Design of Ultra Wideband Power Transfer Networks

DESIGN OF ULTRA WIDEBAND POWER TRANSFER NETWORKS......Page 5
Contents......Page 9
About the Author......Page 15
Preface......Page 17
1.1 Introduction......Page 23
1.2 Ideal Circuit Elements......Page 24
1.3 Average Power Dissipation and Effective Voltage and Current......Page 25
1.4 Definitions of Voltage and Current Phasors......Page 27
1.6 Definition of Resistor......Page 28
1.7 Definition of Capacitor......Page 29
1.8 Definition of Inductor......Page 30
1.9 Definition of an Ideal Transformer......Page 33
1.11 Definitions: Laplace and Fourier Transformations of a Time Domain Function f(t)......Page 34
1.12 Useful Mathematical Properties of Laplace and Fourier Transforms of a Causal Function......Page 36
1.13 Numerical Evaluation of Hilbert Transform......Page 42
1.15 Signal Energy......Page 43
1.16 Definition of Impedance and Admittance......Page 44
1.17 Immittance of One-port Networks......Page 45
1.18 Definition: ‘Positive Real Functions’......Page 47
2.1 Introduction......Page 57
2.2 Coulomb’s Law and Electric Fields......Page 58
2.3 Definition of Electric Field......Page 59
2.4 Definition of Electric Potential......Page 60
2.5 Units of Force, Energy and Potential......Page 63
2.6 Uniform Electric Field......Page 64
2.8 Definition of Displacement Vector or ‘Electric Flux Density Vector’ D......Page 65
2.9 Boundary Conditions in an Electric Field......Page 68
2.10 Differential Relation between the Potential and the Electric Field......Page 69
2.11 Parallel Plate Capacitor......Page 71
2.12 Capacitance of a Transmission Line......Page 74
2.13 Capacitance of Coaxial Cable......Page 76
2.14 Resistance of a Conductor of Length L: Ohm’s Law......Page 77
2.15 Principle of Charge Conservation and the Continuity Equation......Page 82
2.17 The Magnetic Field......Page 83
2.18 Generation of Magnetic Fields: Biot–Savart and Ampère’s Law......Page 86
2.20 Unit of Magnetic Field: Related Quantities......Page 89
2.23 Definition of Inductance L......Page 90
2.24 Permeability μ and its Unit......Page 91
2.25 Magnetic Force between Two Parallel Wires......Page 92
2.26 Magnetic Field Generated by a Circular Current-Carrying Wire......Page 93
2.28 The Toroid......Page 95
2.29 Inductance of N-Turn Wire Loops......Page 96
2.30 Inductance of a Coaxial Transmission Line......Page 98
2.31 Parallel Wire Transmission Line......Page 103
2.32 Faraday’s Law......Page 104
2.34 Magnetic Energy Density in a Given Volume......Page 105
2.35 Transformer......Page 106
2.36 Mutual Inductance......Page 109
2.37 Boundary Conditions and Maxwell Equations......Page 111
2.38 Summary of Maxwell Equations and Electromagnetic Wave Propagation......Page 118
2.40 General Form of Electromagnetic Wave Equation......Page 123
2.41 Solutions of Maxwell Equations Using Complex Phasors......Page 125
2.42 Determination of the Electromagnetic Field Distribution of a Short Current Element: Hertzian Dipole Problem......Page 127
2.44 Magnetic Dipole......Page 130
2.45 Long Straight Wire Antenna: Half-Wave Dipole......Page 131
2.46 Fourier Transform of Maxwell Equations: Phasor Representation......Page 132
3.1 Ideal Transmission Lines......Page 139
3.3 Model for a Two-Pair Wire Transmission Line as an Ideal TEM Line......Page 144
3.5 Field Solutions for TEM Lines......Page 145
3.6 Phasor Solutions for Ideal TEM Lines......Page 146
3.7 Steady State Time Domain Solutions for Voltage and Current at Any Point z on the TEM Line......Page 147
3.8 Transmission Lines as Circuit Elements......Page 148
3.9 TEM Lines as Circuit or ‘Distributed’ Elements......Page 149
3.10 Ideal TEM Lines with No Reflection: Perfectly Matched and Mismatched Lines......Page 164
4.1 Ideal TEM Lines as Lossless Two-ports......Page 171
4.2 Scattering Parameters of a TEM Line as a Lossless Two-port......Page 173
4.3 Input Reflection Coefficient under Arbitrary Termination......Page 175
4.5 Derivation of the Actual Voltage-Based Input and Output Incident and Reflected Waves......Page 176
4.6 Incident and Reflected Waves for Arbitrary Normalization Numbers......Page 179
4.7 Lossless Two-ports Constructed with Commensurate Transmission Lines......Page 187
4.8 Cascade Connection of Two UEs......Page 190
4.9 Major Properties of the Scattering Parameters for Passive Two-ports......Page 192
4.10 Rational Form of the Scattering Matrix for a Resistively Terminated Lossless Two-port Constructed by Transmission Lines......Page 198
4.11 Kuroda Identities......Page 209
4.12 Normalization Change and Richard Extractions......Page 210
4.13 Transmission Zeros in the Richard Domain......Page 218
4.15 Generation of Lossless Two-ports with Desired Topology......Page 219
4.16 Stepped Line Butterworth Gain Approximation......Page 233
4.17 Design of Chebyshev Filters Employing Stepped Lines......Page 238
4.18 MATLAB® Codes to Design Stepped Line Filters Using Chebyshev Polynomials......Page 252
4.19 Summary and Concluding Remarks on the Circuits Designed Using Commensurate Transmission Lines......Page 263
5.1 Arbitrary Gain Approximation......Page 277
5.2 Filter Design via SRFT for Arbitrary Gain and Phase Approximation......Page 278
5.3 Conclusion......Page 289
6.1 Introduction......Page 299
6.2 Formal Definition of Scattering Parameters......Page 300
6.3 Generation of Scattering Parameters for Linear Two-ports......Page 312
6.4 Transducer Power Gain in Forward and Backward Directions......Page 314
6.5 Properties of the Scattering Parameters of Lossless Two-ports......Page 315
6.6 Blashke Products or All-Pass Functions......Page 322
6.7 Possible Zeros of a Proper Polynomial f(p)......Page 323
6.8 Transmission Zeros......Page 324
6.9 Lossless Ladders......Page 329
6.10 Further Properties of the Scattering Parameters of Lossless Two-ports......Page 330
6.11 Transfer Scattering Parameters......Page 332
6.12 Cascaded (or Tandem) Connections of Two-ports......Page 333
6.13 Comments......Page 335
6.14 Generation of Scattering Parameters from Transfer Scattering Parameters......Page 337
7.1 Introduction......Page 339
7.2 Generation of Positive Real Functions via the Parametric Approach using MATLAB®......Page 340
7.3 Major Polynomial Operations in MATLAB®......Page 343
7.4 Algorithm: Computation of Residues in Bode Form on MATLAB®......Page 345
7.5 Generation of Minimum Functions from the Given All-Zero, All-Pole Form of the Real Part......Page 357
7.6 Immittance Modeling via the Parametric Approach......Page 371
7.7 Direct Approach for Minimum Immittance Modeling via the Parametric Approach......Page 381
8.1 Introduction......Page 395
8.2 Gewertz Procedure......Page 396
8.3 Gewertz Algorithm......Page 399
8.4 MATLAB® Codes for the Gewertz Algorithm......Page 400
8.5 Comparison of the Bode Method to the Gewertz Procedure......Page 408
8.6 Immittance Modeling via the Gewertz Procedure......Page 414
9.2 Power Dissipation P[sub(L)]over a Load Impedance Z[sub(L)]......Page 427
9.3 Power Transfer......Page 428
9.4 Maximum Power Transfer Theorem......Page 429
9.6 Formal Definition of a Broadband Matching Problem......Page 430
9.7 Darlington’s Description of Lossless Two-ports......Page 432
9.8 Description of Lossless Two-ports via Z Parameters......Page 445
9.9 Driving Point Input Impedance of a Lossless Two-port......Page 448
9.10 Proper Selection of Cases to Construct Lossless Two-ports from the Driving Point Immittance Function......Page 452
9.11 Synthesis of a Compact Pole......Page 457
9.12 Cauer Realization of Lossless Two-ports......Page 458
10.1 Introduction......Page 461
10.2 Filter or Insertion Loss Problem from the Viewpoint of Broadband Matching......Page 466
10.3 Construction of Doubly Terminated Lossless Reciprocal Filters......Page 468
10.4 Analytic Solutions to Broadband Matching Problems......Page 469
10.5 Analytic Approach to Double Matching Problems......Page 475
10.6 Unified Analytic Approach to Design Broadband Matching Networks......Page 485
10.7 Design of Lumped Element Filters Employing Chebyshev Functions......Page 486
10.8 Synthesis of Lumped Element Low-Pass Chebyshev Filter Prototype......Page 496
10.9 Algorithm to Construct Monotone Roll-Off Chebyshev Filters......Page 499
10.10 Denormalization of the Element Values for Monotone Roll-off Chebyshev Filters......Page 512
10.11 Transformation from Low-Pass LC Ladder Filters to Bandpass Ladder Filters......Page 514
10.12 Simple Single Matching Problems......Page 516
10.13 Simple Double Matching Problems......Page 521
10.15 Algorithm to Design Idealized Equalizer Data for Double Matching Problems......Page 522
10.16 General Form of Monotone Roll-Off Chebyshev Transfer Functions......Page 533
10.17 LC Ladder Solutions to Matching Problems Using the General Form Chebyshev Transfer Function......Page 539
10.18 Conclusion......Page 548
11.1 Introduction......Page 561
11.2 Real Frequency Line Segment Technique......Page 562
11.3 Real Frequency Direct Computational Technique for Double Matching Problems......Page 593
11.4 Initialization of RFDT Algorithm......Page 621
11.5 Design of a Matching Equalizer for a Short Monopole Antenna......Page 622
11.6 Design of a Single Matching Equalizer for the Ultrasonic T1350 Transducer......Page 633
11.7 Simplified Real Frequency Technique (SRFT): ‘A Scattering Approach’......Page 638
11.8 Antenna Tuning Using SRFT: Design of a Matching Network for a Helix Antenna......Page 641
11.9 Performance Assessment of Active and Passive Components by Employing SRFT......Page 656
12.1 Introduction......Page 713
12.3 Verification via SS-ELIP......Page 715
12.4 Verification via PS-EIP......Page 718
12.5 Interpolation of a Given Foster Data Set X[sub(f)](ω)......Page 720
12.6 Practical and Numerical Aspects......Page 723
12.7 Estimation of the Minimum Degree n of the Denominator Polynomial D(ω[sup(2)]......Page 724
12.8 Comments on the Error in the Interpolation Process and Proper Selection of Sample Points......Page 725
12.9 Examples......Page 726
12.10 Conclusion......Page 738
13.1 Introduction......Page 741
13.2 Construction of Low-Pass Ladders with UEs......Page 747
13.3 Application......Page 749
13.4 Conclusion......Page 753
Index......Page 773