amirthavkm
Newbie level 2
conformal mapping in a groove waveguide
I would like to know the issues in Coplanar waveguide.
I would like to know the issues in Coplanar waveguide.
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Manjunatha_hv said:Hi,
Excellent book on Coplanar Circuits:
Coplanar Waveguide Circuits, Components, and Systems
By: RaineeN. Simons, Wiley Interscience
Contents:
1 Introduction 1
1.1 Advantages of Coplanar Waveguide Circuits 1
1.1.1 Design 1
1.1.2 Manufacturing 2
1.1.3 Performance 2
1.2 Types of Coplanar Waveguides 3
1.3 Software Tools for Coplanar Waveguide Circuit Simulation 4
1.4Typical Applications of Coplanar Waveguides 4
1.4.1 Ampli?ers, Active Combiners, Frequency Doublers,
Mixers, and Switches 4
1.4.2 Microelectromechanical Systems (MEMS) Metal
Membrane Capacitive Switches 4
1.4.3 Thin Film High-Temperature Superconducting/
Ferroelectric Tunable Circuits and Components 5
1.4.4 Photonic Bandgap Structures 5
1.4.5 Printed Antennas 5
1.5 Organization of This Book 6
References 7
2 Conventional Coplanar Waveguide 11
2.1 Introduction 11
2.2 Conventional Coplanar Waveguide on a Multilayer
Dielectric Substrate 12
2.2.1 Analytical Expression Based on Quasi-static
Conformal Mapping Techniques to Determine
Effective Dielectric Constant and Characteristic
Impedance 12
2.2.2 Conventional Coplanar Waveguide on an In?nitely
Thick Dielectric Substrate 17
2.2.3 Conventional Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness 20
2.2.4Conventional Coplanar Waveguide on a Finite
Thickness Dielectric Substrate and with a Top
Metal Cover 21
2.2.5 Conventional Coplanar Waveguide Sandwiched
between Two Dielectric Substrates 24
2.2.6 Conventional Coplanar Waveguide on a Double-
Layer Dielectric Substrate 25
2.2.7 Experimental Validation 29
2.3 Quasi-static TEM Iterative Techniques to Determine
and Z
32
2.3.1 Relaxation Method 32
2.3.2 Hybrid Method 33
2.4Frequency-Dependent Techniques for Dispersion and
Characteristic Impedance 33
2.4.1 Spectral Domain Method 33
2.4.2 Experimental Validation 44
2.5 Empirical Formula to Determine Dispersion Based on
Spectral Domain Results 47
2.5.1 Comparison of Coplanar Waveguide Dispersion
with Microstrip 48
2.6 Synthesis Formulas to Determine and Z
Based on
Quasi-static Equations 49
2.7 Coplanar Waveguide with Elevated or Buried Center
Strip Conductor 52
2.7.1 CPW with Elevated Center Strip Conductor
Supported on Dielectric Layers 54
2.7.2 CPW with Elevated Center Strip Conductor
Supported on Posts 54
2.8 Coplanar Waveguide with Ground Plane or Center Strip
Conductor Underpasses 56
2.9 Coplanar Waveguide Field
2.10 Coplanar Waveguide on a Cylindrical Surface 63
2.10.1 Analytical Expressions Based on Quasi-static
Conformal Mapping Technique 63
2.10.2 Computed Effective Dielectric Constant and
Characteristic Impedance 67
2.11 Effect of Metalization Thickness on Coplanar Waveguide
Characteristics 67
Appendix 2A: Spectral Domain Dyadic Green’s Function
Components 69
Appendix 2B: Time Average Power Flow in the Three Spatial
Regions 77
References 83
3 Conductor-Backed Coplanar Waveguide 87
3.1 Introduction 87
3.2 Conductor-Backed Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness 88
3.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Technique to Determine
Effective Dielectric Constant and Characteristic
Impedance 88
3.2.2 Experimental Validation 89
3.2.3 Analytical Expressions for CBCPW and Z
in the Presence of a Top Metal Cover 93
3.2.4Dispersion and Characteristic Impedance from
Full-Wave Analysis 96
3.3 Effect of Conducting Lateral Walls on the Dominant
Mode Propagation Characteristics of CBCPW and
Closed Form Equations for Z
98
3.3.1 Experimental Validation 101
3.4Ef fect of Lateral Walls on the Higher-Order Mode
Propagation on CBCPW 102
3.4.1 Perfect Conductors and Lossless Dielectric 102
3.4.2 Conductors with Finite Thickness, Finite
Conductivity, and Lossless or Lossy Dielectric 104
3.4.3 Experimental Validation 107
3.5 Channelized Coplanar Waveguide 107
3.6 Realization of Lateral Walls in Practical Circuits 108
References 109
4 Coplanar Waveguide with Finite-Width Ground Planes 112
4.1 Introduction 112
4.2 Conventional Coplanar Waveguide with Finite-
Width Ground Planes on a Dielectric Substrate of
Finite Thickness 113
4.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Techniques to
Determine Effective Dielectric Constant and
Characteristic Impedance 113
4.2.2 Dispersion and Characteristic Impedance from
Full-Wave Analysis 117
4.3 Conductor-Backed Coplanar Waveguide with Finite-
Width Ground Planes on a Dielectric Substrate of
Finite Thickness and Finite Width 119
4.4 Simple Models to Estimate Finite Ground Plane
Resonance in Conductor-Backed Coplanar Waveguide 123
4.4.1 Experimental Validation 124
References 125
5 Coplanar Waveguide Suspended inside a Conducting Enclosure 127
5.1 Introduction 127
5.2 Quasi-static TEM Iterative Technique to Determine
and Z
of Suspended CPW 128
5.2.1 Computed Quasi-static Characteristics and
Experimental Validation 128
5.3 Frequency-Dependent Numerical Techniques for Dispersion
and Characteristic Impedance of Suspended CPW 132
5.3.1 Effect of Shielding on the Dispersion and
Characteristic Impedance 133
5.3.2 Experimental Validation of Dispersion 135
5.3.3 Effect of Conductor Thickness on the Dispersion
and Characteristic Impedance 135
5.3.4Modal Bandwidth of a Suspended CPW 136
5.3.5 Pulse Propagation on a Suspended CPW 140
5.3.6 Pulse Distortion—Experimental Validation 142
5.4Dispersion and Higher-Order Modes of a Shielded
Grounded CPW 142
5.5 Dispersion, Characteristic Impedance, and Higher-Order
Modes of a CPW Suspended inside a Nonsymmetrical
Shielding Enclosure 143
5.5.1 Experimental Validation of the Dispersion
Characteristics 146
5.6 Dispersion and Characteristic Impedance of Suspended
CPW on Multilayer Dielectric Substrate 147
References 150
6 Coplanar Striplines 152
6.1 Introduction 152
6.2 Analytical Expressions Based on Quasi-Static TEM
Conformal Mapping Techniques to Determine Effective
Dielectric Constant and Characteristic Impedance 153
6.2.1 Coplanar Stripline on aMultilayer Dielectric Substrate 153
6.2.2 Coplanar Stripline on a Dielectric Substrate of Finite
Thickness 155
6.2.3 Asymmetric Coplanar Stripline on a Dielectric
Substrate of Finite Thickness 157
6.2.4Coplanar Stripline with In?nitely Wide Ground Plane
on a Dielectric Substrate of Finite Thickness 160
6.2.5 Coplanar Stripline with Isolating Ground Planes on a
Dielectric Substrate of Finite Thickness 161
6.3 Coplanar Stripline Synthesis Formulas to Determine the
Slot Width and the Strip Conductor Width 162
6.4Novel Variants of the Coplanar Stripline 164
6.4.1 Micro-coplanar Stripline 164
6.4.2 Coplanar Stripline with a Groove 164
References 169
7 Microshield Lines and Coupled Coplanar Waveguide 171
7.1 Introduction 171
7.2 Microshield Lines 171
7.2.1 Rectangular Shaped Microshield Line 173
7.2.2 V-Shaped Microshield Line 176
7.2.3 Elliptic Shaped Microshield Line 180
7.2.4Circular Shaped Microshield Line 180
7.3 Edge Coupled Coplanar Waveguide without a Lower
Ground Plane 182
7.3.1 Even Mode 182
7.3.2 Odd Mode 186
7.3.3 Computed Even- and Odd-Mode Characteristic
Impedance and Coupling Coef?cient 189
7.4Conductor-Backed Edge Coupled Coplanar Waveguide 190
7.4.1 Even Mode 192
7.4.2 Odd Mode 192
7.4.3 Even- and Odd-Mode Characteristics with Elevated
Strip Conductors 193
7.5 Broadside Coupled Coplanar Waveguide 193
7.5.1 Even Mode 194
7.5.2 Odd Mode 197
7.5.3 Computed Even- and Odd-Mode Effective Dielectric
Constant, Characteristic Impedance, Coupling
Coef?cient, and Mode Velocity Ratio 198
References 201
8 Attenuation Characteristics of Conventional,
Micromachined, and Superconducting Coplanar Waveguides 203
8.1 Introduction 203
8.2 Closed Form Equations for Conventional CPW Attenuation
Constant 204
8.2.1 Conformal Mapping Method 205
8.2.2 Mode-Matching Method and Quasi-TEM Model 207
8.2.3 Matched Asymptotic Technique and Closed Form
Expressions 207
8.2.4Measurement-Based Design Equations 212
8.2.5 Accuracy of Closed Form Equations 215
8.3 In?uence of Geometry on Coplanar Waveguide Attenuation 217
8.3.1 Attenuation Constant Independent of the Substrate
Thickness and Dielectric Constant 217
8.3.2 Attenuation Constant Dependent on the Aspect Ratio 217
8.3.3 Attenuation Constant Varying with the Elevation of
the Center Strip Conductor 218
8.4Attenuation Characteristics of Coplanar Waveguide on
Silicon Wafer 218
8.4.1 High-Resistivity Silicon Wafer 218
8.4.2 Low-Resistivity Silicon Wafer 221
8.5 Attenuation Characteristics of Coplanar Waveguide on
Micromachined Silicon Wafer 221
8.5.1 Microshield Line 221
8.5.2 Coplanar Waveguide with V-Shaped Grooves 223
8.5.3 Coplanar Waveguide Suspended by a Silicon Dioxide
Membrane over a Micromachined Wafer 223
8.6 Attenuation Constant for Superconducting Coplanar
Waveguides 225
8.6.1 Stopping Distance 225
8.6.2 Closed Form Equations 230
8.6.3 Comparison with Numerical Calculations and
Measured Results 233
References 233
9 Coplanar Waveguide Discontinuities and Circuit Elements 237
9.1 Introduction 237
9.2 Coplanar Waveguide Open Circuit 237
9.2.1 Approximate Formula for Length Extension When
the Gap Is Large 239
9.2.2 Closed Form Equation for Open End Capacitance
When the Gap Is Narrow 239
9.2.3 Radiation Loss 240
9.2.4Ef fect of Conductor Thickness and Edge Pro?le Angle 241
9.3 Coplanar Waveguide Short Circuit 241
9.3.1 Approximate Formula for Length Extension 241
9.3.2 Closed Form Equations for Short-Circuit Inductance 242
9.3.3 Effect of Conductor Thickness and Edge Pro?le Angle 243
9.4Coplanar Waveguide MIM Short Circuit 243
9.5 Series Gap in the Center Strip Conductor of a Coplanar
Waveguide 245
9.6 Step Change in the Width of Center Strip Conductor of a
Coplanar Waveguide 245
9.7 Coplanar Waveguide Right Angle Bend 247
9.8 Air-Bridges in Coplanar Waveguide 249
9.8.1 Type A Air-Bridge 250
9.8.2 Type B Air-Bridge 250
9.8.3 Air-Bridge Characteristics 250
9.8.4Air-Bridge Discontinuity Characteristics 254
9.9 Coplanar Waveguide T-Junction 254
9.9.1 Conventional T-Junction 254
9.9.2 Air-Bridge T-Junction 259
9.9.3 Mode Conversion in CPW T-Junction 260
9.9.4CPW T-Junction Characteristics 261
9.10 Coplanar Waveguide Spiral Inductor 262
9.11 Coplanar Waveguide Capacitors 265
9.11.1 Interdigital Capacitor 266
9.11.2 Series Metal-Insulator-Metal Capacitor 269
9.11.3 Parallel Metal-Insulator-Metal Capacitor 270
9.11.4Comparison between Coplanar Waveguide
Interdigital and Metal-Insulator-Metal
Capacitors 271
9.12 Coplanar Waveguide Stubs 272
9.12.1 Open-End Coplanar Waveguide Series Stub 273
9.12.2 Short-End Coplanar Waveguide Series Stub 275
9.12.3 Combined Short- and Open End Coplanar
Waveguide Series Stubs 278
9.12.4Coplanar Waveguide Shunt Stubs 278
9.12.5 Coplanar Waveguide Radial Line Stub 278
9.13 Coplanar Waveguide Shunt Inductor 282
References 285
10 Coplanar Waveguide Transitions 288
10.1 Introduction 288
10.2 Coplanar Waveguide-to-Microstrip Transition 289
10.2.1 Coplanar Waveguide-to-Microstrip Transition
Using Ribbon Bond 289
10.2.2 Coplanar Waveguide-to-Microstrip
Surface-to-Surface Transition via Electromagnetic
Coupling 290
10.2.3 Coplanar Waveguide-to-Microstrip Transition via
a Phase-Shifting Network 292
10.2.4Coplanar Waveguide-to-Microstrip Transition via
a Metal Post 292
10.2.5 Coplanar Waveguide-to-Microstrip Transition
Using a Via-Hole Interconnect 294
10.2.6 Coplanar Waveguide-to-Microstrip Orthogonal
Transition via Direct Connection 296
10.3 Transitions for Coplanar Waveguide Wafer probes 298
10.3.1 Coplanar Waveguide Wafer Probe-to-Microstrip
Transitions Using a Radial Stub 298
10.3.2 Coplanar Waveguide Wafer Probe-to-Microstrip
Transition Using Metal Vias 299
10.4Transitions between Coplanar Waveguides 300
10.4.1 Grounded Coplanar Waveguide-to-Microshield
Coplanar Line 300
10.4.2 Vertical Fed-through Interconnect between
Coplanar Waveguides with Finite-Width
Ground Planes 301
10.4.3 Orthogonal Transition between Coplanar
Waveguides 302
10.4.4 Electromagnetically Coupled Transition between
Stacked Coplanar Waveguides 303
10.4.5 Electromagnetically Coupled Transition between
Orthogonal Coplanar Waveguides 304
10.5 Coplanar Waveguide-to-Rectangular Waveguide
Transition 306
10.5.1 Coplanar Waveguide-to-Ridge Waveguide In-line
Transition 306
10.5.2 Coplanar Waveguide-to-Trough Waveguide
Transition 308
10.5.3 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Tapered Ridge 313
10.5.4Coplanar Waveguide-to-Rectangular Waveguide
End Launcher 314
10.5.5 Coplanar Waveguide-to-Rectangular Waveguide
Launcher with a Post 315
10.5.6 Channelized Coplanar Waveguide-to-Rectangular
Waveguide Launcher with an Aperture 317
10.5.7 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Printed Probe 318
10.6 Coplanar Waveguide-to-Slotline Transition 318
10.6.1 Coplanar Waveguide-to-Slotline Compensated
Marchand Balun or Transition 319
10.6.2 Coplanar Waveguide-to-Slotline Transition with
Radial or Circular Stub Termination 321
10.6.3 Coplanar Waveguide-to-Slotline Double-Y Balun
or Transition 323
10.6.4Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Notches in the Ground Plane 327
10.6.5 Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Extended Center Strip Conductor 328
10.6.6 Air-Bridge Coupled Coplanar Waveguide-to-
Slotline Transition 329
10.7 Coplanar Waveguide-to-Coplanar Stripline Transition 331
10.7.1 Coplanar Stripline-to-Coplanar Waveguide Balun 331
10.7.2 Coplanar Stripline-to-Coplanar Waveguide Balun
with Slotline Radial Stub 332
10.7.3 Coplanar Stripline-to-Coplanar Waveguide
Double-Y Balun 333
10.8 Coplanar Stripline-to-Microstrip Transition 334
10.8.1 Coplanar Stripline-to-Microstrip Transition with
an Electromagnetically Coupled Radial Stub 334
10.8.2 Uniplanar Coplanar Stripline-to-Microstrip
Transition 336
10.8.3 Coplanar Stripline-to-Microstrip Transition 337
10.8.4Micro-coplanar Stripline-to-Microstrip Transition 338
10.9 Coplanar Stripline-to-Slotline Transition 339
10.10 Coplanar Waveguide-to-Balanced Stripline Transition 342
References 342
11 Directional Couplers, Hybrids, and Magic-Ts 346
11.1 Introduction 346
11.2 Coupled-Line Directional Couplers 346
11.2.1 Edge Coupled CPW Directional Couplers 349
11.2.2 Edge Coupled Grounded CPW Directional
Couplers 350
11.2.3 Broadside Coupled CPW Directional Coupler 351
11.3 Quadrature (90°) Hybrid 352
11.3.1 Standard 3-dB Branch-Line Hybrid 354
11.3.2 Size Reduction Procedure for Branch-Line Hybrid 355
11.3.3 Reduced Size 3-dB Branch-Line Hybrid 356
11.3.4Reduced Size Impedance Transforming Branch-Line
Hybrid 358
11.4180° Hybrid 361
11.4.1 Standard 180° Ring Hybrid 363
11.4.2 Size Reduction Procedure for 180° Ring Hybrid 364
11.4.3 Reduced Size 180° Ring Hybrid 364
11.4.4 Reverse-Phase 180° Ring Hybrid 368
11.4.5 Reduced Size Reverse-Phase 180° Ring Hybrid 369
11.5 Standard 3-dB Magic-T 371
11.5.1 Reduced Size 3-dB Magic-T 375
11.6 Active Magic-T 378
References 383
12 Coplanar Waveguide Applications 384
12.1 Introduction 384
12.2 MEMS Coplanar Waveguide Capacitive Metal Membrane
Shunt Switch 384
12.2.1 OFF and ON Capacitances 384
12.2.2 Figure of Merit 386
12.2.3 Pull Down Voltage 387
12.2.4Fabrication Process 389
12.2.5 Switching Time and Switching Energy 391
12.2.6 Insertion Loss and Isolation 391
12.3 MEMS Coplanar Waveguide Distributed Phase Shifter 393
12.3.1 MEMS Air-Bridge Capacitance 395
12.3.2 Fabrication and Measured Performance 397
12.4High-Temperature Superconducting Coplanar Waveguide
Circuits 398
12.4.1 High-Frequency Electrical Properties of Normal
Metal Films 398
12.4.2 High-Frequency Electrical Properties of Epitaxial
High-T Superconducting Films 399
12.4.3 Kinetic and External Inductances of a
Superconducting Coplanar Waveguide 401
12.4.4 Resonant Frequency and Unloaded Quality Factor 402
12.4.5 Surface Resistance of High-T Superconducting
Coplanar Waveguide 407
12.4.6 Attenuation Constant 409
12.5 Ferroelectric Coplanar Waveguide Circuits 410
12.5.1 Characteristics of Barium Strontium Titanate Thin
Films 410
12.5.2 Characteristics of Strontium Titanate Thin Films 413
12.5.3 Grounded Coplanar Waveguide Phase Shifter 414
12.6 Coplanar Photonic-Bandgap Structure 417
12.6.1 Nonleaky Conductor-Backed Coplanar Waveguide 417
12.7 Coplanar Waveguide fix Antennas 422
12.7.1 Grounded Coplanar Waveguide fix Antenna 422
12.7.2 fix Antenna with Electromagnetically Coupled
Coplanar Waveguide Feed 424
12.7.3 Coplanar Waveguide Aperture-Coupled fix
Antenna 425
References 430
Index 434