Preface ...................................................... xiii
Chapter ......................................................... 1
Introduction .................................................... 1
1.1. Systematics of Microwave Integrated Circuits ............ 5
1.2. Circuit Design Methods .................................. 7
1.2.1. Empirical Design ................................. 7
1.2.2. Modern Computer Aided Design ..................... 9
References .................................................. 13
Chapter 2. Overview of Strip Transmission Lines ................ 15
2.1. Microstrip Line ........................................ 19
2.2. Shielded Microstrip Line ............................... 25
2.3. Triplate ............................................... 26
2.4. Suspended Stripline .................................... 26
2.5. Sandwich Line .......................................... 27
2.6. Slot Line .............................................. 28
2.7. Coplanar Line .......................................... 30
2.8. Coupled Microstrip Line ................................ 34
2.9. Antipodal Slot Line 36.
2.10.Finline ................................................ 38
References .................................................. 40
Chapter 3. Methods of Microstrip Analysis ...................... 43
3.1. Conformal Transformation Method After Wheeler .......... 47
3.1.1. Air-Filled Microstrip Line ...................... 48
3.1.2. Mapping of the Microstrip Conductor Boundaries
into a Parallel Plate Structure ................. 50
3.1.3. Dielectric-Filled Microstrip Line ............... 57
3.1.4. Effect of Strip Thickness ....................... 69
3.1.5. Microstrip Inductance per Unit Length ........... 72
3.2. Theory After Schneider ................................. 75
3.2.1. Single-Dielectric Microstrip Line ............... 75
3.2.2. Effective Dielectric Constant ................... 85
3.2.3. Analysis and Synthesis Equations After
Wheeler ......................................... 86
3.3. Impedance Design Formulas After Hammerstad ............. 87
3.4. Full-Wave Analysis ..................................... 91
3.4.1. Modes of Inhomogeneous Parallel Plate
Structure ....................................... 91
3.4.2. Surface Waves on Dielectric Plate ............... 96
3.4.3. Shielded Microstrip Transmission Line
Laterally Open ................................. 107
3.5. Comparison of Discussed Analysis Methods .............. 119
References ................................................. 119
Chapter 4. Dispersion on Microstrip Line ...................... 123
4.1. Frequency-Dependent Effective Dielectric Constant ..... 125
4.2. Frequency-Dependent Characteristic Impedance .......... 132
4.3. Measurement of Dispersion ............................. 138
4.3.1. Sliding Load Method ............................ 142
4.3.2. Resonance Method ............................... 147
4.3.3. Dispersion Measurements of Higher-Order
Modes .......................................... 160
References ................................................. 167
Chapter 5. Planar Waveguide Model ............................. 169
5.1. Definition of Dynamic Waveguide Model ................. 174
References ................................................. 184
Chapter 6. Microstrip Discontinuities, Junctions, and
Associated Circuit Elements ........................ 187
6.1. Open End .............................................. 189
6.1.1. Open End Capacitance and Excess Length ......... 191
6.1.2. Radiation Resistance ........................... 194
6.2. Step .................................................. 208
6.2.1. Quasi-Static Equivalent Circuit ................ 208
6.2.2. Full-Wave Analysis Using the Planar Waveguide
Model .......................................... 215
6.2.3. Cascaded Step Discontinuities .................. 228
6.2.4. Quarter-Wavelength Transformer ................. 230
6.2.5. Stepped Microstrip Transformer ................. 234
6.3. T-junction ............................................ 236
6.3.1. Quasi-Static Equivalent Circuit ................ 237
6.3.2. Dynamic Equivalent Circuit ..................... 237
6.3.3. Compensated T-Junction ......................... 241
6.3.4. Special Structures ............................. 242
6.4. Stub .................................................. 243
6.5. Bend .................................................. 249
6.5.1. Right-Angled Bend .............................. 249
6.5.2. Compensated Bend ............................... 251
6.5.3. Curved Microstrip Bend ......................... 254
6.6. Quasi-Lumped Elements ................................. 256
6.6.1. Series Inductance .............................. 256
6.6.2. Shunt Capacitance .............................. 261
6.7. Circular Disk Resonator ............................... 265
6.7.1. Radial Transmission Line ....................... 265
6.7.2. Circular Disk Capacitor ........................ 270
6.7.3. Magnetic Wall Model After Watkins .............. 272
6.7.4. Magnetic Wall Model After Wolff ................ 275
6.8. Radial Line Stub ...................................... 280
6.8.1. Model After Vinding ............................ 282
6.8.2. Model After Giannini ........................... 284
6.8.3. Model After Atwater ............................ 286
6.8.4. Biasing Network ................................ 288
6.9. Series Gap ............................................ 291
6.10.Cross Junction ........................................ 293
References ................................................. 296
Chapter 7. Microstrip Loss .................................... 301
7.1. Conductor Loss ........................................ 303
7.1.1. Skin Effect .................................... 305
7.1.2. Incremental Inductance Rule .................... 315
7.2. Dielectric Loss ....................................... 324
7.3. Conductor Roughness ................................... 327
7.4. Total Loss ............................................ 327
References ................................................. 328
Chapter 8. Applications ....................................... 331
8.1. Microstrip Filter Design .............................. 331
8.1.1. Basics in Filter Design ........................ 333
8.1.2. Filter Response Types .......................... 338
8.1.3. Design Examples ................................ 347
8.1.4. Frequency Transformations ...................... 355
8.2. Impedance Matching Networks ........................... 357
8.3. Coupled-Line Directional Coupler ...................... 362
8.3.1. Impedance Matrix of Coupled Lines .............. 363
8.3.2. Scattering Matrix of Coupled Lines ............. 367
8.3.3. TEM Directional Coupler ........................ 370
8.3.4. Quasi-TEM Directional Coupler .................. 372
8.3.5. Design Example ................................. 372
References ................................................. 374
Chapter 9. Technology ......................................... 377
9.1. Substrate ............................................. 377
9.1.1. Rigid Substrates ............................... 378
9.1.2. Soft Substrates ................................ 380
9.1.3. Substrate Height ............................... 382
9.2. Chip Devices .......................................... 383
9.2.1. Resistor ....................................... 384
9.2.2. Capacitor ...................................... 385
9.3. Circuit Fabrication ................................... 386
9.3.1. Hybrid Microwave Circuits ...................... 386
9.3.2. Monolithic Microwave Integrated Circuits ....... 387
9.3.3. Quasi-Monolithic Microwave Integrated
Circuits ....................................... 388
References ................................................. 392
Appendix A. Method of Conformal Transformation ................ 397
A.1. Theory of Functions of a Complex Variable ............. 397
A.1.1. Application to Electrostatic Problems .......... 404
A.2. The Schwarz-Christoffel Mapping Theorem ............... 409
A.2.1. Schwarz-Christoffel Theorem .................... 410
References ................................................. 416
Appendix B. Smith Chart ....................................... 417
B.1. Construction of the Smith Chart ....................... 418
B.1.1. Analysis of Im(z) = const. ..................... 418
B.1.2. Analysis of Re(z) = const. ..................... 419
B.1.3. Analysis of |z| = const. ....................... 420
B.l.4. Analysis of φ = const. ......................... 421
B.2. Smith Chart as a Graphic Aid for the Solution of
Transmission Line and Network Problems ................ 423
B.3. Using the Smith Chart ................................. 426
B.3.1. Series and Parallel Combination of
Resistances, Capacitances, and Inductances ..... 427
B.3.2. Power Matching with Lumped Elements
(Resonance Transformation) ..................... 428
B.3.3. Matching Network Comprising Sections of
Transmission Line .............................. 429
B.3.4. Reading of Voltage (and/or Current) from
Smith Chart .................................... 433
References 434
Appendix C. Pulse Shaping with Coupled Microstrip and Slot
Line .............................................. 435
References ................................................. 438
Appendix D. Modes in Waveguiding Structures ................... 439
D.1. Maxwell Equations ..................................... 439
D.1.1. Boundary Conditions ............................ 442
D.1.2. Particular Boundary Conditions ................. 445
D.2. Modified Maxwell Equations for Solving Waveguiding
Boundary Problems ..................................... 446
D.2.1. Wave Equation for the Longitudinal Field
Components ..................................... 449
D.2.2. Electric and Magnetic Vector Potentials ........ 456
D.3. Longitudinal Section Modes ............................ 461
D.3.1. Vector Potential in x Direction ................ 462
D.3.2. Vector Potential in y Direction ................ 462
D.4. Classification of Field Modes in Waveguiding
Structures ............................................ 463
D.4.1. TEM Mode ....................................... 464
D.4.2. E Modes ........................................ 465
D.4.3. H Modes ........................................ 465
References ................................................. 468
Appendix E. Definition of Insertion Loss ...................... 469
Reference .................................................. 470
Appendix F. Table of QuasiyStatic Line Parameters after
Hammerstad ........................................ 471
Appendix G. Circuit Therory ................................... 477
G.1. Circuit Parameters Interrelating Voltage and
Current ............................................... 477
G.2. S Matrix Concept ...................................... 480
References ................................................. 484
Appendix H. Orthogonal Series Expansion Method ................ 485
Reference .................................................. 490
Appendix I. Impedance Matrix of Step Discontinuity ............ 491
References ................................................. 495
Appendix J. Coupled Microstrip Lines .......................... 497
J.1. Quasi-Static Coupled Line Parameters .................. 497
J.2. Dispersive Coupled Line Parameters .................... 505
References ................................................. 511
About the Author .............................................. 513
Index ......................................................... 515
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