Design of Ultra Wideband Power Transfer Networks

Binboga Siddik Yarman, Tokyo Institute of TechnologyProfessor Binboga Siddik Yarman is currently on a sabbatical in the Department of Physical Electronics, at the Tokyo Institute of Technology, Japan. His full-time position is with the Department of Electrical and Electronics Engineering, at the College of Engineering, Istanbul University. Professor Yarman is very experienced in the field of communication networks, being one of the first engineers to establish computer-aided design (CAD) tools for constructing practical broadband matching networks and multistage microwave amplifiers for optimized communication systems. In doing this, he paved the way for the generation of CAD algorithms to construct practical circuits in the field of communications engineering, including commercial and military communication sub-systems such as antenna matching networks, and multistage microwave amplifiers for mobile and fixed communication systems. He has published a number of book chapters and journal papers on the design of microwave amplifiers, modeling techniques and other design issues concerning power transfer networks, including a section on 'Broadband Networks' for the Wiley Encyclopedia of Electrical and Electronics Engineering (Vol II, 1999). He has also lectured to both students, and practising engineers on these topics for the last 25 years, in Europe, the USA and Japan.

• About the Author xiii Preface xv1 Circuit Theory for Power Transfer Networks 11.1 Introduction 11.2 Ideal Circuit Elements 21.3 Average Power Dissipation and Effective Voltage and Current 31.4 Definitions of Voltage and Current Phasors 51.5 Definitions of Active, Passive and Lossless One-ports 61.6 Definition of Resistor 61.7 Definition of Capacitor 71.8 Definition of Inductor 81.9 Definition of an Ideal Transformer 111.10 Coupled Coils 121.11 Definitions: Laplace and Fourier Transformations of a Time Domain Function f(t) 121.12 Useful Mathematical Properties of Laplace and Fourier Transforms of a Causal Function 141.13 Numerical Evaluation of Hilbert Transform 201.14 Convolution 211.15 Signal Energy 211.16 Definition of Impedance and Admittance 221.17 Immittance of One-port Networks 231.18 Definition: ‘Positive Real Functions’ 252 Electromagnetic Field Theory for Power Transfer Networks: Fields, Waves and Lumped Circuit Models 352.1 Introduction 352.2 Coulomb’s Law and Electric Fields 362.3 Definition of Electric Field 372.4 Definition of Electric Potential 382.5 Units of Force, Energy and Potential 412.6 Uniform Electric Field 422.7 Units of Electric Field 432.8 Definition of Displacement Vector or ‘Electric Flux Density Vector’ D 432.9 Boundary Conditions in an Electric Field 462.10 Differential Relation between the Potential and the Electric Field 472.11 Parallel Plate Capacitor 492.12 Capacitance of a Transmission Line 522.13 Capacitance of Coaxial Cable 542.14 Resistance of a Conductor of Length L: Ohm’s Law 552.15 Principle of Charge Conservation and the Continuity Equation 602.16 Energy Density in an Electric Field 612.17 The Magnetic Field 612.18 Generation of Magnetic Fields: Biot–Savart and Ampe`re’s Law 642.19 Direction of Magnetic Field: Right Hand Rule 672.20 Unit of Magnetic Field: Related Quantities 672.21 Unit of Magnetic Flux Density B 682.22 Unit of Magnetic Flux 682.23 Definition of Inductance L 682.24 Permeability m and its Unit 692.25 Magnetic Force between Two Parallel Wires 702.26 Magnetic Field Generated by a Circular Current-Carrying Wire 712.27 Magnetic Field of a Tidily Wired Solenoid of N Turns 732.28 The Toroid 732.29 Inductance of N-Turn Wire Loops 742.30 Inductance of a Coaxial Transmission Line 762.31 Parallel Wire Transmission Line 812.32 Faraday’s Law 822.33 Energy Stored in a Magnetic Field 832.34 Magnetic Energy Density in a Given Volume 832.35 Transformer 842.36 Mutual Inductance 872.37 Boundary Conditions and Maxwell Equations 892.38 Summary of Maxwell Equations and Electromagnetic Wave Propagation 962.39 Power Flow in Electromagnetic Fields: Poynting’s Theorem 1012.40 General Form of Electromagnetic Wave Equation 1012.41 Solutions of Maxwell Equations Using Complex Phasors 1032.42 Determination of the Electromagnetic Field Distribution of a Short Current Element: Hertzian Dipole Problem 1052.43 Antenna Loss 1082.44 Magnetic Dipole 1082.45 Long Straight Wire Antenna: Half-Wave Dipole 1092.46 Fourier Transform of Maxwell Equations: Phasor Representation 1103 Transmission Lines for Circuit Designers: Transmission Lines as Circuit Elements 1173.1 Ideal Transmission Lines 1173.2 Time Domain Solutions of Voltage and Current Wave Equations 1223.3 Model for a Two-Pair Wire Transmission Line as an Ideal TEM Line 1223.4 Model for a Coaxial Cable as an Ideal TEM Line 1233.5 Field Solutions for TEM Lines 1233.6 Phasor Solutions for Ideal TEM Lines 1243.7 Steady State Time Domain Solutions for Voltage and Current at Any Point z on the TEM Line 1253.8 Transmission Lines as Circuit Elements 1263.9 TEM Lines as Circuit or ‘Distributed’ Elements 1273.10 Ideal TEM Lines with No Reflection: Perfectly Matched and Mismatched Lines 1424 Circuits Constructed with Commensurate Transmission Lines: Properties of Transmission Line Circuits in the Richard Domain 1494.1 Ideal TEM Lines as Lossless Two-ports 1494.2 Scattering Parameters of a TEM Line as a Lossless Two-port 1514.3 Input Reflection Coefficient under Arbitrary Termination 1534.4 Choice of the Port Normalizations 1544.5 Derivation of the Actual Voltage-Based Input and Output Incident and Reflected Waves 1544.6 Incident and Reflected Waves for Arbitrary Normalization Numbers 1574.7 Lossless Two-ports Constructed with Commensurate Transmission Lines 1654.8 Cascade Connection of Two UEs 1684.9 Major Properties of the Scattering Parameters for Passive Two-ports 1704.10 Rational Form of the Scattering Matrix for a Resistively Terminated Lossless Two-port Constructed by Transmission Lines 1764.11 Kuroda Identities 1874.12 Normalization Change and Richard Extractions 1884.13 Transmission Zeros in the Richard Domain 1964.14 Rational Form of the Scattering Parameters and Generation of g(l) via the Losslessness Condition 1974.15 Generation of Lossless Two-ports with Desired Topology 1974.16 Stepped Line Butterworth Gain Approximation 2114.17 Design of Chebyshev Filters Employing Stepped Lines 2164.18 MATLABCodes to Design Stepped Line Filters Using Chebyshev Polynomials 2304.19 Summary and Concluding Remarks on the Circuits Designed Using Commensurate Transmission Lines 2415 Insertion Loss Approximation for Arbitrary Gain Forms via the Simplified Real Frequency Technique: Filter Design via SRFT 2555.1 Arbitrary Gain Approximation 2555.2 Filter Design via SRFT for Arbitrary Gain and Phase Approximation 2565.3 Conclusion 2676 Formal Description of Lossless Two-ports in Terms of Scattering Parameters: Scattering Parameters in the p Domain 2776.1 Introduction 2776.2 Formal Definition of Scattering Parameters 2786.3 Generation of Scattering Parameters for Linear Two-ports 2906.4 Transducer Power Gain in Forward and Backward Directions 2926.5 Properties of the Scattering Parameters of Lossless Two-ports 2936.6 Blashke Products or All-Pass Functions 3006.7 Possible Zeros of a Proper Polynomial f(p) 3016.8 Transmission Zeros 3026.9 Lossless Ladders 3076.10 Further Properties of the Scattering Parameters of Lossless Two-ports 3086.11 Transfer Scattering Parameters 3106.12 Cascaded (or Tandem) Connections of Two-ports 3116.13 Comments 3136.14 Generation of Scattering Parameters from Transfer Scattering Parameters 3157 Numerical Generation of Minimum Functions via the Parametric Approach 3177.1 Introduction 3177.2 Generation of Positive Real Functions via the Parametric Approach using MATLAB3187.3 Major Polynomial Operations in MATLAB3217.4 Algorithm: Computation of Residues in Bode Form on MATLAB3237.5 Generation of Minimum Functions from the Given All-Zero, All-Pole Form of the Real Part 3357.6 Immittance Modeling via the Parametric Approach 3497.7 Direct Approach for Minimum Immittance Modeling via the Parametric Approach 3598 Gewertz Procedure to Generate a Minimum Function from its Even Part: Generation of Minimum Function in Rational Form 3738.1 Introduction 3738.2 Gewertz Procedure 3748.3 Gewertz Algorithm 3778.4 MATLABCodes for the Gewertz Algorithm 3788.5 Comparison of the Bode Method to the Gewertz Procedure 3868.6 Immittance Modeling via the Gewertz Procedure 3929 Description of Power Transfer Networks via Driving Point Input Immittance: Darlington’s Theorem 4059.1 Introduction 4059.2 Power Dissipation PL over a Load Impedance ZL 4059.3 Power Transfer 4069.4 Maximum Power Transfer Theorem 4079.5 Transducer Power Gain for Matching Problems 4089.6 Formal Definition of a Broadband Matching Problem 4089.7 Darlington’s Description of Lossless Two-ports 4109.8 Description of Lossless Two-ports via Z Parameters 4239.9 Driving Point Input Impedance of a Lossless Two-port 4269.10 Proper Selection of Cases to Construct Lossless Two-ports from the Driving Point Immittance Function 4309.11 Synthesis of a Compact Pole 4359.12 Cauer Realization of Lossless Two-ports 43610 Design of Power Transfer Networks: A Glimpse of the Analytic Theory via a Unified Approach 43910.1 Introduction 43910.2 Filter or Insertion Loss Problem from the Viewpoint of Broadband Matching 44410.3 Construction of Doubly Terminated Lossless Reciprocal Filters 44610.4 Analytic Solutions to Broadband Matching Problems 44710.5 Analytic Approach to Double Matching Problems 45310.6 Unified Analytic Approach to Design Broadband Matching Networks 46310.7 Design of Lumped Element Filters Employing Chebyshev Functions 46410.8 Synthesis of Lumped Element Low-Pass Chebyshev Filter Prototype 47410.9 Algorithm to Construct Monotone Roll-Off Chebyshev Filters 47710.10 Denormalization of the Element Values for Monotone Roll-off Chebyshev Filters 49010.11 Transformation from Low-Pass LC Ladder Filters to Bandpass Ladder Filters 49210.12 Simple Single Matching Problems 49410.13 Simple Double Matching Problems 49910.14 A Semi-analytic Approach for Double Matching Problems 50010.15 Algorithm to Design Idealized Equalizer Data for Double Matching Problems 50010.16 General Form of Monotone Roll-Off Chebyshev Transfer Functions 51110.17 LC Ladder Solutions to Matching Problems Using the General Form Chebyshev Transfer Function 51710.18 Conclusion 52611 Modern Approaches to Broadband Matching Problems: Real Frequency Solutions 53911.1 Introduction 53911.2 Real Frequency Line Segment Technique 54011.3 Real Frequency Direct Computational Technique for Double Matching Problems 57111.4 Initialization of RFDT Algorithm 59911.5 Design of a Matching Equalizer for a Short Monopole Antenna 60011.6 Design of a Single Matching Equalizer for the Ultrasonic T1350 Transducer 61111.7 Simplified Real Frequency Technique (SRFT): ‘A Scattering Approach’ 61611.8 Antenna Tuning Using SRFT: Design of a Matching Network for a Helix Antenna 61911.9 Performance Assessment of Active and Passive Components by Employing SRFT 63412 Immittance Data Modeling via Linear Interpolation Techniques: A Classical Circuit Theory Approach 69112.1 Introduction 69112.2 Interpolation of the Given Real Part Data Set 69312.3 Verification via SS-ELIP 69312.4 Verification via PS-EIP 69612.5 Interpolation of a Given Foster Data Set Xf (!) 69812.6 Practical and Numerical Aspects 70112.7 Estimation of the Minimum Degree n of the Denominator Polynomial D(!2) 70212.8 Comments on the Error in the Interpolation Process and Proper Selection of Sample Points 70312.9 Examples 70412.10 Conclusion 71613 Lossless Two-ports Formed with Mixed Lumped and Distributed Elements: Design of Matching Networks with Mixed Elements 71913.1 Introduction 71913.2 Construction of Low-Pass Ladders with UEs 72513.3 Application 72713.4 Conclusion 731Index 751