1 ELECTROMAGNETIC THEORY 1
1.1 Introduction to Microwave Engineering 1
Applications of Microwave Engineering 2
A Short History of Microwave Engineering 4
1.2 Maxwell’s Equations 6
1.3 Fields in Media and Boundary Conditions 10
Fields at a General Material Interface 12 Fields at a Dielectric Interface 14
Fields at the Interface with a Perfect Conductor (Electric Wall) 14
The MagneticWall Boundary Condition 15 The Radiation Condition 15
1.4 The Wave Equation and Basic Plane Wave Solutions 15
The Helmholtz Equation 15 Plane Waves in a Lossless Medium 16
Plane Waves in a General Lossy Medium 17
Plane Waves in a Good Conductor 19
1.5 General Plane Wave Solutions 20
Circularly Polarized Plane Waves 24
1.6 Energy and Power 25
Power Absorbed by a Good Conductor 27
1.7 Plane Wave Reflection from a Media Interface 28
General Medium 28 Lossless Medium 30
Good Conductor 31 Perfect Conductor 32
The Surface Impedance Concept 33
1.8 Oblique Incidence at a Dielectric Interface 35
Parallel Polarization 36 Perpendicular Polarization 37
Total Reflection and Surface Waves 38
1.9 Some Useful Theorems 40
The Reciprocity Theorem 40 Image Theory 42
ix
x Contents
2 TRANSMISSION LINE THEORY 48
2.1 The Lumped-Element Circuit Model for a Transmission Line 48
Wave Propagation on a Transmission Line 50 The Lossless Line 51
2.2 Field Analysis of Transmission Lines 51
Transmission Line Parameters 51
The Telegrapher Equations Derived from Field Analysis of a Coaxial Line 54
Propagation Constant, Impedance, and Power Flow for the Lossless
Coaxial Line 56
2.3 The Terminated Lossless Transmission Line 56
Special Cases of Lossless Terminated Lines 59
2.4 The Smith Chart 63
The Combined Impedance–Admittance Smith Chart 67
The Slotted Line 68
2.5 The Quarter-Wave Transformer 72
The Impedance Viewpoint 72 The Multiple-Reflection Viewpoint 74
2.6 Generator and Load Mismatches 76
Load Matched to Line 77 Generator Matched to Loaded Line 77
Conjugate Matching 77
2.7 Lossy Transmission Lines 78
The Low-Loss Line 79 The Distortionless Line 80
The Terminated Lossy Line 81
The Perturbation Method for Calculating Attenuation 82
The Wheeler Incremental Inductance Rule 83
2.8 Transients on Transmission Lines 85
Reflection of Pulses from a Terminated Transmission Line 86
Bounce Diagrams for Transient Propagation 87
3 TRANSMISSION LINES AND WAVEGUIDES 95
3.1 General Solutions for TEM, TE, and TM Waves 96
TEM Waves 98 TE Waves 100
TM Waves 100 Attenuation Due to Dielectric Loss 101
3.2 Parallel PlateWaveguide 102
TEM Modes 103 TM Modes 104 TE Modes 107
3.3 Rectangular Waveguide 110
TE Modes 110 TM Modes 115
TEm0 Modes of a Partially Loaded Waveguide 119
3.4 Circular Waveguide 121
TE Modes 122 TM Modes 125
3.5 Coaxial Line 130
TEM Modes 130 Higher Order Modes 131
Contents xi
3.6 Surface Waves on a Grounded Dielectric Sheet 135
TM Modes 135 TE Modes 137
3.7 Stripline 141
Formulas for Propagation Constant, Characteristic Impedance,
and Attenuation 141 An Approximate Electrostatic Solution 144
3.8 Microstrip Line 147
Formulas for Effective Dielectric Constant, Characteristic Impedance,
and Attenuation 148
Frequency-Dependent Effects and Higher Order Modes 150
3.9 The Transverse Resonance Technique 153
TE0n Modes of a Partially Loaded Rectangular Waveguide 153
3.10 Wave Velocities and Dispersion 154
Group Velocity 155
3.11 Summary of Transmission Lines and Waveguides 157
Other Types of Lines and Guides 158
4 MICROWAVE NETWORK ANALYSIS 165
4.1 Impedance and Equivalent Voltages and Currents 166
Equivalent Voltages and Currents 166 The Concept of Impedance 170
Even and Odd Properties of Z(ω) and (ω) 173
4.2 Impedance and Admittance Matrices 174
Reciprocal Networks 175 Lossless Networks 177
4.3 The Scattering Matrix 178
Reciprocal Networks and Lossless Networks 181
A Shift in Reference Planes 184
Power Waves and Generalized Scattering Parameters 185
4.4 The Transmission (ABCD) Matrix 188
Relation to Impedance Matrix 191
Equivalent Circuits for Two-Port Networks 191
4.5 Signal Flow Graphs 194
Decomposition of Signal Flow Graphs 195
Application to Thru-Reflect-Line Network Analyzer Calibration 197
4.6 Discontinuities and Modal Analysis 203
Modal Analysis of an H-Plane Step in Rectangular Waveguide 203
4.7 Excitation of Waveguides—Electric and Magnetic Currents 210
Current Sheets That Excite Only One Waveguide Mode 210
Mode Excitation from an Arbitrary Electric or Magnetic Current Source 212
4.8 Excitation of Waveguides—Aperture Coupling 215
Coupling Through an Aperture in a Transverse Waveguide Wall 218
Coupling Through an Aperture in the Broad Wall of a Waveguide 220
xii Contents
5 IMPEDANCE MATCHING AND TUNING 228
5.1 Matching with Lumped Elements (L Networks) 229
Analytic Solutions 230 Smith Chart Solutions 231
5.2 Single-Stub Tuning 234
Shunt Stubs 235 Series Stubs 238
5.3 Double-Stub Tuning 241
Smith Chart Solution 242 Analytic Solution 245
5.4 The Quarter-Wave Transformer 246
5.5 The Theory of Small Reflections 250
Single-Section Transformer 250 Multisection Transformer 251
5.6 Binomial Multisection Matching Transformers 252
5.7 Chebyshev Multisection Matching Transformers 256
Chebyshev Polynomials 257 Design of Chebyshev Transformers 258
5.8 Tapered Lines 261
Exponential Taper 262 Triangular Taper 263
Klopfenstein Taper 264
5.9 The Bode–Fano Criterion 266
6 MICROWAVE RESONATORS 272
6.1 Series and Parallel Resonant Circuits 272
Series Resonant Circuit 272 Parallel Resonant Circuit 275
Loaded and Unloaded Q 277
6.2 Transmission Line Resonators 278
Short-Circuited λ/2 Line 278 Short-Circuited λ/4 Line 281
Open-Circuited λ/2 Line 282
6.3 Rectangular Waveguide Cavity Resonators 284
Resonant Frequencies 284 Unloaded Q of the TE10 Mode 286
6.4 Circular Waveguide Cavity Resonators 288
Resonant Frequencies 289 Unloaded Q of the TEnm Mode 291
6.5 Dielectric Resonators 293
Resonant Frequencies of TE01δ Mode 294
6.6 Excitation of Resonators 297
The Coupling Coefficient and Critical Coupling 298
A Gap-Coupled Microstrip Resonator 299
An Aperture-Coupled Cavity 302
Determining Unloaded Q from Two-Port Measurements 305
6.7 Cavity Perturbations 306
Material Perturbations 306 Shape Perturbations 309
Contents xiii
7 POWER DIVIDERS AND DIRECTIONAL COUPLERS 317
7.1 Basic Properties of Dividers and Couplers 317
Three-Port Networks (T-Junctions) 318
Four-Port Networks (Directional Couplers) 320
7.2 The T-Junction Power Divider 324
Lossless Divider 324 Resistive Divider 326
7.3 The Wilkinson Power Divider 328
Even-Odd Mode Analysis 328
Unequal Power Division and N-Way Wilkinson Dividers 332
7.4 Waveguide Directional Couplers 333
Bethe Hole Coupler 334 Design of Multihole Couplers 338
7.5 The Quadrature (90◦) Hybrid 343
Even-Odd Mode Analysis 344
7.6 Coupled Line Directional Couplers 347
Coupled Line Theory 347 Design of Coupled Line Couplers 351
Design of Multisection Coupled Line Couplers 356
7.7 The Lange Coupler 359
7.8 The 180◦ Hybrid 362
Even-Odd Mode Analysis of the Ring Hybrid 364
Even-Odd Mode Analysis of the Tapered Coupled Line Hybrid 367
Waveguide Magic-T 371
7.9 Other Couplers 372
8 MICROWAVE FILTERS 380
8.1 Periodic Structures 381
Analysis of Infinite Periodic Structures 382
Terminated Periodic Structures 384
k-β Diagrams and Wave Velocities 385
8.2 Filter Design by the Image Parameter Method 388
Image Impedances and Transfer Functions for Two-Port Networks 388
Constant-k Filter Sections 390 m-Derived Filter Sections 393
Composite Filters 396
8.3 Filter Design by the Insertion Loss Method 399
Characterization by Power Loss Ratio 399
Maximally Flat Low-Pass Filter Prototype 402
Equal-Ripple Low-Pass Filter Prototype 404
Linear Phase Low-Pass Filter Prototypes 406
8.4 Filter Transformations 408
Impedance and Frequency Scaling 408
Bandpass and Bandstop Transformations 411
xiv Contents
8.5 Filter Implementation 415
Richards’ Transformation 416 Kuroda’s Identities 416
Impedance and Admittance Inverters 421
8.6 Stepped-Impedance Low-Pass Filters 422
Approximate Equivalent Circuits for Short Transmission Line Sections 422
8.7 Coupled Line Filters 426
Filter Properties of a Coupled Line Section 426
Design of Coupled Line Bandpass Filters 430
8.8 Filters Using Coupled Resonators 437
Bandstop and Bandpass Filters Using Quarter-Wave Resonators 437
Bandpass Filters Using Capacitively Coupled Series Resonators 441
Bandpass Filters Using Capacitively Coupled Shunt Resonators 443
9 THEORY AND DESIGN OF FERRIMAGNETIC COMPONENTS 451
9.1 Basic Properties of Ferrimagnetic Materials 452
The Permeability Tensor 452 Circularly Polarized Fields 458
Effect of Loss 460 Demagnetization Factors 462
9.2 Plane Wave Propagation in a Ferrite Medium 465
Propagation in Direction of Bias (Faraday Rotation) 465
Propagation Transverse to Bias (Birefringence) 469
9.3 Propagation in a Ferrite-Loaded Rectangular Waveguide 471
TEm0 Modes of Waveguide with a Single Ferrite Slab 471
TEm0 Modes of Waveguide with Two Symmetrical Ferrite Slabs 474
9.4 Ferrite Isolators 475
Resonance Isolators 476 The Field Displacement Isolator 479
9.5 Ferrite Phase Shifters 482
Nonreciprocal Latching Phase Shifter 482
Other Types of Ferrite Phase Shifters 485 The Gyrator 486
9.6 Ferrite Circulators 487
Properties of a Mismatched Circulator 488 Junction Circulator 488
10 NOISE AND NONLINEAR DISTORTION 496
10.1 Noise in Microwave Circuits 496
Dynamic Range and Sources of Noise 497
Noise Power and Equivalent Noise Temperature 498
Measurement of Noise Temperature 501
10.2 Noise Figure 502
Definition of Noise Figure 502 Noise Figure of a Cascaded System 504
Noise Figure of a Passive Two-Port Network 506
Noise Figure of a Mismatched Lossy Line 508
Noise Figure of a Mismatched Amplifier 510
Contents xv
10.3 Nonlinear Distortion 511
Gain Compression 512 Harmonic and Intermodulation Distortion 513
Third-Order Intercept Point 515 Intercept Point of a Cascaded System 516
Passive Intermodulation 519
10.4 Dynamic Range 519
Linear and Spurious Free Dynamic Range 519
11 ACTIVE RF AND MICROWAVE DEVICES 524
11.1 Diodes and Diode Circuits 525
Schottky Diodes and Detectors 525
PIN Diodes and Control Circuits 530
Varactor Diodes 537 Other Diodes 538 Power Combining 539
11.2 Bipolar Junction Transistors 540
Bipolar Junction Transistor 540 Heterojunction Bipolar Transistor 542
11.3 Field Effect Transistors 543
Metal Semiconductor Field Effect Transistor 544
Metal Oxide Semiconductor Field Effect Transistor 546
High Electron Mobility Transistor 546
11.4 Microwave Integrated Circuits 547
Hybrid Microwave Integrated Circuits 548
Monolithic Microwave Integrated Circuits 548
11.5 Microwave Tubes 552
12 MICROWAVE AMPLIFIER DESIGN 558
12.1 Two-Port Power Gains 558
Definitions of Two-Port Power Gains 559
Further Discussion of Two-Port Power Gains 562
12.2 Stability 564
Stability Circles 564 Tests for Unconditional Stability 567
12.3 Single-Stage Transistor Amplifier Design 571
Design for Maximum Gain (Conjugate Matching) 571
Constant-Gain Circles and Design for Specified Gain 575
Low-Noise Amplifier Design 580 Low-Noise MOSFET Amplifier 582
12.4 Broadband Transistor Amplifier Design 585
Balanced Amplifiers 586 Distributed Amplifiers 588
Differential Amplifiers 593
12.5 Power Amplifiers 596
Characteristics of Power Amplifiers and Amplifier Classes 597
Large-Signal Characterization of Transistors 598
Design of Class A Power Amplifiers 599
xvi Contents
13 OSCILLATORS AND MIXERS 604
13.1 RF Oscillators 605
General Analysis 606 Oscillators Using a Common Emitter BJT 607
Oscillators Using a Common Gate FET 609 Practical Considerations 610
Crystal Oscillators 612
13.2 Microwave Oscillators 613
Transistor Oscillators 615 Dielectric Resonator Oscillators 617
13.3 Oscillator Phase Noise 622
Representation of Phase Noise 623
Leeson’s Model for Oscillator Phase Noise 624
13.4 Frequency Multipliers 627
Reactive Diode Multipliers (Manley–Rowe Relations) 628
Resistive Diode Multipliers 631 Transistor Multipliers 633
13.5 Mixers 637
Mixer Characteristics 637 Single-Ended Diode Mixer 642
Single-Ended FET Mixer 643 Balanced Mixer 646
Image Reject Mixer 649
Differential FET Mixer and Gilbert Cell Mixer 650 Other Mixers 652
14 INTRODUCTION TO MICROWAVE SYSTEMS 658
14.1 System Aspects of Antennas 658
Fields and Power Radiated by an Antenna 660
Antenna Pattern Characteristics 662
Antenna Gain and Efficiency 664
Aperture Efficiency and Effective Area 665
Background and Brightness Temperature 666
Antenna Noise Temperature and G/T 669
14.2 Wireless Communications 671
The Friis Formula 673
Link Budget and Link Margin 674
Radio Receiver Architectures 676
Noise Characterization of a Receiver 679
Digital Modulation and Bit Error Rate 681
Wireless Communication Systems 684
14.3 Radar Systems 690
The Radar Equation 691 Pulse Radar 693 Doppler Radar 694
Radar Cross Section 695
14.4 Radiometer Systems 696
Theory and Applications of Radiometry 697 Total Power Radiometer 699
The Dicke Radiometer 700
14.5 Microwave Propagation 701
Atmospheric Effects 701 Ground Effects 703 Plasma Effects 704
Contents xvii
14.6 Other Applications and Topics 705
Microwave Heating 705 Power Transfer 705
Biological Effects and Safety 706
APPENDICES 712
A Prefixes 713
B Vector Analysis 713
C Bessel Functions 715
D Other Mathematical Results 718
E Physical Constants 718
F Conductivities for Some Materials 719
G Dielectric Constants and Loss Tangents for Some Materials 719
H Properties of Some Microwave Ferrite Materials 720
I Standard Rectangular Waveguide Data 720
J Standard Coaxial Cable Data 721
ANSWERS TO SELECTED PROBLEMS 722
INDEX 725
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