6
1.7 Row and column-reduced polynomial matrices .............. 7
1.8 Some key results in the theory of equations ............. 8
1.9 Optimality and the classical Riccati equation .......... 16
1.10 Appendix ............................................... 22
1.11 References ............................................. 28
2 Transforms and passivity .................................... 29
2.1 Description ............................................ 29
2.2 Transforms ............................................. 31
2.3 Passive 1-ports ........................................ 33
2.4 Properties of positive-real functions .................. 37
2.5 References ............................................. 42
3 Some classical passive 1-port synthesis ..................... 43
3.1 Preliminary mathematical background .................... 43
3.2 Brune synthesis ........................................ 46
3.3 Transformerless Bott-Duffin synthesis .................. 58
3.4 A broader proof of Corollary 1 of Theorem 3 ............ 73
3.5 References ............................................. 75
4 Tellegen's Theorem and 2-element 1-ports .................... 76
4.1 The RCLM and Tellegen's Theorem ....................... 76
4.2 Lossless passive 1-ports ............................... 79
4.3 Scaling and other 2-element 1-ports .................... 96
4.4 Magnetic coupling and 2-winding transformers .......... 102
4.5 References ............................................ 107
5 Elements of filters and reactance-ladders .................. 108
5.1 Fundamentals of insertion-loss filter design .......... 108
5.2 Reactance-ladders ..................................... 116
5.3 Low-pass reactance-ladders ............................ 125
5.4 Concluding remarks .................................... 142
5.5 References ............................................ 143
6 Passive n-ports ............................................ 144
6.1 Foundations ........................................... 144
6.2 Operational significance of S(s) ...................... 154
6.3 The McMillan degree of a rational matrix .............. 159
6.4 Gyrators and reciprocity .............................. 172
6.5 References ............................................ 176
7 Procedures of passive л-port synthesis ..................... 177
7.1 Counting reactances, resistances, and gyrators ........ 177
7.2 Factorizing parahermitian-positive matrices ........... 180
7.3 n-port synthesis via resistance extraction ............ 194
7.4 Paraunitary matrices .................................. 219
7.5 Non-tight embeddings .................................. 226
7.6 л-port synthesis via reactance extraction ............. 240
7.7 Numerical considerations .............................. 254
7.8 и-port synthesis via gyrator extraction ............... 265
7.9 Auxiliary techniques .................................. 279
7.10 References ............................................ 288
8 Basic design of reactance 2-ports .......................... 289
8.1 The Belevitch description of a reactance 2-port ....... 289
8.2 Darlington equivalents ................................ 293
8.3 Symmetric and antimetric filters ...................... 297
8.4 References ............................................ 309
9 Cascade synthesis of passive 1-ports ....................... 310
9.1 Transmission zeros of a p.r. function ................. 310
9.2 On the extraction of transmission zeros ............... 313
9.3 Designing with the indices of z(s) .................... 326
9.4 Overview .............................................. 331
9.5 References ............................................ 332
10 A theory of broadband matching ............................. 333
10.1 Fundamentals .......................................... 333
10.2 Single broadband matching ............................. 337
10.3 Double broadband matching ............................. 352
10.4 Numerical interlude ................................... 368
10.5 The restrictions in integral form ..................... 371
10.6 References ............................................ 383
11 Stability and complex normalization ........................ 384
11.1 The role of stability ................................. 384
11.2 Stability and steady-state ............................ 392
11.3 Complex normalization ................................. 393
11.4 Measuring the elements of S(jω) ....................... 395
11.5 The concept of exchangeable power ..................... 400
11.6 References ............................................ 401
12 Design of passive multiplexers ............................. 402
12.1 The standard configuration ............................ 402
12.2 Standard magnitude and phase multiplexers ............. 408
12.3 The general case ...................................... 412
12.4 Reactance-ladder diplexers ............................ 421
12.5 Optimal reactance-ladder diplexer design .............. 422
12.6 Concluding remarks .................................... 428
12.7 References ............................................ 428
13 Selected topics ............................................ 429
13.1 All-s normalization ................................... 429
13.2 Special results ....................................... 436
13.3 Bisection of symmetric and antimetric filters ......... 439
13.4 2-port synthesis from partial data .................... 448
13.5 Compatible impedances ................................. 455
13.6 The Garloff-Wagner (GW) Theorem ....................... 466
13.7 Addenda ............................................... 477
13.8 References ............................................ 480
14 Multiconductor ТЕМ transmission lines ...................... 481
14.1 Introduction .......................................... 481
14.2 Analytical formulation ................................ 481
14.3 The telegrapher's equations ........................... 486
14.4 The ТЕМ line transducer ............................... 489
14.5 Decoupling the telegrapher's equations ................ 494
14.6 Transient performance ................................. 497
14.7 Appendix .............................................. 516
14.8 References ............................................ 523
15 The ideal ТЕМ 2-port ....................................... 525
15.1 Preliminaries ......................................... 525
15.2 Commensurate 2-port ideal TEM-line synthesis .......... 528
15.3 Design of TEM-line transformers and filters ........... 535
15.4 The quest for optimal power gains ..................... 538
15.5 Key properties of Tchebycheff polynomials ............. 541
15.6 The LLN-ideal TEM-line τ-cascade ...................... 552
15.7 Appendix .............................................. 563
15.8 References ............................................ 570
16 Single frequency n-port geometry ........................... 571
16.1 Introduction .......................................... 571
16.2 n-port tuning via 2n-port embedding ................... 573
16.3 Geometry of the cross-ratio matrix .................... 576
16.4 Canonic forms ......................................... 580
16.5 Invariants of noisy linear n-ports .................... 590
16.6 Overview .............................................. 598
16.7 Appendix .............................................. 603
16.8 References ............................................ 606
17 Immittances of n-terminal networks ......................... 608
17.1 Introduction .......................................... 608
17.2 Analysis .............................................. 609
17.3 Direct admittance measurement of Y .................... 614
17.4 The indefinite loop impedance matrix .................. 616
17.5 References ............................................ 619
18 Two-state passive devices .................................. 620
18.1 Introduction .......................................... 620
18.2 Preliminaries ......................................... 620
18.3 Analysis, lemmas, and theorems ........................ 621
18.4 Performance ........................................... 628
18.5 Appendix: Derivation of (18.110) ...................... 637
18.6 References ............................................ 638
Index ......................................................... 639
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