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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
Kirchho¤ ’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
vii
viii CONTENTS
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 Series Impedance 42
Loss Due to 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 m Inductor Cores—the Hysteresis Curve 47
Estimating Wire Inductance 48
Parallel Plate Capacitors 49
2.13
Skin E¤ect 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
CONTENTS ix
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 Circuit Design 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 Coe‰cient 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 Coe‰cient 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 ¼ r 139
5.7
Negative Resistance Smith Chart 140
5.8
Navigating the Smith Chart 140
5.9
Smith Chart Software 141
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
x
CONTENTS
6 Matrix Analysis
6.1
6.2
6.3
6.4
6.5
6.6
Matrix Algebra
Z and Y Matrices
Reciprocity
The ABCD Matrix
The Scattering Matrix
The Transmission Matrix
7 Electromagnetic Fields and Waves
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.23
7.24
7.25
7.26
Vector Force Fields
E and H Fields
Electric Field E
Magnetic Flux Density
Vector Cross Product
Electrostatics and Gauss’s Law
Vector Dot Product and Divergence
Static Potential Function and the Gradient
Divergence of the ~B Field
Ampere’s Law Maxwell’s Four Equations Auxiliary Relations and Definitions Visualizing Maxwell’s Equations General Waveguide Solution Waveguides Types Rectangular Waveguide Field Applying Boundary Conditions
Vector Curl
Faraday’s Law of Induction
Maxwell’s Equations
Primary Vector Operations
The Laplacian
Vector and Scalar Identities
Free Charge within a Conductor
Skin E¤ect
Conductor Internal Impedance
The Wave Equation
The Helmholtz Equations
Plane Propagating Waves
Poynting’s Theorem
Wave Polarization
EH Fields on Transmission Lines
Waveguides
161
161
164
166
167
172
177
183
183
185
185
187
188
193
194
196
200
201
202
208
209
209
210
211
214
215
218
219
221
224
227
229
230
233
236
240
246
246
250
251
252
Propagation Constants and Waveguide Modes 253
7.27
Fourier Series and Green’s Functions 261
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
7.33
Path Loss
290
7.34
Electromagnetic (EM) Simulation
294
CONTENTS xi
Characteristic Wave Impedance for Waveguides 256
Phase and Group Velocities 257
TE and TM Mode Summary for Rectangular Waveguide 257
Fourier Series 261
Green’s Functions 263
Short Straight Wire Antenna
275 279 280 280 283 284 285 286 288
Radiation Resistance
Radiation Pattern
Half-Wavelength Dipole
Antenna Gain
Antenna E¤ective Area
Monopole Antenna
Aperture Antennas
Phased Arrays
307
8 Directional Couplers
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 (Rat Race) Coupler 330
8.11
Wilkinson 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
xii CONTENTS
Bandstop Filters
Chebyshev Filters
Phase and Group Delay
Filter Q
Diplexer Filters
Top-Coupled Bandpass Filters
Elliptic Filters
Distributed Filters
The Richards Transformation
Kuroda’s Identities
Mumford’s Maximally Flat Stub Filters
Filter Design with the Optimizer
Statistical Design and Yield Analysis
Unilateral Design
Amplifier Stability
K Factor
Transducer Gain
Unilateral Gain Design
Unilateral Gain Circles
Simultaneous Conjugate Match Design
Various Gain Definitions
Operating Gain Design
10.10
Available Gain Design
10.11
Noise in Systems
10.12
Low-Noise Amplifiers
Gain Saturation Intermodulation Distortion
9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 9.19 Using Standard Part Values The Normal Distribution Other Distributions 10 Transistor Amplifier Design 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 Evaluating S Parameters Transistor Biasing Evaluating RF Performance Input Gain Circles Output Gain Circles Thermal Noise Limit Other Noise Sources Noise Figure of a Two-Port Network Noise Factor of a Cascade Noise Temperature 10.13 Amplifier Nonlinearity 349
351
356
361
364
367
369
370
374
379
381
384
385
385
386
391
399
399
399
400
403
405
409
413
416
422
422
424
428
430
433
437
442
442
444
445
447
448
450
455
455
456
CONTENTS xiii
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
Index 487 |
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