High Frequency Techniques

Joseph F. White is an instructor and consultant at JFW Industries, Inc. He has twenty-five years of design experience, was technical director at M/A-COM, Inc., and received the IEEE Microwave Theory and Techniques Society's Application Award for "Contributions to Phased Array Antennas." Dr. White edited Microwave Journal, Applied Microwave and Wireless, and Microwave Semiconductor Engineering. He is a Fellow of the IEEE.

• Preface xv Acknowledgments xvii1 Introduction 11.1 Beginning of Wireless 11.2 Current Radio Spectrum 41.3 Conventions Used in This Text 8Sections 8Equations 8Figures 8Exercises 8Symbols 8Prefixes 10Fonts 101.4 Vectors and Coordinates 111.5 General Constants and Useful Conversions 142 Review of AC Analysis and Network Simulation 162.1 Basic Circuit Elements 16The Resistor 16Ohm’s Law 18The Inductor 19The Capacitor 202.2 Kirchhoff’s Laws 222.3 Alternating Current (AC) Analysis 23Ohm’s Law in Complex Form 262.4 Voltage and Current Phasors 262.5 Impedance 28Estimating Reactance 28Addition of Series Impedances 292.6 Admittance 30Admittance Definition 30Addition of Parallel Admittances 30The Product over the Sum 322.7 LLFPB Networks 332.8 Decibels, dBW, and dBm 33Logarithms (Logs) 33Multiplying by Adding Logs 34Dividing by Subtracting Logs 34Zero Powers 34Bel Scale 34Decibel Scale 35Decibels—Relative Measures 35Absolute Power Levels—dBm and dBW 37Decibel Power Scales 382.9 Power Transfer 38Calculating Power Transfer 38Maximum Power Transfer 392.10 Specifying Loss 40Insertion Loss 40Transducer Loss 41Loss Due to a Series Impedance 42Loss Due to a Shunt Admittance 43Loss in Terms of Scattering Parameters 442.11 Real RLC Models 44Resistor with Parasitics 44Inductor with Parasitics 44Capacitor with Parasitics 442.12 Designing LC Elements 46Lumped Coils 46High μ Inductor Cores—the Hysteresis Curve 47Estimating Wire Inductance 48Parallel Plate Capacitors 492.13 Skin Effect 512.14 Network Simulation 533 LC Resonance and Matching Networks 593.1 LC Resonance 593.2 Series Circuit Quality Factors 60Q of Inductors and Capacitors 60QE, External Q 61QL, Loaded Q 623.3 Parallel Circuit Quality Factors 623.4 Coupled Resonators 63Direct Coupled Resonators 63Lightly Coupled Resonators 633.5 Q Matching 67Low to High Resistance 67Broadbanding the Q Matching Method 70High to Low Resistance 714 Distributed Circuits 784.1 Transmission Lines 784.2 Wavelength in a Dielectric 814.3 Pulses on Transmission Lines 824.4 Incident and Reflected Waves 834.5 Reflection Coefficient 854.6 Return Loss 864.7 Mismatch Loss 864.8 Mismatch Error 874.9 The Telegrapher Equations 914.10 Transmission Line Wave Equations 924.11 Wave Propagation 944.12 Phase and Group Velocities 974.13 Reflection Coefficient and Impedance 1004.14 Impedance Transformation Equation 1014.15 Impedance Matching with One Transmission Line 1084.16 Fano’s (and Bode’s) Limit 109Type A Mismatched Loads 109Type B Mismatched Loads 112Impedance Transformation Not Included 1135 The Smith Chart 1195.1 Basis of the Smith Chart 1195.2 Drawing the Smith Chart 1245.3 Admittance on the Smith Chart 1305.4 Tuning a Mismatched Load 1325.5 Slotted-Line Impedance Measurement 1355.6 VSWR = r 1395.7 Negative Resistance Smith Chart 1405.8 Navigating the Smith Chart 1405.9 Smith Chart Software 1455.10 Estimating Bandwidth on the Smith Chart 1475.11 Approximate Tuning May Be Better 1485.12 Frequency Contours on the Smith Chart 1505.13 Using the Smith Chart without Transmission Lines 1505.14 Constant Q Circles 1515.15 Transmission Line Lumped Circuit Equivalent 1536 Matrix Analysis 1616.1 Matrix Algebra 1616.2 Z and Y Matrices 1646.3 Reciprocity 1666.4 The ABCD Matrix 1676.5 The Scattering Matrix 1726.6 The Transmission Matrix 1777 Electromagnetic Fields and Waves 1837.1 Vector Force Fields 1837.2 E and H Fields 1857.3 Electric Field E 1857.4 Magnetic Flux Density 1877.5 Vector Cross Product 1887.6 Electrostatics and Gauss’s Law 1937.7 Vector Dot Product and Divergence 1947.8 Static Potential Function and the Gradient 1967.9 Divergence of the B Field 2007.10 Ampere’s Law 2017.11 Vector Curl 2027.12 Faraday’s Law of Induction 2087.13 Maxwell’s Equations 209Maxwell’s Four Equations 209Auxiliary Relations and Definitions 210Visualizing Maxwell’s Equations 2117.14 Primary Vector Operations 2147.15 The Laplacian 2157.16 Vector and Scalar Identities 2187.17 Free Charge within a Conductor 2197.18 Skin Effect 2217.19 Conductor Internal Impedance 2247.20 The Wave Equation 2277.21 The Helmholtz Equations 2297.22 Plane Propagating Waves 2307.23 Poynting’s Theorem 2337.24 Wave Polarization 2367.25 EH Fields on Transmission Lines 2407.26 Waveguides 246General Waveguide Solution 246Waveguide Types 250Rectangular Waveguide Fields 251Applying Boundary Conditions 252Propagation Constants and Waveguide Modes 253Characteristic Wave Impedance for Waveguides 256Phase and Group Velocities 257TE and TM Mode Summary for Rectangular Waveguide 2577.27 Fourier Series and Green’s Functions 261Fourier Series 261Green’s Functions 2637.28 Higher Order Modes in Circuits 2697.29 Vector Potential 2717.30 Retarded Potentials 2747.31 Potential Functions in the Sinusoidal Case 2757.32 Antennas 275Short Straight Wire Antenna 275Radiation Resistance 279Radiation Pattern 280Half-Wavelength Dipole 280Antenna Gain 283Antenna Effective Area 284Monopole Antenna 285Aperture Antennas 286Phased Arrays 2887.33 Path Loss 2907.34 Electromagnetic (EM) Simulation 2948 Directional Couplers 3078.1 Wavelength Comparable Dimensions 3078.2 The Backward Wave Coupler 3078.3 Even- and Odd-Mode Analysis 3098.4 Reflectively Terminated 3-dB Coupler 3208.5 Coupler Specifications 3238.6 Measurements Using Directional Couplers 3258.7 Network Analyzer Impedance Measurements 3268.8 Two-Port Scattering Measurements 3278.9 Branch Line Coupler 3278.10 Hybrid Ring Coupler 3308.11 Wilkinson Power Divider 3309 Filter Design 3359.1 Voltage Transfer Function 3359.2 Low-Pass Prototype 3369.3 Butterworth or Maximally Flat Filter 3379.4 Denormalizing the Prototype Response 3399.5 High-Pass Filters 3439.6 Bandpass Filters 3459.7 Bandstop Filters 3499.8 Chebyshev Filters 3519.9 Phase and Group Delay 3569.10 Filter Q 3619.11 Diplexer Filters 3649.12 Top-Coupled Bandpass Filters 3679.13 Elliptic Filters 3699.14 Distributed Filters 3709.15 The Richards Transformation 3749.16 Kuroda’s Identities 3799.17 Mumford’s Maximally Flat Stub Filters 3819.18 Filter Design with the Optimizer 3849.19 Statistical Design and Yield Analysis 386Using Standard Part Values 386The Normal Distribution 387Other Distributions 39110 Transistor Amplifier Design 39910.1 Unilateral Design 399Evaluating S Parameters 399Transistor Biasing 400Evaluating RF Performance 40310.2 Amplifier Stability 40510.3 K Factor 40910.4 Transducer Gain 41310.5 Unilateral Gain Design 41610.6 Unilateral Gain Circles 422Input Gain Circles 422Output Gain Circles 42410.7 Simultaneous Conjugate Match Design 42810.8 Various Gain Definitions 43110.9 Operating Gain Design 43310.10 Available Gain Design 43710.11 Noise in Systems 442Thermal Noise Limit 442Other Noise Sources 444Noise Figure of a Two-Port Network 445Noise Factor of a Cascade 447Noise Temperature 44810.12 Low-Noise Amplifiers 45010.13 Amplifier Nonlinearity 455Gain Saturation 455Intermodulation Distortion 45610.14 Broadbanding with Feedback 46010.15 Cascading Amplifier Stages 46610.16 Amplifier Design Summary 468AppendicesA. Symbols and Units 474B. Complex Mathematics 478C. Diameter and Resistance of Annealed Copper Wire by Gauge Size 483D. Properties of Some Materials 485E. Standard Rectangular Waveguides 486Frequently Used Relations 487Index 491

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