Table of Contents
1 Review of Electromagnetic Theory 1
1.1 Introduction to Microwave Engineering 1
Applications of Microwave Engineering 2
A Short History of Microwave Engineering 6
Electromagnetic Compatibility and Electromagnetic Interference 6
1.2 Maxwell’s Equations 7
1.3 Fields in Media and Boundary Conditions 11
Fields at a General Material Interface 13
Fields at a Dielectric Interface 14
Fields at the Interface with a Perfect Conductor (Electric Wall) 14
The Magnetic Wall 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 18
1.5 General Plane Wave Solutions 20
Circularly Polarized Plane Waves 23
1.6 Energy and Power 24
Power Absorbed by a Good Conductor 25
1.7 Plane Wave Reflection from a Media Interface 27
General Medium 27
Lossless Medium 28
Good Conductor 30
Perfect Conductor 31
The Surface Impedance Concept 31
1.8 Oblique Incidence at a Dielectric Interface 33
Parallel Polarization 34
Perpendicular Polarization 35
Total Reflection and Surface Waves 37
1.9 Some Useful Theorems 38
The Reciprocity Theorem 38
Image Theory 39
2 Transmission Line Theory 47
2.1 The Lumped-Element Circuit Model for a Transmission Line 47
Wave Propagation on a Transmission Line 48
The Lossless Line 49
2.2 Field Analysis of Transmission Lines 50
Transmission Line Parameters 50
The Telegrapher Equations Derived from Field Analysis of a Coaxial Line 52
Propagation Constant, Impedance, and Power Flow for the Lossless Coaxial Line 53
2.3 The Terminated Lossless Transmission Line 54
Special Cases of Lossless Terminated Lines 57
2.4 The Smith Chart 60
The Combined Impedance-Admittance Smith Chart 63
The Slotted Line 65
Online Smith Chart 68
2.5 Generator and Load Mismatches 68
Load Matched to Line 70
Generator Matched to Loaded Line 70
Conjugate Matching 70
2.6 Lossy Transmission Lines 72
The Low-Loss Line 72
The Distortionless Line 73
The Terminated Lossy Line 74
The Perturbation Method for Calculating Attenuation 74
The Wheeler Incremental Inductance Rule 76
2.7 Transients on Transmission Lines 78
Reflection of Pulses from a Terminated Transmission Line 78
Bounce Diagrams for Transient Propagation 80
3 Transmission Lines and Waveguides 87
3.1 General Solutions for TEM, TE, and TM Waves 88
TEM Waves 89
Impossibility of TEM Mode 91
TE Waves 91
TM Waves 92
Attenuation Due to Dielectric Loss 92
3.2 Parallel Plate Waveguide 93
TEM Modes 93
TM Modes 95
TE Modes 98
3.3 Rectangular Waveguide 101
TE Modes 101
TM Modes 105
TEm0 Modes of a Partially Loaded Waveguide 109
3.4 Circular Waveguide 112
TE Modes 113
TM Modes 116
3.5 Coaxial Line 121
TEM Modes 121
Higher Order Modes 122
3.6 Surface Waves on a Grounded Dielectric Sheet 125
TM Modes 125
TE Modes 127
3.7 Stripline 130
Formulas for Propagation Constant, Characteristic Impedance, and Attenuation 132
An Approximate Electrostatic Solution 134
3.8 Microstrip Line 136
Formulas for Effective Dielectric Constant, Characteristic Impedance, and Attenuation 137
Frequency-Dependent Effects and Higher Order Modes 139
3.9 The Transverse Resonance Technique 141
TE0n Modes of a Partially Loaded Rectangular Waveguide 142
3.10 Wave Velocities and Dispersion 143
Group Velocity 143
3.11 Summary of Transmission Lines and Waveguides 145
Other Types of Lines and Guides 146
4 Microwave Network Analysis 153
4.1 Impedance and Equivalent Voltages and Currents 154
Equivalent Voltages and Currents 154
The Concept of Impedance 157
Even and Odd Properties of Z(𝜔) and Γ(𝜔) 159
4.2 Impedance and Admittance Matrices 160
Reciprocal Networks 162
Lossless Networks 163
4.3 The Scattering Matrix 164
Reciprocal Networks and Lossless Networks 167
A Shift in Reference Planes 169
Power Waves and Generalized Scattering Parameters 171
4.4 The Transmission (ABCD) Matrix 174
Relation to Impedance Matrix 175
Equivalent Circuits for Two-Port Networks 177
4.5 Signal Flow Graphs 177
Decomposition of Signal Flow Graphs 180
Application to Thru-Reflect-Line Network Analyzer Calibration 183
4.6 Discontinuities and Modal Analysis 187
Modal Analysis of an H-Plane Step in Rectangular Waveguide 187
4.7 Excitation of Waveguides - Electric and Magnetic Currents 193
Current Sheets That Excite Only One Waveguide Mode 193
Mode Excitation from an Arbitrary Electric or Magnetic Current Source 195
5 Impedance Matching and Tuning 204
5.1 Matching with Lumped Elements (L Networks) 205
Analytical Solutions 205
Smith Chart Solutions 206
5.2 Single-Stub Tuning 209
Shunt Stubs 210
Series Stubs 213
5.3 Double-Stub Tuning 216
Smith Chart Solution 216
Analytical Solution 219
5.4 The Quarter-Wave Transformer 220
The Impedance Viewpoint 220
The Multiple-Reflection Viewpoint 222
Impedance Matching of the
Quarter-Wave Transformer 223
5.5 The Theory of Small Reflections 226
Single-Section Transformer 226
Multisection Transformer 228
5.6 Binomial Multisection Matching Transformers 228
5.7 Chebyshev Multisection Matching Transformers 232
Chebyshev Polynomials 232
Design of Chebyshev Transformers 233
5.8 Tapered Lines 236
Exponential Taper 237
Triangular Taper 238
Klopfenstein Taper 238
6 Microwave Resonators 244
6.1 Series and Parallel Resonant Circuits 244
Series Resonant Circuit 244
Parallel Resonant Circuit 247
Loaded and Unloaded Q 249
6.2 Transmission Line Resonators 249
Short-Circuited 𝜆∕2 Line 250
Short-Circuited 𝜆∕4 Line 252
Open-Circuited 𝜆∕2 Line 252
6.3 Rectangular Waveguide Cavity Resonators 254
Resonant Frequencies 254
Unloaded Q of the TE10𝓁 Mode 256
6.4 Circular Waveguide Cavity Resonators 258
Resonant Frequencies 258
Unloaded Q of the TEnm𝓁 Mode 260
6.5 Dielectric Resonators 263
Resonant Frequencies of TE01𝛿 Mode 263
6.6 Excitation of Resonators 266
The Coupling Coefficient and Critical Coupling 266
A Gap-Coupled Microstrip Resonator 268
7 Power Dividers and Directional Couplers 275
7.1 Basic Properties of Dividers and Couplers 275
Three-Port Networks (T-Junctions) 275
Four-Port Networks (Directional Couplers) 278
7.2 The T-Junction Power Divider 282
Lossless Divider 282
Resistive Divider 284
7.3 The Wilkinson Power Divider 285
Even-Odd Mode Analysis 285
Unequal Power Division and N-Way Wilkinson Dividers 288
7.4 Waveguide Directional Couplers 290
Bethe Hole Coupler 290
Design of Multihole Couplers 294
7.5 The Quadrature (90◦) Hybrid 298
Even-Odd Mode Analysis 299
7.6 Coupled Line Directional Couplers 302
Coupled Line Theory 302
Design of Coupled Line Couplers 306
Design of Multisection Coupled Line Couplers 310
7.7 The Lange Coupler 313
7.8 The 180◦ Hybrid 316
Even-Odd Mode Analysis of the Ring Hybrid 318
Even-Odd Mode Analysis of the Tapered Coupled Line Hybrid 321
Waveguide Magic-T 324
7.9 Other Couplers 325
8 Microwave Filters 333
8.1 Periodic Structures 334
Analysis of Infinite Periodic Structures 334
Terminated Periodic Structures 336
k-𝛽 Diagrams and Wave Velocities 337
8.2 Filter Design by the Image Parameter Method 340
Image Impedances and Transfer Functions for Two-Port Networks 340
Constant-k Filter Sections 342
m-Derived Filter Sections 344
Composite Filters 347
8.3 Filter Design by the Insertion Loss Method 349
Characterization by Power Loss Ratio 350
Maximally Flat Low-Pass Filter Prototype 352
Equal-Ripple Low-Pass Filter Prototype 355
Linear Phase Low-Pass Filter Prototypes 355
8.4 Filter Transformations 355
Impedance and Frequency Scaling 356
Bandpass and Bandstop Transformations 361
8.5 Filter Implementation 364
Richards’ Transformation 364
Kuroda’s Identities 364
Impedance and Admittance Inverters 369
8.6 Stepped-Impedance Low-Pass Filters 370
Approximate Equivalent Circuits for Short Transmission Line Sections 370
Comparison of Richards’ Transformation and Stepped-Impedance Method 373
8.7 Coupled Line Filters 373
Filter Properties of a Coupled Line Section 374
Design of Coupled Line Bandpass Filters 377
9 Theory and Design of Ferrimagnetic Components 387
9.1 Basic Properties of Ferrimagnetic Materials 388
The Permeability Tensor 388
Circularly Polarized Fields 392
Effect of Loss 394
Demagnetization Factors 396
9.2 Plane Wave Propagation in a Ferrite Medium 399
Propagation in Direction of Bias (Faraday Rotation) 399
Propagation Transverse to Bias (Birefringence) 402
9.3 Propagation in a Ferrite-Loaded Rectangular Waveguide 404
TEm0 Modes of Waveguide with a Single Ferrite Slab 404
TEm0 Modes of Waveguide with Two Symmetric Ferrite Slabs 407
9.4 Ferrite Isolators 408
Resonance Isolators 409
The Field Displacement Isolator 411
9.5 Ferrite Phase Shifters 413
Nonreciprocal Latching Phase Shifter 414
Other Types of Ferrite Phase Shifters 416
The Gyrator 417
9.6 Ferrite Circulators 418
Properties of a Mismatched Circulator 418
Junction Circulator 419
10 Noise and Nonlinear Distortion 427
10.1 Noise in Microwave Circuits 427
Dynamic Range and Sources of Noise 427
Noise Power and Equivalent Noise Temperature 429
Measurement of Noise Temperature 431
10.2 Noise Figure 432
Definition of Noise Figure 432
Noise Figure of a Cascaded System 434
Noise Figure of a Passive Two-Port Network 436
Noise Figure of a Mismatched Lossy Line 437
Noise Figure of a Mismatched Amplifier 439
10.3 Nonlinear Distortion 440
Gain Compression 441
Harmonic and Intermodulation Distortion 442
Third-Order Intercept Point 443
Intercept Point of a Cascaded System 444
Passive Intermodulation 446
10.4 Dynamic Range 447
Linear and Spurious Free Dynamic Range 447
11 Active RF and Microwave Devices 453
11.1 Diodes and Diode Circuits 453
Schottky Diodes and Detectors 454
PIN Diodes and Control Circuits 458
Varactor Diodes 464
Ridley-Watkins-Hilsum (RWH) Theory 465
Two-Valley Model Theory 465
Other Diodes 467
Power Combining 468
11.2 Bipolar Junction Transistors 469
Bipolar Junction Transistor 469
Heterojunction Bipolar Transistor 470
11.3 Field Effect Transistors 471
Metal Semiconductor Field Effect Transistor 472
Metal Oxide Semiconductor Field Effect Transistor 473
High Electron Mobility Transistor 474
11.4 Microwave Integrated Circuits 475
Hybrid Microwave Integrated Circuits 475
Monolithic Microwave Integrated Circuits 476
11.5 Microwave Tubes 479
Klystron 480
Traveling Wave Tube 482
Backward Wave Oscillator 482
Extended Interaction Oscillator 483
Magnetrons 483
Cross-Field Amplifier 483
Gyratron 483
12 Microwave Amplifier Design 487
12.1 Two-Port Power Gains 487
Definitions of Two-Port Power Gains 487
Further Discussion of Two-Port Power Gains 491
12.2 Stability 492
Stability Circles 493
Tests for Unconditional Stability 495
12.3 Single-Stage Transistor Amplifier Design 498
Design for Maximum Gain (Conjugate Matching) 498
Constant-Gain Circles and Design for Specified Gain 503
Low-Noise Amplifier Design 506
Low-Noise MOSFET Amplifier 510
12.4 Broadband Transistor Amplifier Design 511
Balanced Amplifiers 512
Distributed Amplifiers 514
Differential Amplifiers 518
12.5 Power Amplifiers 521
Characteristics of Power Amplifiers and Amplifier Classes 521
Large-Signal Characterization of Transistors 522
Design of Class A Power Amplifiers 523
13 Oscillators and Mixers 529
13.1 RF Oscillators 530
General Analysis 530
Oscillators Using a Common Emitter BJT 531
Oscillators Using a Common Gate FET 533
Practical Considerations 534
Crystal Oscillators 535
13.2 Microwave Oscillators 536
Transistor Oscillators 538
Dielectric Resonator Oscillators 541
13.3 Oscillator Phase Noise 544
Representation of Phase Noise 544
Leeson’s Model for Oscillator Phase Noise 545
13.4 Frequency Multipliers 549
Reactive Diode Multipliers (Manley-Rowe Relations) 549
Resistive Diode Multipliers 552
Transistor Multipliers 553
13.5 Mixers 557
Mixer Characteristics 557
Single-Ended Diode Mixer 561
Single-Ended FET Mixer 562
Balanced Mixer 564
Image Reject Mixer 567
Differential FET Mixer and Gilbert Cell Mixer 568
Other Mixers 570
14 Introduction To Microwave Systems 576
14.1 System Aspects of Antennas 576
Fields and Power Radiated by an Antenna 579
Antenna Pattern Characteristics 580
Antenna Gain and Efficiency 582
Aperture Efficiency and Effective Area 583
Background and Brightness Temperature 583
Antenna Noise Temperature and G/T 586
14.2 Wireless Communication 588
The Friis Formula 589
Link Budget and Link Margin 590
Radio Receiver Architectures 592
Noise Characterization of a Receiver 594
Digital Modulation and Bit Error Rate 597
Wireless Communication Systems 599
14.3 Radar Systems 603
The Radar Equation 604
Pulse Radar 606
Doppler Radar 607
Radar Cross Section 608
14.4 Radiometer Systems 609
Theory and Applications of Radiometry 609
Total Power Radiometer 611
The Dicke Radiometer 612
14.5 Microwave Propagation 613
Atmospheric Effects 614
Ground Effects 615
Plasma Effects 616
14.6 Other Applications and Topics 616
Microwave Heating 616
Power Transfer 617
Biological Effects and Safety 618
Appendices 624
A Prefixes 625
B Vector Analysis 625
C Bessel Functions 627
D Useful Results 629
E Other Mathematical Results 631
F Physical Constants 631
G Conductivities for Some Materials 632
H Dielectric Constants and Loss Tangents for Some Materials 632
I Properties of Some Microwave Ferrite Materials 633
J Standard Rectangular Waveguide Data 633
K Standard Coaxial Cable Data 634
Answers to selected Problems 635
Index 637
