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1 Introduction
1.1 Advantages of Coplanar Waveguide Circuits
1.1.1 Design
1.1.2 Manufacturing
1.1.3 Performance
1.2 Types of Coplanar Waveguides
1.3 Software Tools for Coplanar Waveguide Circuit Simulation
1.4Typical Applications of Coplanar Waveguides
1.4.1 Amplifiers, Active Combiners, Frequency Doublers,
Mixers, and Switches
1.4.2 Microelectromechanical Systems (MEMS) Metal
Membrane Capacitive Switches
1.4.3 Thin Film High-Temperature Superconducting/
Ferroelectric Tunable Circuits and Components
1.4.4 Photonic Bandgap Structures
1.4.5 Printed Antennas
1.5 Organization of This Book
References
2 Conventional Coplanar Waveguide
2.1 Introduction
2.2 Conventional Coplanar Waveguide on a Multilayer
Dielectric Substrate
2.2.1 Analytical Expression Based on Quasi-static
Conformal Mapping Techniques to Determine
Effective Dielectric Constant and Characteristic
Impedance
2.2.2 Conventional Coplanar Waveguide on an Infinitely
Thick Dielectric Substrate
2.2.3 Conventional Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness
2.2.4Conventional Coplanar Waveguide on a Finite
Thickness Dielectric Substrate and with a Top
Metal Cover
2.2.5 Conventional Coplanar Waveguide Sandwiched
between Two Dielectric Substrates
2.2.6 Conventional Coplanar Waveguide on a Double
Layer Dielectric Substrate
2.2.7 Experimental Validation
2.3 Quasi-static TEM Iterative Techniques to Determine
and Z
2.3.1 Relaxation Method
2.3.2 Hybrid Method
2.4Frequency-Dependent Techniques for Dispersion and
Characteristic Impedance
2.4.1 Spectral Domain Method
2.4.2 Experimental Validation
2.5 Empirical Formula to Determine Dispersion Based on
Spectral Domain Results
2.5.1 Comparison of Coplanar Waveguide Dispersion
with Microstrip
2.6 Synthesis Formulas to Determine
and Z Based on
Quasi-static Equations
2.7 Coplanar Waveguide with Elevated or Buried Center
Strip Conductor
2.7.1 CPW with Elevated Center Strip Conductor
Supported on Dielectric Layers
2.7.2 CPW with Elevated Center Strip Conductor
Supported on Posts
2.8 Coplanar Waveguide with Ground Plane or Center Strip
Conductor Underpasses
2.9 Coplanar Waveguide Field Components
CONTENTS
2.10 Coplanar Waveguide on a Cylindrical Surface
2.10.1 Analytical Expressions Based on Quasi-static
Conformal Mapping Technique
2.10.2 Computed Effective Dielectric Constant and
Characteristic Impedance
2.11 Effect of Metalization Thickness on Coplanar Waveguide
Characteristics
Appendix 2A: Spectral Domain Dyadic Green’s Function
Components
Appendix 2B: Time Average Power Flow in the Three Spatial
Regions
References
3 Conductor-Backed Coplanar Waveguide
3.1 Introduction
3.2 Conductor-Backed Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness
3.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Technique to Determine
Effective Dielectric Constant and Characteristic
Impedance
3.2.2 Experimental Validation
3.2.3 Analytical Expressions for CBCPW
and Z
in the Presence of a Top Metal Cover
3.2.4Dispersion and Characteristic Impedance from
Full-Wave Analysis
3.3 Effect of Conducting Lateral Walls on the Dominant
Mode Propagation Characteristics of CBCPW and
Closed Form Equations for Z
3.3.1 Experimental Validation
3.4Effect of Lateral Walls on the Higher-Order Mode
Propagation on CBCPW
3.4.1 Perfect Conductors and Lossless Dielectric
3.4.2 Conductors with Finite Thickness, Finite
Conductivity, and Lossless or Lossy Dielectric
3.4.3 Experimental Validation
3.5 Channelized Coplanar Waveguide
3.6 Realization of Lateral Walls in Practical Circuits
References
CONTENTS
4 Coplanar Waveguide with Finite-Width Ground Planes
4.1 Introduction
4.2 Conventional Coplanar Waveguide with Finite
Width Ground Planes on a Dielectric Substrate of
Finite Thickness
4.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Techniques to
Determine Effective Dielectric Constant and
Characteristic Impedance
4.2.2 Dispersion and Characteristic Impedance from
Full-Wave Analysis
4.3 Conductor-Backed Coplanar Waveguide with Finite
Width Ground Planes on a Dielectric Substrate of
Finite Thickness and Finite Width
4.4 Simple Models to Estimate Finite Ground Plane
Resonance in Conductor-Backed Coplanar Waveguide
4.4.1 Experimental Validation
References
5 Coplanar Waveguide Suspended inside a Conducting Enclosure
5.1 Introduction
5.2 Quasi-static TEM Iterative Technique to Determine
and Z
of Suspended CPW
5.2.1 Computed Quasi-static Characteristics and
Experimental Validation
5.3 Frequency-Dependent Numerical Techniques for Dispersion
and Characteristic Impedance of Suspended CPW
5.3.1 Effect of Shielding on the Dispersion and
Characteristic Impedance
5.3.2 Experimental Validation of Dispersion
5.3.3 Effect of Conductor Thickness on the Dispersion
and Characteristic Impedance
5.3.4Modal Bandwidth of a Suspended CPW
5.3.5 Pulse Propagation on a Suspended CPW
5.3.6 Pulse Distortion—Experimental Validation
5.4Dispersion and Higher-Order Modes of a Shielded
Grounded CPW
5.5 Dispersion, Characteristic Impedance, and Higher-Order
x CONTENTS
Modes of a CPW Suspended inside a Nonsymmetrical
Shielding Enclosure
5.5.1 Experimental Validation of the Dispersion
Characteristics
5.6 Dispersion and Characteristic Impedance of Suspended
CPW on Multilayer Dielectric Substrate
References
6 Coplanar Striplines
6.1 Introduction
6.2 Analytical Expressions Based on Quasi-Static TEM
Conformal Mapping Techniques to Determine Effective
Dielectric Constant and Characteristic Impedance
6.2.1 Coplanar Stripline on a Multilayer Dielectric Substrate
6.2.2 Coplanar Stripline on a Dielectric Substrate of Finite
Thickness
6.2.3 Asymmetric Coplanar Stripline on a Dielectric
Substrate of Finite Thickness
6.2.4Coplanar Stripline with Infinitely Wide Ground Plane
on a Dielectric Substrate of Finite Thickness
6.2.5 Coplanar Stripline with Isolating Ground Planes on a
Dielectric Substrate of Finite Thickness
6.3 Coplanar Stripline Synthesis Formulas to Determine the
Slot Width and the Strip Conductor Width
6.4Novel Variants of the Coplanar Stripline
6.4.1 Micro-coplanar Stripline
6.4.2 Coplanar Stripline with a Groove
References
7 Microshield Lines and Coupled Coplanar Waveguide
7.1 Introduction
7.2 Microshield Lines
7.2.1 Rectangular Shaped Microshield Line
7.2.2 V-Shaped Microshield Line
7.2.3 Elliptic Shaped Microshield Line
7.2.4Circular Shaped Microshield Line
7.3 Edge Coupled Coplanar Waveguide without a Lower
Ground Plane
CONTENTS
7.3.1 Even Mode
7.3.2 Odd Mode
7.3.3 Computed Even- and Odd-Mode Characteristic
Impedance and Coupling Coefficient
7.4Conductor-Backed Edge Coupled Coplanar Waveguide
7.4.1 Even Mode
7.4.2 Odd Mode
7.4.3 Even- and Odd-Mode Characteristics with Elevated
Strip Conductors
7.5 Broadside Coupled Coplanar Waveguide
7.5.1 Even Mode
7.5.2 Odd Mode
7.5.3 Computed Even- and Odd-Mode Effective Dielectric
Constant, Characteristic Impedance, Coupling
Coefficient, and Mode Velocity Ratio
References
8 Attenuation Characteristics of Conventional,
Micromachined, and Superconducting Coplanar Waveguides
8.1 Introduction
8.2 Closed Form Equations for Conventional CPW Attenuation
Constant
8.2.1 Conformal Mapping Method
8.2.2 Mode-Matching Method and Quasi-TEM Model
8.2.3 Matched Asymptotic Technique and Closed Form
Expressions
8.2.4Measurement-Based Design Equations
8.2.5 Accuracy of Closed Form Equations
8.3 Influence of Geometry on Coplanar Waveguide Attenuation
8.3.1 Attenuation Constant Independent of the Substrate
Thickness and Dielectric Constant
8.3.2 Attenuation Constant Dependent on the Aspect Ratio
8.3.3 Attenuation Constant Varying with the Elevation of
the Center Strip Conductor
8.4Attenuation Characteristics of Coplanar Waveguide on
Silicon Wafer
8.4.1 High-Resistivity Silicon Wafer
8.4.2 Low-Resistivity Silicon Wafer
xii CONTENTS
8.5 Attenuation Characteristics of Coplanar Waveguide on
Micromachined Silicon Wafer
8.5.1 Microshield Line
8.5.2 Coplanar Waveguide with V-Shaped Grooves
8.5.3 Coplanar Waveguide Suspended by a Silicon Dioxide
Membrane over a Micromachined Wafer
8.6 Attenuation Constant for Superconducting Coplanar
Waveguides
8.6.1 Stopping Distance
8.6.2 Closed Form Equations
8.6.3 Comparison with Numerical Calculations and
Measured Results
References
9 Coplanar Waveguide Discontinuities and Circuit Elements
9.1 Introduction
9.2 Coplanar Waveguide Open Circuit
9.2.1 Approximate Formula for Length Extension When
the Gap Is Large
9.2.2 Closed Form Equation for Open End Capacitance
When the Gap Is Narrow
9.2.3 Radiation Loss
9.2.4Effect of Conductor Thickness and Edge Profile Angle
9.3 Coplanar Waveguide Short Circuit
9.3.1 Approximate Formula for Length Extension
9.3.2 Closed Form Equations for Short-Circuit Inductance
9.3.3 Effect of Conductor Thickness and Edge Profile Angle
9.4Coplanar Waveguide MIM Short Circuit
9.5 Series Gap in the Center Strip Conductor of a Coplanar
Waveguide
9.6 Step Change in the Width of Center Strip Conductor of a
Coplanar Waveguide
9.7 Coplanar Waveguide Right Angle Bend
9.8 Air-Bridges in Coplanar Waveguide
9.8.1 Type A Air-Bridge
9.8.2 Type B Air-Bridge
9.8.3 Air-Bridge Characteristics
CONTENTS
9.8.4Air-Bridge Discontinuity Characteristics
9.9 Coplanar Waveguide T-Junction
9.9.1 Conventional T-Junction
9.9.2 Air-Bridge T-Junction
9.9.3 Mode Conversion in CPW T-Junction
9.9.4CPW T-Junction Characteristics
9.10 Coplanar Waveguide Spiral Inductor
9.11 Coplanar Waveguide Capacitors
9.11.1 Interdigital Capacitor
9.11.2 Series Metal-Insulator-Metal Capacitor
9.11.3 Parallel Metal-Insulator-Metal Capacitor
9.11.4Comparison between Coplanar Waveguide
Interdigital and Metal-Insulator-Metal
Capacitors
9.12 Coplanar Waveguide Stubs
9.12.1 Open-End Coplanar Waveguide Series Stub
9.12.2 Short-End Coplanar Waveguide Series Stub
9.12.3 Combined Short- and Open End Coplanar
Waveguide Series Stubs
9.12.4Coplanar Waveguide Shunt Stubs
9.12.5 Coplanar Waveguide Radial Line Stub
9.13 Coplanar Waveguide Shunt Inductor
References
10 Coplanar Waveguide Transitions
10.1 Introduction
10.2 Coplanar Waveguide-to-Microstrip Transition
10.2.1 Coplanar Waveguide-to-Microstrip Transition
Using Ribbon Bond
10.2.2 Coplanar Waveguide-to-Microstrip
Surface-to-Surface Transition via Electromagnetic
Coupling
10.2.3 Coplanar Waveguide-to-Microstrip Transition via
a Phase-Shifting Network
10.2.4Coplanar Waveguide-to-Microstrip Transition via
a Metal Post
10.2.5 Coplanar Waveguide-to-Microstrip Transition
Using a Via-Hole Interconnect
xiv CONTENTS
10.2.6 Coplanar Waveguide-to-Microstrip Orthogonal
Transition via Direct Connection
10.3 Transitions for Coplanar Waveguide Wafer probes
10.3.1 Coplanar Waveguide Wafer Probe-to-Microstrip
Transitions Using a Radial Stub
10.3.2 Coplanar Waveguide Wafer Probe-to-Microstrip
Transition Using Metal Vias
10.4Transitions between Coplanar Waveguides
10.4.1 Grounded Coplanar Waveguide-to-Microshield
Coplanar Line
10.4.2 Vertical Fed-through Interconnect between
Coplanar Waveguides with Finite-Width
Ground Planes
10.4.3 Orthogonal Transition between Coplanar
Waveguides
10.4.4 Electromagnetically Coupled Transition between
Stacked Coplanar Waveguides
10.4.5 Electromagnetically Coupled Transition between
Orthogonal Coplanar Waveguides
10.5 Coplanar Waveguide-to-Rectangular Waveguide
Transition
10.5.1 Coplanar Waveguide-to-Ridge Waveguide In-line
Transition
10.5.2 Coplanar Waveguide-to-Trough Waveguide
Transition
10.5.3 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Tapered Ridge
10.5.4Coplanar Waveguide-to-Rectangular Waveguide
End Launcher
10.5.5 Coplanar Waveguide-to-Rectangular Waveguide
Launcher with a Post
10.5.6 Channelized Coplanar Waveguide-to-Rectangular
Waveguide Launcher with an Aperture
10.5.7 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Printed Probe
10.6 Coplanar Waveguide-to-Slotline Transition
10.6.1 Coplanar Waveguide-to-Slotline Compensated
Marchand Balun or Transition
10.6.2 Coplanar Waveguide-to-Slotline Transition with
Radial or Circular Stub Termination
CONTENTS
10.6.3 Coplanar Waveguide-to-Slotline Double-Y Balun
or Transition
10.6.4Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Notches in the Ground Plane
10.6.5 Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Extended Center Strip Conductor
10.6.6 Air-Bridge Coupled Coplanar Waveguide-to
Slotline Transition
10.7 Coplanar Waveguide-to-Coplanar Stripline Transition
10.7.1 Coplanar Stripline-to-Coplanar Waveguide Balun
10.7.2 Coplanar Stripline-to-Coplanar Waveguide Balun
with Slotline Radial Stub
10.7.3 Coplanar Stripline-to-Coplanar Waveguide
Double-Y Balun
10.8 Coplanar Stripline-to-Microstrip Transition
10.8.1 Coplanar Stripline-to-Microstrip Transition with
an Electromagnetically Coupled Radial Stub
10.8.2 Uniplanar Coplanar Stripline-to-Microstrip
Transition
10.8.3 Coplanar Stripline-to-Microstrip Transition
10.8.4Micro-coplanar Stripline-to-Microstrip Transition
10.9 Coplanar Stripline-to-Slotline Transition
10.10 Coplanar Waveguide-to-Balanced Stripline Transition
References
11 Directional Couplers, Hybrids, and Magic-Ts
11.1 Introduction
11.2 Coupled-Line Directional Couplers
11.2.1 Edge Coupled CPW Directional Couplers
11.2.2 Edge Coupled Grounded CPW Directional
Couplers
11.2.3 Broadside Coupled CPW Directional Coupler
11.3 Quadrature (90°) Hybrid
11.3.1 Standard 3-dB Branch-Line Hybrid
11.3.2 Size Reduction Procedure for Branch-Line Hybrid
11.3.3 Reduced Size 3-dB Branch-Line Hybrid
xvi CONTENTS
11.3.4Reduced Size Impedance Transforming Branch-Line
Hybrid
11.4180° Hybrid
11.4.1 Standard 180° Ring Hybrid
11.4.2 Size Reduction Procedure for 180° Ring Hybrid
11.4.3 Reduced Size 180° Ring Hybrid
11.4.4 Reverse-Phase 180° Ring Hybrid
11.4.5 Reduced Size Reverse-Phase 180° Ring Hybrid
11.5 Standard 3-dB Magic-T
11.5.1 Reduced Size 3-dB Magic-T
11.6 Active Magic-T
References
12 Coplanar Waveguide Applications
12.1 Introduction
12.2 MEMS Coplanar Waveguide Capacitive Metal Membrane
Shunt Switch
12.2.1 OFF and ON Capacitances
12.2.2 Figure of Merit
12.2.3 Pull Down Voltage
12.2.4Fabrication Process
12.2.5 Switching Time and Switching Energy
12.2.6 Insertion Loss and Isolation
12.3 MEMS Coplanar Waveguide Distributed Phase Shifter
12.3.1 MEMS Air-Bridge Capacitance
12.3.2 Fabrication and Measured Performance
12.4High-Temperature Superconducting Coplanar Waveguide
Circuits
12.4.1 High-Frequency Electrical Properties of Normal
Metal Films
12.4.2 High-Frequency Electrical Properties of Epitaxial
High-T
Superconducting Films
12.4.3 Kinetic and External Inductances of a
Superconducting Coplanar Waveguide
12.4.4 Resonant Frequency and Unloaded Quality Factor
12.4.5 Surface Resistance of High-T
Superconducting
Coplanar Waveguide
12.4.6 Attenuation Constant
12.5 Ferroelectric Coplanar Waveguide Circuits
12.5.1 Characteristics of Barium Strontium Titanate Thin
Films
12.5.2 Characteristics of Strontium Titanate Thin Films
12.5.3 Grounded Coplanar Waveguide Phase Shifter
12.6 Coplanar Photonic-Bandgap Structure
12.6.1 Nonleaky Conductor-Backed Coplanar Waveguide
12.7 Coplanar Waveguide Patch Antennas
12.7.1 Grounded Coplanar Waveguide Patch Antenna
12.7.2 Patch Antenna with Electromagnetically Coupled
Coplanar Waveguide Feed
12.7.3 Coplanar Waveguide Aperture-Coupled Patch
Antenna
References
Index
xviii CONTENTS
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1 Introduction
1.1 Advantages of Coplanar Waveguide Circuits
1.1.1 Design
1.1.2 Manufacturing
1.1.3 Performance
1.2 Types of Coplanar Waveguides
1.3 Software Tools for Coplanar Waveguide Circuit Simulation
1.4Typical Applications of Coplanar Waveguides
1.4.1 Amplifiers, Active Combiners, Frequency Doublers,
Mixers, and Switches
1.4.2 Microelectromechanical Systems (MEMS) Metal
Membrane Capacitive Switches
1.4.3 Thin Film High-Temperature Superconducting/
Ferroelectric Tunable Circuits and Components
1.4.4 Photonic Bandgap Structures
1.4.5 Printed Antennas
1.5 Organization of This Book
References
2 Conventional Coplanar Waveguide
2.1 Introduction
2.2 Conventional Coplanar Waveguide on a Multilayer
Dielectric Substrate
2.2.1 Analytical Expression Based on Quasi-static
Conformal Mapping Techniques to Determine
Effective Dielectric Constant and Characteristic
Impedance
2.2.2 Conventional Coplanar Waveguide on an Infinitely
Thick Dielectric Substrate
2.2.3 Conventional Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness
2.2.4Conventional Coplanar Waveguide on a Finite
Thickness Dielectric Substrate and with a Top
Metal Cover
2.2.5 Conventional Coplanar Waveguide Sandwiched
between Two Dielectric Substrates
2.2.6 Conventional Coplanar Waveguide on a Double
Layer Dielectric Substrate
2.2.7 Experimental Validation
2.3 Quasi-static TEM Iterative Techniques to Determine
and Z
2.3.1 Relaxation Method
2.3.2 Hybrid Method
2.4Frequency-Dependent Techniques for Dispersion and
Characteristic Impedance
2.4.1 Spectral Domain Method
2.4.2 Experimental Validation
2.5 Empirical Formula to Determine Dispersion Based on
Spectral Domain Results
2.5.1 Comparison of Coplanar Waveguide Dispersion
with Microstrip
2.6 Synthesis Formulas to Determine
and Z Based on
Quasi-static Equations
2.7 Coplanar Waveguide with Elevated or Buried Center
Strip Conductor
2.7.1 CPW with Elevated Center Strip Conductor
Supported on Dielectric Layers
2.7.2 CPW with Elevated Center Strip Conductor
Supported on Posts
2.8 Coplanar Waveguide with Ground Plane or Center Strip
Conductor Underpasses
2.9 Coplanar Waveguide Field Components
CONTENTS
2.10 Coplanar Waveguide on a Cylindrical Surface
2.10.1 Analytical Expressions Based on Quasi-static
Conformal Mapping Technique
2.10.2 Computed Effective Dielectric Constant and
Characteristic Impedance
2.11 Effect of Metalization Thickness on Coplanar Waveguide
Characteristics
Appendix 2A: Spectral Domain Dyadic Green’s Function
Components
Appendix 2B: Time Average Power Flow in the Three Spatial
Regions
References
3 Conductor-Backed Coplanar Waveguide
3.1 Introduction
3.2 Conductor-Backed Coplanar Waveguide on a Dielectric
Substrate of Finite Thickness
3.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Technique to Determine
Effective Dielectric Constant and Characteristic
Impedance
3.2.2 Experimental Validation
3.2.3 Analytical Expressions for CBCPW
and Z
in the Presence of a Top Metal Cover
3.2.4Dispersion and Characteristic Impedance from
Full-Wave Analysis
3.3 Effect of Conducting Lateral Walls on the Dominant
Mode Propagation Characteristics of CBCPW and
Closed Form Equations for Z
3.3.1 Experimental Validation
3.4Effect of Lateral Walls on the Higher-Order Mode
Propagation on CBCPW
3.4.1 Perfect Conductors and Lossless Dielectric
3.4.2 Conductors with Finite Thickness, Finite
Conductivity, and Lossless or Lossy Dielectric
3.4.3 Experimental Validation
3.5 Channelized Coplanar Waveguide
3.6 Realization of Lateral Walls in Practical Circuits
References
CONTENTS
4 Coplanar Waveguide with Finite-Width Ground Planes
4.1 Introduction
4.2 Conventional Coplanar Waveguide with Finite
Width Ground Planes on a Dielectric Substrate of
Finite Thickness
4.2.1 Analytical Expressions Based on Quasi-static
TEM Conformal Mapping Techniques to
Determine Effective Dielectric Constant and
Characteristic Impedance
4.2.2 Dispersion and Characteristic Impedance from
Full-Wave Analysis
4.3 Conductor-Backed Coplanar Waveguide with Finite
Width Ground Planes on a Dielectric Substrate of
Finite Thickness and Finite Width
4.4 Simple Models to Estimate Finite Ground Plane
Resonance in Conductor-Backed Coplanar Waveguide
4.4.1 Experimental Validation
References
5 Coplanar Waveguide Suspended inside a Conducting Enclosure
5.1 Introduction
5.2 Quasi-static TEM Iterative Technique to Determine
and Z
of Suspended CPW
5.2.1 Computed Quasi-static Characteristics and
Experimental Validation
5.3 Frequency-Dependent Numerical Techniques for Dispersion
and Characteristic Impedance of Suspended CPW
5.3.1 Effect of Shielding on the Dispersion and
Characteristic Impedance
5.3.2 Experimental Validation of Dispersion
5.3.3 Effect of Conductor Thickness on the Dispersion
and Characteristic Impedance
5.3.4Modal Bandwidth of a Suspended CPW
5.3.5 Pulse Propagation on a Suspended CPW
5.3.6 Pulse Distortion—Experimental Validation
5.4Dispersion and Higher-Order Modes of a Shielded
Grounded CPW
5.5 Dispersion, Characteristic Impedance, and Higher-Order
x CONTENTS
Modes of a CPW Suspended inside a Nonsymmetrical
Shielding Enclosure
5.5.1 Experimental Validation of the Dispersion
Characteristics
5.6 Dispersion and Characteristic Impedance of Suspended
CPW on Multilayer Dielectric Substrate
References
6 Coplanar Striplines
6.1 Introduction
6.2 Analytical Expressions Based on Quasi-Static TEM
Conformal Mapping Techniques to Determine Effective
Dielectric Constant and Characteristic Impedance
6.2.1 Coplanar Stripline on a Multilayer Dielectric Substrate
6.2.2 Coplanar Stripline on a Dielectric Substrate of Finite
Thickness
6.2.3 Asymmetric Coplanar Stripline on a Dielectric
Substrate of Finite Thickness
6.2.4Coplanar Stripline with Infinitely Wide Ground Plane
on a Dielectric Substrate of Finite Thickness
6.2.5 Coplanar Stripline with Isolating Ground Planes on a
Dielectric Substrate of Finite Thickness
6.3 Coplanar Stripline Synthesis Formulas to Determine the
Slot Width and the Strip Conductor Width
6.4Novel Variants of the Coplanar Stripline
6.4.1 Micro-coplanar Stripline
6.4.2 Coplanar Stripline with a Groove
References
7 Microshield Lines and Coupled Coplanar Waveguide
7.1 Introduction
7.2 Microshield Lines
7.2.1 Rectangular Shaped Microshield Line
7.2.2 V-Shaped Microshield Line
7.2.3 Elliptic Shaped Microshield Line
7.2.4Circular Shaped Microshield Line
7.3 Edge Coupled Coplanar Waveguide without a Lower
Ground Plane
CONTENTS
7.3.1 Even Mode
7.3.2 Odd Mode
7.3.3 Computed Even- and Odd-Mode Characteristic
Impedance and Coupling Coefficient
7.4Conductor-Backed Edge Coupled Coplanar Waveguide
7.4.1 Even Mode
7.4.2 Odd Mode
7.4.3 Even- and Odd-Mode Characteristics with Elevated
Strip Conductors
7.5 Broadside Coupled Coplanar Waveguide
7.5.1 Even Mode
7.5.2 Odd Mode
7.5.3 Computed Even- and Odd-Mode Effective Dielectric
Constant, Characteristic Impedance, Coupling
Coefficient, and Mode Velocity Ratio
References
8 Attenuation Characteristics of Conventional,
Micromachined, and Superconducting Coplanar Waveguides
8.1 Introduction
8.2 Closed Form Equations for Conventional CPW Attenuation
Constant
8.2.1 Conformal Mapping Method
8.2.2 Mode-Matching Method and Quasi-TEM Model
8.2.3 Matched Asymptotic Technique and Closed Form
Expressions
8.2.4Measurement-Based Design Equations
8.2.5 Accuracy of Closed Form Equations
8.3 Influence of Geometry on Coplanar Waveguide Attenuation
8.3.1 Attenuation Constant Independent of the Substrate
Thickness and Dielectric Constant
8.3.2 Attenuation Constant Dependent on the Aspect Ratio
8.3.3 Attenuation Constant Varying with the Elevation of
the Center Strip Conductor
8.4Attenuation Characteristics of Coplanar Waveguide on
Silicon Wafer
8.4.1 High-Resistivity Silicon Wafer
8.4.2 Low-Resistivity Silicon Wafer
xii CONTENTS
8.5 Attenuation Characteristics of Coplanar Waveguide on
Micromachined Silicon Wafer
8.5.1 Microshield Line
8.5.2 Coplanar Waveguide with V-Shaped Grooves
8.5.3 Coplanar Waveguide Suspended by a Silicon Dioxide
Membrane over a Micromachined Wafer
8.6 Attenuation Constant for Superconducting Coplanar
Waveguides
8.6.1 Stopping Distance
8.6.2 Closed Form Equations
8.6.3 Comparison with Numerical Calculations and
Measured Results
References
9 Coplanar Waveguide Discontinuities and Circuit Elements
9.1 Introduction
9.2 Coplanar Waveguide Open Circuit
9.2.1 Approximate Formula for Length Extension When
the Gap Is Large
9.2.2 Closed Form Equation for Open End Capacitance
When the Gap Is Narrow
9.2.3 Radiation Loss
9.2.4Effect of Conductor Thickness and Edge Profile Angle
9.3 Coplanar Waveguide Short Circuit
9.3.1 Approximate Formula for Length Extension
9.3.2 Closed Form Equations for Short-Circuit Inductance
9.3.3 Effect of Conductor Thickness and Edge Profile Angle
9.4Coplanar Waveguide MIM Short Circuit
9.5 Series Gap in the Center Strip Conductor of a Coplanar
Waveguide
9.6 Step Change in the Width of Center Strip Conductor of a
Coplanar Waveguide
9.7 Coplanar Waveguide Right Angle Bend
9.8 Air-Bridges in Coplanar Waveguide
9.8.1 Type A Air-Bridge
9.8.2 Type B Air-Bridge
9.8.3 Air-Bridge Characteristics
CONTENTS
9.8.4Air-Bridge Discontinuity Characteristics
9.9 Coplanar Waveguide T-Junction
9.9.1 Conventional T-Junction
9.9.2 Air-Bridge T-Junction
9.9.3 Mode Conversion in CPW T-Junction
9.9.4CPW T-Junction Characteristics
9.10 Coplanar Waveguide Spiral Inductor
9.11 Coplanar Waveguide Capacitors
9.11.1 Interdigital Capacitor
9.11.2 Series Metal-Insulator-Metal Capacitor
9.11.3 Parallel Metal-Insulator-Metal Capacitor
9.11.4Comparison between Coplanar Waveguide
Interdigital and Metal-Insulator-Metal
Capacitors
9.12 Coplanar Waveguide Stubs
9.12.1 Open-End Coplanar Waveguide Series Stub
9.12.2 Short-End Coplanar Waveguide Series Stub
9.12.3 Combined Short- and Open End Coplanar
Waveguide Series Stubs
9.12.4Coplanar Waveguide Shunt Stubs
9.12.5 Coplanar Waveguide Radial Line Stub
9.13 Coplanar Waveguide Shunt Inductor
References
10 Coplanar Waveguide Transitions
10.1 Introduction
10.2 Coplanar Waveguide-to-Microstrip Transition
10.2.1 Coplanar Waveguide-to-Microstrip Transition
Using Ribbon Bond
10.2.2 Coplanar Waveguide-to-Microstrip
Surface-to-Surface Transition via Electromagnetic
Coupling
10.2.3 Coplanar Waveguide-to-Microstrip Transition via
a Phase-Shifting Network
10.2.4Coplanar Waveguide-to-Microstrip Transition via
a Metal Post
10.2.5 Coplanar Waveguide-to-Microstrip Transition
Using a Via-Hole Interconnect
xiv CONTENTS
10.2.6 Coplanar Waveguide-to-Microstrip Orthogonal
Transition via Direct Connection
10.3 Transitions for Coplanar Waveguide Wafer probes
10.3.1 Coplanar Waveguide Wafer Probe-to-Microstrip
Transitions Using a Radial Stub
10.3.2 Coplanar Waveguide Wafer Probe-to-Microstrip
Transition Using Metal Vias
10.4Transitions between Coplanar Waveguides
10.4.1 Grounded Coplanar Waveguide-to-Microshield
Coplanar Line
10.4.2 Vertical Fed-through Interconnect between
Coplanar Waveguides with Finite-Width
Ground Planes
10.4.3 Orthogonal Transition between Coplanar
Waveguides
10.4.4 Electromagnetically Coupled Transition between
Stacked Coplanar Waveguides
10.4.5 Electromagnetically Coupled Transition between
Orthogonal Coplanar Waveguides
10.5 Coplanar Waveguide-to-Rectangular Waveguide
Transition
10.5.1 Coplanar Waveguide-to-Ridge Waveguide In-line
Transition
10.5.2 Coplanar Waveguide-to-Trough Waveguide
Transition
10.5.3 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Tapered Ridge
10.5.4Coplanar Waveguide-to-Rectangular Waveguide
End Launcher
10.5.5 Coplanar Waveguide-to-Rectangular Waveguide
Launcher with a Post
10.5.6 Channelized Coplanar Waveguide-to-Rectangular
Waveguide Launcher with an Aperture
10.5.7 Coplanar Waveguide-to-Rectangular Waveguide
Transition with a Printed Probe
10.6 Coplanar Waveguide-to-Slotline Transition
10.6.1 Coplanar Waveguide-to-Slotline Compensated
Marchand Balun or Transition
10.6.2 Coplanar Waveguide-to-Slotline Transition with
Radial or Circular Stub Termination
CONTENTS
10.6.3 Coplanar Waveguide-to-Slotline Double-Y Balun
or Transition
10.6.4Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Notches in the Ground Plane
10.6.5 Electromagnetically Coupled Finite-Width
Coplanar Waveguide-to-Slotline Transition with
Extended Center Strip Conductor
10.6.6 Air-Bridge Coupled Coplanar Waveguide-to
Slotline Transition
10.7 Coplanar Waveguide-to-Coplanar Stripline Transition
10.7.1 Coplanar Stripline-to-Coplanar Waveguide Balun
10.7.2 Coplanar Stripline-to-Coplanar Waveguide Balun
with Slotline Radial Stub
10.7.3 Coplanar Stripline-to-Coplanar Waveguide
Double-Y Balun
10.8 Coplanar Stripline-to-Microstrip Transition
10.8.1 Coplanar Stripline-to-Microstrip Transition with
an Electromagnetically Coupled Radial Stub
10.8.2 Uniplanar Coplanar Stripline-to-Microstrip
Transition
10.8.3 Coplanar Stripline-to-Microstrip Transition
10.8.4Micro-coplanar Stripline-to-Microstrip Transition
10.9 Coplanar Stripline-to-Slotline Transition
10.10 Coplanar Waveguide-to-Balanced Stripline Transition
References
11 Directional Couplers, Hybrids, and Magic-Ts
11.1 Introduction
11.2 Coupled-Line Directional Couplers
11.2.1 Edge Coupled CPW Directional Couplers
11.2.2 Edge Coupled Grounded CPW Directional
Couplers
11.2.3 Broadside Coupled CPW Directional Coupler
11.3 Quadrature (90°) Hybrid
11.3.1 Standard 3-dB Branch-Line Hybrid
11.3.2 Size Reduction Procedure for Branch-Line Hybrid
11.3.3 Reduced Size 3-dB Branch-Line Hybrid
xvi CONTENTS
11.3.4Reduced Size Impedance Transforming Branch-Line
Hybrid
11.4180° Hybrid
11.4.1 Standard 180° Ring Hybrid
11.4.2 Size Reduction Procedure for 180° Ring Hybrid
11.4.3 Reduced Size 180° Ring Hybrid
11.4.4 Reverse-Phase 180° Ring Hybrid
11.4.5 Reduced Size Reverse-Phase 180° Ring Hybrid
11.5 Standard 3-dB Magic-T
11.5.1 Reduced Size 3-dB Magic-T
11.6 Active Magic-T
References
12 Coplanar Waveguide Applications
12.1 Introduction
12.2 MEMS Coplanar Waveguide Capacitive Metal Membrane
Shunt Switch
12.2.1 OFF and ON Capacitances
12.2.2 Figure of Merit
12.2.3 Pull Down Voltage
12.2.4Fabrication Process
12.2.5 Switching Time and Switching Energy
12.2.6 Insertion Loss and Isolation
12.3 MEMS Coplanar Waveguide Distributed Phase Shifter
12.3.1 MEMS Air-Bridge Capacitance
12.3.2 Fabrication and Measured Performance
12.4High-Temperature Superconducting Coplanar Waveguide
Circuits
12.4.1 High-Frequency Electrical Properties of Normal
Metal Films
12.4.2 High-Frequency Electrical Properties of Epitaxial
High-T
Superconducting Films
12.4.3 Kinetic and External Inductances of a
Superconducting Coplanar Waveguide
12.4.4 Resonant Frequency and Unloaded Quality Factor
12.4.5 Surface Resistance of High-T
Superconducting
Coplanar Waveguide
12.4.6 Attenuation Constant
12.5 Ferroelectric Coplanar Waveguide Circuits
12.5.1 Characteristics of Barium Strontium Titanate Thin
Films
12.5.2 Characteristics of Strontium Titanate Thin Films
12.5.3 Grounded Coplanar Waveguide Phase Shifter
12.6 Coplanar Photonic-Bandgap Structure
12.6.1 Nonleaky Conductor-Backed Coplanar Waveguide
12.7 Coplanar Waveguide Patch Antennas
12.7.1 Grounded Coplanar Waveguide Patch Antenna
12.7.2 Patch Antenna with Electromagnetically Coupled
Coplanar Waveguide Feed
12.7.3 Coplanar Waveguide Aperture-Coupled Patch
Antenna
References
Index
xviii CONTENTS
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