About the Author |
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xiii | |
Preface |
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xv | |
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1 Circuit Theory for Power Transfer Networks |
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1 | (34) |
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1 | (1) |
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1.2 Ideal Circuit Elements |
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2 | (1) |
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1.3 Average Power Dissipation and Effective Voltage and Current |
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3 | (2) |
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1.4 Definitions of Voltage and Current Phasors |
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5 | (1) |
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1.5 Definitions of Active, Passive and Lossless One-ports |
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6 | (1) |
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1.6 Definition of Resistor |
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6 | (1) |
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1.7 Definition of Capacitor |
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7 | (1) |
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1.8 Definition of Inductor |
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8 | (3) |
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1.9 Definition of an Ideal Transformer |
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11 | (1) |
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12 | (1) |
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1.11 Definitions: Laplace and Fourier Transformations of a Time Domain Function f(t) |
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12 | (2) |
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1.12 Useful Mathematical Properties of Laplace and Fourier Transforms of a Causal Function |
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14 | (6) |
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1.13 Numerical Evaluation of Hilbert Transform |
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20 | (1) |
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21 | (1) |
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21 | (1) |
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1.16 Definition of Impedance and Admittance |
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22 | (1) |
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1.17 Immittance of One-port Networks |
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23 | (2) |
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1.18 Definition: `Positive Real Functions' |
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25 | (10) |
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2 Electromagnetic Field Theory for Power Transfer Networks: Fields, Waves and Lumped Circuit Models |
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35 | (82) |
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35 | (1) |
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2.2 Coulomb's Law and Electric Fields |
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36 | (1) |
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2.3 Definition of Electric Field |
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37 | (1) |
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2.4 Definition of Electric Potential |
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38 | (3) |
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2.5 Units of Force, Energy and Potential |
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41 | (1) |
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2.6 Uniform Electric Field |
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42 | (1) |
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2.7 Units of Electric Field |
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43 | (1) |
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2.8 Definition of Displacement Vector or `Electric Flux Density Vector'D |
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43 | (3) |
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2.9 Boundary Conditions in an Electric Field |
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46 | (1) |
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2.10 Differential Relation between the Potential and the Electric Field |
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47 | (2) |
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2.11 Parallel Plate Capacitor |
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49 | (3) |
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2.12 Capacitance of a Transmission Line |
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52 | (2) |
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2.13 Capacitance of Coaxial Cable |
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54 | (1) |
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2.14 Resistance of a Conductor of Length L: Ohm's Law |
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55 | (5) |
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2.15 Principle of Charge Conservation and the Continuity Equation |
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60 | (1) |
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2.16 Energy Density in an Electric Field |
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61 | (1) |
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61 | (3) |
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2.18 Generation of Magnetic Fields: Biot-Savart and Ampere's Law |
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64 | (3) |
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2.19 Direction of Magnetic Field: Right Hand Rule |
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67 | (1) |
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2.20 Unit of Magnetic Field: Related Quantities |
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67 | (1) |
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2.21 Unit of Magnetic Flux Density B |
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68 | (1) |
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2.22 Unit of Magnetic Flux φ |
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68 | (1) |
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2.23 Definition of Inductance L |
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68 | (1) |
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2.24 Permeability μ and its Unit |
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69 | (1) |
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2.25 Magnetic Force between Two Parallel Wires |
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70 | (1) |
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2.26 Magnetic Field Generated by a Circular Current-Carrying Wire |
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71 | (2) |
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2.27 Magnetic Field of a Tidily Wired Solenoid of N Turns |
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73 | (1) |
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73 | (1) |
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2.29 Inductance of N-Turn Wire Loops |
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74 | (2) |
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2.30 Inductance of a Coaxial Transmission Line |
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76 | (5) |
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2.31 Parallel Wire Transmission Line |
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81 | (1) |
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82 | (1) |
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2.33 Energy Stored in a Magnetic Field |
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83 | (1) |
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2.34 Magnetic Energy Density in a Given Volume |
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83 | (1) |
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84 | (3) |
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87 | (2) |
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2.37 Boundary Conditions and Maxwell Equations |
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89 | (7) |
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2.38 Summary of Maxwell Equations and Electromagnetic Wave Propagation |
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96 | (5) |
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2.39 Power Flow in Electromagnetic Fields: Poynting's Theorem |
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101 | (1) |
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2.40 General Form of Electromagnetic Wave Equation |
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101 | (2) |
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2.41 Solutions of Maxwell Equations Using Complex Phasors |
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103 | (2) |
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2.42 Determination of the Electromagnetic Field Distribution of a Short Current Element: Hertzian Dipole Problem |
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105 | (3) |
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108 | (1) |
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108 | (1) |
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2.45 Long Straight Wire Antenna: Half-Wave Dipole |
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109 | (1) |
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2.46 Fourier Transform of Maxwell Equations: Phasor Representation |
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110 | (7) |
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3 Transmission Lines for Circuit Designers: Transmission Lines as Circuit Elements |
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117 | (32) |
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3.1 Ideal Transmission Lines |
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117 | (5) |
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3.2 Time Domain Solutions of Voltage and Current Wave Equations |
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122 | (1) |
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3.3 Model for a Two-Pair Wire Transmission Line as an Ideal TEM Line |
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122 | (1) |
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3.4 Model for a Coaxial Cable as an Ideal TEM Line |
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123 | (1) |
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3.5 Field Solutions for TEM Lines |
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123 | (1) |
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3.6 Phasor Solutions for Ideal TEM Lines |
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124 | (1) |
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3.7 Steady State Time Domain Solutions for Voltage and Current at Any Point z on the TEM Line |
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125 | (1) |
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3.8 Transmission Lines as Circuit Elements |
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126 | (1) |
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3.9 TEM Lines as Circuit or `Distributed' Elements |
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127 | (15) |
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3.10 Ideal TEM Lines with No Reflection: Perfectly Matched and Mismatched Lines |
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142 | (7) |
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4 Circuits Constructed with Commensurate Transmission Lines: Properties of Transmission Line Circuits in the Richard Domain |
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149 | (106) |
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4.1 Ideal TEM Lines as Lossless Two-ports |
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149 | (2) |
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4.2 Scattering Parameters of a TEM Line as a Lossless Two-port |
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151 | (2) |
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4.3 Input Reflection Coefficient under Arbitrary Termination |
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153 | (1) |
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4.4 Choice of the Port Normalizations |
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154 | (1) |
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4.5 Derivation of the Actual Voltage-Based Input and Output Incident and Reflected Waves |
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154 | (3) |
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4.6 Incident and Reflected Waves for Arbitrary Normalization Numbers |
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157 | (8) |
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4.7 Lossless Two-ports Constructed with Commensurate Transmission Lines |
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165 | (3) |
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4.8 Cascade Connection of Two UEs |
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168 | (2) |
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4.9 Major Properties of the Scattering Parameters for Passive Two-ports |
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170 | (6) |
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4.10 Rational Form of the Scattering Matrix for a Resistively Terminated Lossless Two-port Constructed by Transmission Lines |
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176 | (11) |
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187 | (1) |
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4.12 Normalization Change and Richard Extractions |
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188 | (8) |
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4.13 Transmission Zeros in the Richard Domain |
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196 | (1) |
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4.14 Rational Form of the Scattering Parameters and Generation of g(λ) via the Losslessness Condition |
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197 | (1) |
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4.15 Generation of Lossless Two-ports with Desired Topology |
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197 | (14) |
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4.16 Stepped Line Butterworth Gain Approximation |
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211 | (5) |
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4.17 Design of Chebyshev Filters Employing Stepped Lines |
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216 | (14) |
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4.18 MATLAB® Codes to Design Stepped Line Filters Using Chebyshev Polynomials |
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230 | (11) |
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4.19 Summary and Concluding Remarks on the Circuits Designed Using Commensurate Transmission Lines |
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241 | (14) |
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5 Insertion Loss Approximation for Arbitrary Gain Forms via the Simplified Real Frequency Technique: Filter Design via SRFT |
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255 | (22) |
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5.1 Arbitrary Gain Approximation |
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255 | (1) |
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5.2 Filter Design via SRFT for Arbitrary Gain and Phase Approximation |
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256 | (11) |
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267 | (10) |
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6 Formal Description of Lossless Two-ports in Terms of Scattering Parameters: Scattering Parameters in the p Domain |
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277 | (40) |
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277 | (1) |
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6.2 Formal Definition of Scattering Parameters |
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278 | (12) |
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6.3 Generation of Scattering Parameters for Linear Two-ports |
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290 | (2) |
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6.4 Transducer Power Gain in Forward and Backward Directions |
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292 | (1) |
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6.5 Properties of the Scattering Parameters of Lossless Two-ports |
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293 | (7) |
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6.6 Blashke Products or All-Pass Functions |
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300 | (1) |
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6.7 Possible Zeros of a Proper Polynomial f(p) |
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301 | (1) |
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302 | (5) |
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307 | (1) |
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6.10 Further Properties of the Scattering Parameters of Lossless Two-ports |
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308 | (2) |
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6.11 Transfer Scattering Parameters |
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310 | (1) |
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6.12 Cascaded (or Tandem) Connections of Two-ports |
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311 | (2) |
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313 | (2) |
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6.14 Generation of Scattering Parameters from Transfer Scattering Parameters |
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315 | (2) |
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7 Numerical Generation of Minimum Functions via the Parametric Approach |
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317 | (56) |
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317 | (1) |
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7.2 Generation of Positive Real Functions via the Parametric Approach using MATLAB® |
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318 | (3) |
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7.3 Major Polynomial Operations in MATLAB® |
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321 | (2) |
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7.4 Algorithm: Computation of Residues in Bode Form on MATLAB® |
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323 | (12) |
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7.5 Generation of Minimum Functions from the Given All-Zero, All-Pole Form of the Real Part |
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335 | (14) |
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7.6 Immittance Modeling via the Parametric Approach |
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349 | (10) |
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7.7 Direct Approach for Minimum Immittance Modeling via the Parametric Approach |
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359 | (14) |
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8 Gewertz Procedure to Generate a Minimum Function from its Even Part: Generation of Minimum Function in Rational Form |
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373 | (32) |
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373 | (1) |
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374 | (3) |
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377 | (1) |
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8.4 MATLAB® Codes for the Gewertz Algorithm |
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378 | (8) |
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8.5 Comparison of the Bode Method to the Gewertz Procedure |
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386 | (6) |
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8.6 Immittance Modeling via the Gewertz Procedure |
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392 | (13) |
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9 Description of Power Transfer Networks via Driving Point Input Immittance: Darlington's Theorem |
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405 | (34) |
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405 | (1) |
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9.2 Power Dissipation PL over a Load Impedance ZL |
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405 | (1) |
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406 | (1) |
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9.4 Maximum Power Transfer Theorem |
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407 | (1) |
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9.5 Transducer Power Gain for Matching Problems |
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408 | (1) |
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9.6 Formal Definition of a Broadband Matching Problem |
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408 | (2) |
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9.7 Darlington's Description of Lossless Two-ports |
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410 | (13) |
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9.8 Description of Lossless Two-ports via Z Parameters |
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423 | (3) |
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9.9 Driving Point Input Impedance of a Lossless Two-port |
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426 | (4) |
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9.10 Proper Selection of Cases to Construct Lossless Two-ports from the Driving Point Immittance Function |
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430 | (5) |
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9.11 Synthesis of a Compact Pole |
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435 | (1) |
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9.12 Cauer Realization of Lossless Two-ports |
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436 | (3) |
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10 Design of Power Transfer Networks: A Glimpse of the Analytic Theory via a Unified Approach |
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439 | (100) |
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439 | (5) |
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10.2 Filter or Insertion Loss Problem from the Viewpoint of Broadband Matching |
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444 | (2) |
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10.3 Construction of Doubly Terminated Lossless Reciprocal Filters |
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446 | (1) |
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10.4 Analytic Solutions to Broadband Matching Problems |
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447 | (6) |
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10.5 Analytic Approach to Double Matching Problems |
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453 | (10) |
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10.6 Unified Analytic Approach to Design Broadband Matching Networks |
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463 | (1) |
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10.7 Design of Lumped Element Filters Employing Chebyshev Functions |
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464 | (10) |
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10.8 Synthesis of Lumped Element Low-Pass Chebyshev Filter Prototype |
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474 | (3) |
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10.9 Algorithm to Construct Monotone Roll-Off Chebyshev Filters |
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477 | (13) |
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10.10 Denormalization of the Element Values for Monotone Roll-off Chebyshev Filters |
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490 | (2) |
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10.11 Transformation from Low-Pass LC Ladder Filters to Bandpass Ladder Filters |
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492 | (2) |
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10.12 Simple Single Matching Problems |
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494 | (5) |
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10.13 Simple Double Matching Problems |
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499 | (1) |
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10.14 A Semi-analytic Approach for Double Matching Problems |
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500 | (1) |
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10.15 Algorithm to Design Idealized Equalizer Data for Double Matching Problems |
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500 | (11) |
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10.16 General Form of Monotone Roll-Off Chebyshev Transfer Functions |
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511 | (6) |
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10.17 LC Ladder Solutions to Matching Problems Using the General Form Chebyshev Transfer Function |
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517 | (9) |
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526 | (13) |
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11 Modern Approaches to Broadband Matching Problems: Real Frequency Solutions |
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539 | (152) |
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539 | (1) |
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11.2 Real Frequency Line Segment Technique |
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540 | (31) |
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11.3 Real Frequency Direct Computational Technique for Double Matching Problems |
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571 | (28) |
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11.4 Initialization of RFDT Algorithm |
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599 | (1) |
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11.5 Design of a Matching Equalizer for a Short Monopole Antenna |
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600 | (11) |
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11.6 Design of a Single Matching Equalizer for the Ultrasonic T1350 Transducer |
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611 | (5) |
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11.7 Simplified Real Frequency Technique (SRFT): `A Scattering Approach' |
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616 | (3) |
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11.8 Antenna Tuning Using SRFT: Design of a Matching Network for a Helix Antenna |
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619 | (15) |
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11.9 Performance Assessment of Active and Passive Components by Employing SRFT |
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634 | (57) |
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12 Immittance Data Modeling via Linear Interpolation Techniques: A Classical Circuit Theory Approach |
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691 | (28) |
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691 | (2) |
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12.2 Interpolation of the Given Real Part Data Set |
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693 | (1) |
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12.3 Verification via SS-ELIP |
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693 | (3) |
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12.4 Verification via PS-EIP |
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696 | (2) |
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12.5 Interpolation of a Given Foster Data Set X∫(w) |
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698 | (3) |
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12.6 Practical and Numerical Aspects |
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701 | (1) |
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12.7 Estimation of the Minimum Degree n of the Denominator Polynomial D(w2) |
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702 | (1) |
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12.8 Comments on the Error in the Interpolation Process and Proper Selection of Sample Points |
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703 | (1) |
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704 | (12) |
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716 | (3) |
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13 Lossless Two-ports Formed with Mixed Lumped and Distributed Elements: Design of Matching Networks with Mixed Elements |
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719 | (32) |
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719 | (6) |
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13.2 Construction of Low-Pass Ladders with UEs |
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725 | (2) |
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727 | (4) |
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731 | (20) |
Index |
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