High Frequency Techniques

Preface xv Acknowledgments xvii 1 Introduction 1 1.1 Beginning of Wireless 1 1.2 Current Radio Spectrum 4 1.3 Conventions Used in This Text 8 Sections 8 Equations 8 Figures 8 Exercises 8 Symbols 8 Prefixes 10 Fonts 10 1.4 Vectors and Coordinates 11 1.5 General Constants and Useful Conversions 14 2 Review of AC Analysis and Network Simulation 16 2.1 Basic Circuit Elements 16 The Resistor 16 Ohm's Law 18 The Inductor 19 The Capacitor 20 2.2 Kirchhoff's Laws 22 2.3 Alternating Current (AC) Analysis 23 Ohm's Law in Complex Form 26 2.4 Voltage and Current Phasors 26 2.5 Impedance 28 Estimating Reactance 28 Addition of Series Impedances 29 2.6 Admittance 30 Admittance Definition 30 Addition of Parallel Admittances 30 The Product over the Sum 32 2.7 LLFPB Networks 33 2.8 Decibels, dBW, and dBm 33 Logarithms (Logs) 33 Multiplying by Adding Logs 34 Dividing by Subtracting Logs 34 Zero Powers 34 Bel Scale 34 Decibel Scale 35 Decibels--Relative Measures 35 Absolute Power Levels--dBm and dBW 37 Decibel Power Scales 38 2.9 Power Transfer 38 Calculating Power Transfer 38 Maximum Power Transfer 39 2.10 Specifying Loss 40 Insertion Loss 40 Transducer Loss 41 Loss Due to a Series Impedance 42 Loss Due to a Shunt Admittance 43 Loss in Terms of Scattering Parameters 44 2.11 Real RLC Models 44 Resistor with Parasitics 44 Inductor with Parasitics 44 Capacitor with Parasitics 44 2.12 Designing LC Elements 46 Lumped Coils 46 High mu Inductor Cores--the Hysteresis Curve 47 Estimating Wire Inductance 48 Parallel Plate Capacitors 49 2.13 Skin Effect 51 2.14 Network Simulation 53 3 LC Resonance and Matching Networks 59 3.1 LC Resonance 59 3.2 Series Circuit Quality Factors 60 Q of Inductors and Capacitors 60 QE, External Q 61 QL, Loaded Q 62 3.3 Parallel Circuit Quality Factors 62 3.4 Coupled Resonators 63 Direct Coupled Resonators 63 Lightly Coupled Resonators 63 3.5 Q Matching 67 Low to High Resistance 67 Broadbanding the Q Matching Method 70 High to Low Resistance 71 4 Distributed Circuits 78 4.1 Transmission Lines 78 4.2 Wavelength in a Dielectric 81 4.3 Pulses on Transmission Lines 82 4.4 Incident and Reflected Waves 83 4.5 Reflection Coefficient 85 4.6 Return Loss 86 4.7 Mismatch Loss 86 4.8 Mismatch Error 87 4.9 The Telegrapher Equations 91 4.10 Transmission Line Wave Equations 92 4.11 Wave Propagation 94 4.12 Phase and Group Velocities 97 4.13 Reflection Coefficient and Impedance 100 4.14 Impedance Transformation Equation 101 4.15 Impedance Matching with One Transmission Line 108 4.16 Fano's (and Bode's) Limit 109 Type A Mismatched Loads 109 Type B Mismatched Loads 112 Impedance Transformation Not Included 113 5 The Smith Chart 119 5.1 Basis of the Smith Chart 119 5.2 Drawing the Smith Chart 124 5.3 Admittance on the Smith Chart 130 5.4 Tuning a Mismatched Load 132 5.5 Slotted-Line Impedance Measurement 135 5.6 VSWR = r 139 5.7 Negative Resistance Smith Chart 140 5.8 Navigating the Smith Chart 140 5.9 Smith Chart Software 145 5.10 Estimating Bandwidth on the Smith Chart 147 5.11 Approximate Tuning May Be Better 148 5.12 Frequency Contours on the Smith Chart 150 5.13 Using the Smith Chart without Transmission Lines 150 5.14 Constant Q Circles 151 5.15 Transmission Line Lumped Circuit Equivalent 153 6 Matrix Analysis 161 6.1 Matrix Algebra 161 6.2 Z and Y Matrices 164 6.3 Reciprocity 166 6.4 The ABCD Matrix 167 6.5 The Scattering Matrix 172 6.6 The Transmission Matrix 177 7 Electromagnetic Fields and Waves 183 7.1 Vector Force Fields 183 7.2 E and H Fields 185 7.3 Electric Field E 185 7.4 Magnetic Flux Density 187 7.5 Vector Cross Product 188 7.6 Electrostatics and Gauss's Law 193 7.7 Vector Dot Product and Divergence 194 7.8 Static Potential Function and the Gradient 196 7.9 Divergence of the B Field 200 7.10 Ampere's Law 201 7.11 Vector Curl 202 7.12 Faraday's Law of Induction 208 7.13 Maxwell's Equations 209 Maxwell's Four Equations 209 Auxiliary Relations and Definitions 210 Visualizing Maxwell's Equations 211 7.14 Primary Vector Operations 214 7.15 The Laplacian 215 7.16 Vector and Scalar Identities 218 7.17 Free Charge within a Conductor 219 7.18 Skin Effect 221 7.19 Conductor Internal Impedance 224 7.20 The Wave Equation 227 7.21 The Helmholtz Equations 229 7.22 Plane Propagating Waves 230 7.23 Poynting's Theorem 233 7.24 Wave Polarization 236 7.25 EH Fields on Transmission Lines 240 7.26 Waveguides 246 General Waveguide Solution 246 Waveguide Types 250 Rectangular Waveguide Fields 251 Applying Boundary Conditions 252 Propagation Constants and Waveguide Modes 253 Characteristic Wave Impedance for Waveguides 256 Phase and Group Velocities 257 TE and TM Mode Summary for Rectangular Waveguide 257 7.27 Fourier Series and Green's Functions 261 Fourier Series 261 Green's Functions 263 7.28 Higher Order Modes in Circuits 269 7.29 Vector Potential 271 7.30 Retarded Potentials 274 7.31 Potential Functions in the Sinusoidal Case 275 7.32 Antennas 275 Short Straight Wire Antenna 275 Radiation Resistance 279 Radiation Pattern 280 Half-Wavelength Dipole 280 Antenna Gain 283 Antenna Effective Area 284 Monopole Antenna 285 Aperture Antennas 286 Phased Arrays 288 7.33 Path Loss 290 7.34 Electromagnetic (EM) Simulation 294 8 Directional Couplers 307 8.1 Wavelength Comparable Dimensions 307 8.2 The Backward Wave Coupler 307 8.3 Even- and Odd-Mode Analysis 309 8.4 Reflectively Terminated 3-dB Coupler 320 8.5 Coupler Specifications 323 8.6 Measurements Using Directional Couplers 325 8.7 Network Analyzer Impedance Measurements 326 8.8 Two-Port Scattering Measurements 327 8.9 Branch Line Coupler 327 8.10 Hybrid Ring Coupler 330 8.11 Wilkinson Power Divider 330 9 Filter Design 335 9.1 Voltage Transfer Function 335 9.2 Low-Pass Prototype 336 9.3 Butterworth or Maximally Flat Filter 337 9.4 Denormalizing the Prototype Response 339 9.5 High-Pass Filters 343 9.6 Bandpass Filters 345 9.7 Bandstop Filters 349 9.8 Chebyshev Filters 351 9.9 Phase and Group Delay 356 9.10 Filter Q 361 9.11 Diplexer Filters 364 9.12 Top-Coupled Bandpass Filters 367 9.13 Elliptic Filters 369 9.14 Distributed Filters 370 9.15 The Richards Transformation 374 9.16 Kuroda's Identities 379 9.17 Mumford's Maximally Flat Stub Filters 381 9.18 Filter Design with the Optimizer 384 9.19 Statistical Design and Yield Analysis 386 Using Standard Part Values 386 The Normal Distribution 387 Other Distributions 391 10 Transistor Amplifier Design 399 10.1 Unilateral Design 399 Evaluating S Parameters 399 Transistor Biasing 400 Evaluating RF Performance 403 10.2 Amplifier Stability 405 10.3 K Factor 409 10.4 Transducer Gain 413 10.5 Unilateral Gain Design 416 10.6 Unilateral Gain Circles 422 Input Gain Circles 422 Output Gain Circles 424 10.7 Simultaneous Conjugate Match Design 428 10.8 Various Gain Definitions 431 10.9 Operating Gain Design 433 10.10 Available Gain Design 437 10.11 Noise in Systems 442 Thermal Noise Limit 442 Other Noise Sources 444 Noise Figure of a Two-Port Network 445 Noise Factor of a Cascade 447 Noise Temperature 448 10.12 Low-Noise Amplifiers 450 10.13 Amplifier Nonlinearity 455 Gain Saturation 455 Intermodulation Distortion 456 10.14 Broadbanding with Feedback 460 10.15 Cascading Amplifier Stages 466 10.16 Amplifier Design Summary 468 Appendices A. Symbols and Units 474 B. Complex Mathematics 478 C. Diameter and Resistance of Annealed Copper Wire by Gauge Size 483 D. Properties of Some Materials 485 E. Standard Rectangular Waveguides 486 Frequently Used Relations 487 Index 491