Design of Ultra Wideband Power Transfer NetworksISBN: 9780470319895
774 pages
June 2010

Description
A comprehensive theory of circuits constructed with lumped and distributed elements is covered, as are electromagnetic field theory, filter theory, and broadband matching. Along with detailed roadmaps and accessible algorithms, this book provides uptodate, practical design examples including:
 filters built with microstrip lines in C and X bands;
 various antenna matching networks over HF and microwave frequencies;
 channel equalizers with arbitary gain shapes;
 matching networks for ultrasonic transducers;
 ultra wideband microwave amplifiers constructed with lumped and distributed elements.
A companion website details all Real Frequency Techniques (including line segment and computational techniques) with design tools developed on MatLab.
Essential reading for all RF and circuit design engineers, this is also a great reference text for other electrical engineers and researchers working on the development of communications applications at wideband frequencies. This book is also beneficial to advanced electrical and communications engineering students taking courses in RF and microwave communications technology.
www.wiley.com/go/yarman_wideband
Table of Contents
Preface xv
1 Circuit Theory for Power Transfer Networks 1
1.1 Introduction 1
1.2 Ideal Circuit Elements 2
1.3 Average Power Dissipation and Effective Voltage and Current 3
1.4 Definitions of Voltage and Current Phasors 5
1.5 Definitions of Active, Passive and Lossless Oneports 6
1.6 Definition of Resistor 6
1.7 Definition of Capacitor 7
1.8 Definition of Inductor 8
1.9 Definition of an Ideal Transformer 11
1.10 Coupled Coils 12
1.11 Definitions: Laplace and Fourier Transformations of a Time Domain Function f(t) 12
1.12 Useful Mathematical Properties of Laplace and Fourier Transforms of a Causal Function 14
1.13 Numerical Evaluation of Hilbert Transform 20
1.14 Convolution 21
1.15 Signal Energy 21
1.16 Definition of Impedance and Admittance 22
1.17 Immittance of Oneport Networks 23
1.18 Definition: ‘Positive Real Functions’ 25
2 Electromagnetic Field Theory for Power Transfer Networks: Fields, Waves and Lumped Circuit Models 35
2.1 Introduction 35
2.2 Coulomb’s Law and Electric Fields 36
2.3 Definition of Electric Field 37
2.4 Definition of Electric Potential 38
2.5 Units of Force, Energy and Potential 41
2.6 Uniform Electric Field 42
2.7 Units of Electric Field 43
2.8 Definition of Displacement Vector or ‘Electric Flux Density Vector’ D 43
2.9 Boundary Conditions in an Electric Field 46
2.10 Differential Relation between the Potential and the Electric Field 47
2.11 Parallel Plate Capacitor 49
2.12 Capacitance of a Transmission Line 52
2.13 Capacitance of Coaxial Cable 54
2.14 Resistance of a Conductor of Length L: Ohm’s Law 55
2.15 Principle of Charge Conservation and the Continuity Equation 60
2.16 Energy Density in an Electric Field 61
2.17 The Magnetic Field 61
2.18 Generation of Magnetic Fields: Biot–Savart and Ampe`re’s Law 64
2.19 Direction of Magnetic Field: Right Hand Rule 67
2.20 Unit of Magnetic Field: Related Quantities 67
2.21 Unit of Magnetic Flux Density B 68
2.22 Unit of Magnetic Flux 68
2.23 Definition of Inductance L 68
2.24 Permeability m and its Unit 69
2.25 Magnetic Force between Two Parallel Wires 70
2.26 Magnetic Field Generated by a Circular CurrentCarrying Wire 71
2.27 Magnetic Field of a Tidily Wired Solenoid of N Turns 73
2.28 The Toroid 73
2.29 Inductance of NTurn Wire Loops 74
2.30 Inductance of a Coaxial Transmission Line 76
2.31 Parallel Wire Transmission Line 81
2.32 Faraday’s Law 82
2.33 Energy Stored in a Magnetic Field 83
2.34 Magnetic Energy Density in a Given Volume 83
2.35 Transformer 84
2.36 Mutual Inductance 87
2.37 Boundary Conditions and Maxwell Equations 89
2.38 Summary of Maxwell Equations and Electromagnetic Wave Propagation 96
2.39 Power Flow in Electromagnetic Fields: Poynting’s Theorem 101
2.40 General Form of Electromagnetic Wave Equation 101
2.41 Solutions of Maxwell Equations Using Complex Phasors 103
2.42 Determination of the Electromagnetic Field Distribution of a Short Current Element: Hertzian Dipole Problem 105
2.43 Antenna Loss 108
2.44 Magnetic Dipole 108
2.45 Long Straight Wire Antenna: HalfWave Dipole 109
2.46 Fourier Transform of Maxwell Equations: Phasor Representation 110
3 Transmission Lines for Circuit Designers: Transmission Lines as Circuit Elements 117
3.1 Ideal Transmission Lines 117
3.2 Time Domain Solutions of Voltage and Current Wave Equations 122
3.3 Model for a TwoPair Wire Transmission Line as an Ideal TEM Line 122
3.4 Model for a Coaxial Cable as an Ideal TEM Line 123
3.5 Field Solutions for TEM Lines 123
3.6 Phasor Solutions for Ideal TEM Lines 124
3.7 Steady State Time Domain Solutions for Voltage and Current at Any Point z on the TEM Line 125
3.8 Transmission Lines as Circuit Elements 126
3.9 TEM Lines as Circuit or ‘Distributed’ Elements 127
3.10 Ideal TEM Lines with No Reflection: Perfectly Matched and Mismatched Lines 142
4 Circuits Constructed with Commensurate Transmission Lines: Properties of Transmission Line Circuits in the Richard Domain 149
4.1 Ideal TEM Lines as Lossless Twoports 149
4.2 Scattering Parameters of a TEM Line as a Lossless Twoport 151
4.3 Input Reflection Coefficient under Arbitrary Termination 153
4.4 Choice of the Port Normalizations 154
4.5 Derivation of the Actual VoltageBased Input and Output Incident and Reflected Waves 154
4.6 Incident and Reflected Waves for Arbitrary Normalization Numbers 157
4.7 Lossless Twoports Constructed with Commensurate Transmission Lines 165
4.8 Cascade Connection of Two UEs 168
4.9 Major Properties of the Scattering Parameters for Passive Twoports 170
4.10 Rational Form of the Scattering Matrix for a Resistively Terminated Lossless Twoport Constructed by Transmission Lines 176
4.11 Kuroda Identities 187
4.12 Normalization Change and Richard Extractions 188
4.13 Transmission Zeros in the Richard Domain 196
4.14 Rational Form of the Scattering Parameters and Generation of g(l) via the Losslessness Condition 197
4.15 Generation of Lossless Twoports with Desired Topology 197
4.16 Stepped Line Butterworth Gain Approximation 211
4.17 Design of Chebyshev Filters Employing Stepped Lines 216
4.18 MATLABCodes to Design Stepped Line Filters Using Chebyshev Polynomials 230
4.19 Summary and Concluding Remarks on the Circuits Designed Using Commensurate Transmission Lines 241
5 Insertion Loss Approximation for Arbitrary Gain Forms via the Simplified Real Frequency Technique: Filter Design via SRFT 255
5.1 Arbitrary Gain Approximation 255
5.2 Filter Design via SRFT for Arbitrary Gain and Phase Approximation 256
5.3 Conclusion 267
6 Formal Description of Lossless Twoports in Terms of Scattering Parameters: Scattering Parameters in the p Domain 277
6.1 Introduction 277
6.2 Formal Definition of Scattering Parameters 278
6.3 Generation of Scattering Parameters for Linear Twoports 290
6.4 Transducer Power Gain in Forward and Backward Directions 292
6.5 Properties of the Scattering Parameters of Lossless Twoports 293
6.6 Blashke Products or AllPass Functions 300
6.7 Possible Zeros of a Proper Polynomial f(p) 301
6.8 Transmission Zeros 302
6.9 Lossless Ladders 307
6.10 Further Properties of the Scattering Parameters of Lossless Twoports 308
6.11 Transfer Scattering Parameters 310
6.12 Cascaded (or Tandem) Connections of Twoports 311
6.13 Comments 313
6.14 Generation of Scattering Parameters from Transfer Scattering Parameters 315
7 Numerical Generation of Minimum Functions via the Parametric Approach 317
7.1 Introduction 317
7.2 Generation of Positive Real Functions via the Parametric Approach using MATLAB318
7.3 Major Polynomial Operations in MATLAB321
7.4 Algorithm: Computation of Residues in Bode Form on MATLAB323
7.5 Generation of Minimum Functions from the Given AllZero, AllPole Form of the Real Part 335
7.6 Immittance Modeling via the Parametric Approach 349
7.7 Direct Approach for Minimum Immittance Modeling via the Parametric Approach 359
8 Gewertz Procedure to Generate a Minimum Function from its Even Part: Generation of Minimum Function in Rational Form 373
8.1 Introduction 373
8.2 Gewertz Procedure 374
8.3 Gewertz Algorithm 377
8.4 MATLABCodes for the Gewertz Algorithm 378
8.5 Comparison of the Bode Method to the Gewertz Procedure 386
8.6 Immittance Modeling via the Gewertz Procedure 392
9 Description of Power Transfer Networks via Driving Point Input Immittance: Darlington’s Theorem 405
9.1 Introduction 405
9.2 Power Dissipation PL over a Load Impedance ZL 405
9.3 Power Transfer 406
9.4 Maximum Power Transfer Theorem 407
9.5 Transducer Power Gain for Matching Problems 408
9.6 Formal Definition of a Broadband Matching Problem 408
9.7 Darlington’s Description of Lossless Twoports 410
9.8 Description of Lossless Twoports via Z Parameters 423
9.9 Driving Point Input Impedance of a Lossless Twoport 426
9.10 Proper Selection of Cases to Construct Lossless Twoports from the Driving Point Immittance Function 430
9.11 Synthesis of a Compact Pole 435
9.12 Cauer Realization of Lossless Twoports 436
10 Design of Power Transfer Networks: A Glimpse of the Analytic Theory via a Unified Approach 439
10.1 Introduction 439
10.2 Filter or Insertion Loss Problem from the Viewpoint of Broadband Matching 444
10.3 Construction of Doubly Terminated Lossless Reciprocal Filters 446
10.4 Analytic Solutions to Broadband Matching Problems 447
10.5 Analytic Approach to Double Matching Problems 453
10.6 Unified Analytic Approach to Design Broadband Matching Networks 463
10.7 Design of Lumped Element Filters Employing Chebyshev Functions 464
10.8 Synthesis of Lumped Element LowPass Chebyshev Filter Prototype 474
10.9 Algorithm to Construct Monotone RollOff Chebyshev Filters 477
10.10 Denormalization of the Element Values for Monotone Rolloff Chebyshev Filters 490
10.11 Transformation from LowPass LC Ladder Filters to Bandpass Ladder Filters 492
10.12 Simple Single Matching Problems 494
10.13 Simple Double Matching Problems 499
10.14 A Semianalytic Approach for Double Matching Problems 500
10.15 Algorithm to Design Idealized Equalizer Data for Double Matching Problems 500
10.16 General Form of Monotone RollOff Chebyshev Transfer Functions 511
10.17 LC Ladder Solutions to Matching Problems Using the General Form Chebyshev Transfer Function 517
10.18 Conclusion 526
11 Modern Approaches to Broadband Matching Problems: Real Frequency Solutions 539
11.1 Introduction 539
11.2 Real Frequency Line Segment Technique 540
11.3 Real Frequency Direct Computational Technique for Double Matching Problems 571
11.4 Initialization of RFDT Algorithm 599
11.5 Design of a Matching Equalizer for a Short Monopole Antenna 600
11.6 Design of a Single Matching Equalizer for the Ultrasonic T1350 Transducer 611
11.7 Simplified Real Frequency Technique (SRFT): ‘A Scattering Approach’ 616
11.8 Antenna Tuning Using SRFT: Design of a Matching Network for a Helix Antenna 619
11.9 Performance Assessment of Active and Passive Components by Employing SRFT 634
12 Immittance Data Modeling via Linear Interpolation Techniques: A Classical Circuit Theory Approach 691
12.1 Introduction 691
12.2 Interpolation of the Given Real Part Data Set 693
12.3 Verification via SSELIP 693
12.4 Verification via PSEIP 696
12.5 Interpolation of a Given Foster Data Set Xf (!) 698
12.6 Practical and Numerical Aspects 701
12.7 Estimation of the Minimum Degree n of the Denominator Polynomial D(!2) 702
12.8 Comments on the Error in the Interpolation Process and Proper Selection of Sample Points 703
12.9 Examples 704
12.10 Conclusion 716
13 Lossless Twoports Formed with Mixed Lumped and Distributed Elements: Design of Matching Networks with Mixed Elements 719
13.1 Introduction 719
13.2 Construction of LowPass Ladders with UEs 725
13.3 Application 727
13.4 Conclusion 731
Index 751
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