Networks and Devices Using Planar Transmissions Lines

Front cover
Title page
Copyright
ABSTRACT
The Author
CONTENTS
PREFACE
Chapter 1: Fundamental Theory of Transmission Lines
1.1Generalities
1.2“Telegraphist” and “Transmission line” equations
1.3Solutions of transmission line equations
1.4Propagation constant and characteristic impedance
1.5Transmission lines with typical terminations
a.Terminations at the INPUT of the Line
b.Terminations at the OUTPUT of the Line
1.6“Transmission” and “Impedance” Matrices
1.7Considerations about matching transmission lines
a. Ratio of Bandwidth Limits
b. Fractional
c. Octave
Case a. Line Length Equal to Integer Number of Half Wavelength
Case b. Line Length Equal to an Odd Number of Quarter Wavelength
Case c. Line Terminated With Matched Load
1.8Reflection coefficients and standing wave ratio
1.9Nonuniform transmission lines
1.10Quarter wave transformers
1.11Coupled transmission lines
1.12The Smith chart
1.13Some examples using the Smith chart
1.14Notes on planar transmission line fabrication
References
Chapter 2: Microstrips
2.1Geometrical characteristics
2.2Electric and magnetic field lines
2.3Solution techniques for the electromagnetic problem
2.4Quasi static analysis methods
2.5Coupled modes analysis method
2.6Full wave analysis method
2.7Design equations
2.8Attenuation
2.9Practical considerations
REFERENCES
Chapter 3: Striplines
3.1Geometrical characteristics
3.2Electric and magnetic field lines
3.3Solution techniques for the electromagnetic problem
3.4Extraction of stripline impedance with a conformal transformation
3.5Design equations
3.6Attenuation
3.7Offset striplines
3.8Practical considerations
REFERENCES
Chapter 4: Higher Order Modes and Discontinuities in μStrip and Stripline
4.1Radiation
4.2Surface waves
4.3Higher order modes
4.3.1mStrip Case
4.3.2Stripline Case
4.4Typical discontinuities
4.5Bends
4.5.1mStrip Case
4.5.2Stripline Case
4.6Open End
4.6.1mStrip Case
4.6.2Stripline Case
4.7Gap
4.7.1mStrip Case
4.7.2Stripline Case
4.8Change of Width
4.8.1mStrip Case
4.8.2Stripline Case
4.9“T” Junctions
4.9.1mStrip Case
4.9.2Stripline Case
4.10Cross-Junction
4.10.1mStrip Case
4.10.1Stripline Case
REFERENCES
Chapter 5: Coupled Microstrips
5.1Geometrical Characteristics
5.2Electric and magnetic field lines
5.3Solution techniques for the electromagnetic problem
5.4Quasi static analysis methods
5.5Coupled modes analysis method
5.6Full wave analysis method
5.7Design equations
5.8Attenuation
5.9A particular coupled microstrip structure: the meander line
REFERENCES
Chapter 6: Coupled Striplines
6.1Geometrical Characteristics
6.2Electric and magnetic field lines
6.3Solution techniques for the electromagnetic problem
6.4Design equations
6.4.1SCS
6.4.2BCS
6.4.3OBCS
6.5Attenuation
6.6A particular coupled stripline structure: the meander line
6.7Practical considerations
REFERENCES
Chapter 7: Microstrip Devices
7.1Simple two port networks
a.Stubs
b.Series INDUCTORS
c.Series CAPACITORS
d.TRANSFORMERS
e.RESONATORS
f.FILTERS
g.BALUN
7.2Directional couplers
7.2.1Branch Line
7.2.2.“Rat Race” or “Magic T”
7.2.3“In-Line” or “Wilkinson”
7.2.4Step Coupled Lines
7.2.5Tapered Coupling
7.2.6Interdigital or “Lange”
7.3Signal Combiners
7.3.1Branch Line
7.3.2“Rat Race” or “Magic T”
7.3.3“In Line” or “Wilkinson”
7.3.4Step Coupled Lines
7.4Directional filters
7.4.1Resonant Ring
7.4.2Transverse Resonant Lines
7.5Phase shifters
7.5.1Coupled Lines or “Schiffman”
7.5.2Transverse Stubs or “Wilds”
7.5.3Reflection Type
7.6The Three Port Circulator
7.7Ferrimagnetic Phase Shifters
7.7.1Reciprocal
7.7.2Nonreciprocal
a.Using a Circular Polarized “RF” Magnetic Field
b.Using “Field Displacement”
7.8Ferrimagnetic isolators
7.8.1Field Displacement Isolator
7.8.2Resonance Isolator
7.9Comparison among ferrimagnetic phase shifters
REFERENCES
Chapter 8: Stripline Devices
8.1Introduction
8.2Typical two port networks
8.3Directional couplers
8.4Signal combiners
8.5Directional filters
8.6Phase shifters
8.7The three port circulator
8.8Ferrimagnetic phase shifters
8.8.1Reciprocal
8.8.2Nonreciprocal
a.Using Circular Polarized “RF” Magnetic Field
b.Using “Field Displacement”
8.9Ferrimagnetic isolators
8.9.1Field Displacement
8.9.2Resonance
8.10Comparison among ferrimagnetic phase shifters
REFERENCES
Chapter 9: Slot Lines
9.1Geometrical characteristics
9.2Electric and magnetic field lines
9.3Solution techniques for the electromagnetic problem
a.Line of Magnetic Current Method
b.Transverse Resonance Method
9.4Closed form equations for slot line characteristic impedance
9.5Connections between slot lines and other lines
a.Connection with Coaxial Cable
b.Connection with Microstrip
c.Connection with Stripline
d.Connection with Coplanar Waveguide
9.6Typical nonferrimagnetic devices using slot lines
a.180° Reciprocal Phase Shifters
b.Magic “T”
c.Mixers
d.Directional Couplers
e.Filters
9.7Magnetization of slot lines on ferrimagnetic substrates
9.8Slot line isolators
9.8.1Resonance Isolator
9.8.2Field Displacement Isolator
9.9Slot line ferrimagnetic phase shifters
9.9.1“Discon” Phase Shifter
9.9.2Field Displacement Phase Shifter
9.10Coupled slot lines
9.10.1General Characteristics
9.10.2Analysis
REFERENCES
Chapter 10: Coplanar Waveguides
10.1Geometrical characteristics
10.2Electric and magnetic field lines
10.3Solution techniques for the electromagnetic problem
a.Conformal Transformation Method: CTM
b.Finite Difference Method: FDM
10.4Closed form equations for “CPW” characteristic impedance
10.5Closed form equations for “CPW” attenuation
10.6Connections between “CPW” and other lines
a.Connection with Coaxial Cable
b.Connection with Microstrip
c.Connection with Slot Line
10.7Typical nonferrimagnetic devices using “CPW”
a.Mixers
b.Directional Couplers
c.Filters
10.8Magnetization of “CPW” on ferrimagnetic substrates
10.9“CPW” isolators
10.9.1Resonance Isolator
10.9.2Field Displacement Isolator
10.10“CPW” ferrimagnetic phase shifters
10.10.1“Discon” Phase Shifter
10.10.2Field Displacement Phase Shifter
10.11Practical considerations
10.11.1The “CPW” with Bottom Ground Conductor
10.11.2“CPW” with Bottom Ground Conductor and Lateral Planes with Limited Extension
10.12Coupled coplanar waveguides
10.12.1General Characteristics
10.12.2Analysis
REFERENCES
Chapter 11: Coplanar Strips
11.1Geometrical characteristics
11.2Electric and Magnetic Field Lines
11.3Solution Techniques for the Electromagnetic Problem
11.4Design equations
11.5Attenuation
11.6Connections between “CPS” and other lines
11.7Use of “CPS”
REFERENCES
Appendix A1: Solution Methods for Electrostatic Problems
A1.1The fundamental equations of electrostatics
a.Equations for Electric “E” and Electric Flux Density “D” Fields
b.Poisson and Laplace Equations
c.Boundary Conditions
d.Green’s Function
e.Gauss’s Law
A1.2Generalities on Solution Methods for Electrostatic Problems
a.Finite Difference Method
b.Image Charge Method
c.Conformal Transformation Method
A1.3Finite Difference Method
A1.4Image Charge Method
A1.5Fundamentals on Functions with Complex VariableS
A1.6Conformal Transformation Method
A1.7The Schwarz-Christoffel Transformation
REFERENCES
Appendix A2: Wave Equations, Waves, and Dispersion
A2.1Introduction
A2.2Maxwell’s Equations and Boundary Conditions
A2.3Wave equations in harmonic time dependence
A2.4The propagation vectors and their relationships with electric and magnetic fields
A2.5The time dependence
A2.6Plane wave definitions
A2.7Evaluation of electromagnetic energy
A2.8Waves in guiding structures with curvilinear orthogonal coordinate reference system
A2.9“TE” and “TM” modes in rectangular waveguide
1.TE Mode
2.“TM” Mode
A2.10“TE” and “TM” modes in circular waveguide
1.TE Mode
2.TM Mode
A2.11Uniform plane waves and “TEM” equations
A2.11.1Modes Inside a Coaxial Cable
a.“TM” Mode
b.“TE” Mode
c.“TEM” Mode
A2.11.2Uniform Plane Wave
A2.12Dispersion
A2.13Electrical networks associated With propagation modes
1.Associated Network for a “TM” Mode
2.Associated Network for a “TE” Mode
3.Associated Network for a “TEM” Mode
4.Associated Network for a “UPW”
A2.14Field penetration inside nonideal conductors
REFERENCES
Appendix A3: Diffusion Parameters and Multiport Devices
A3.1Simple analytical network representations
a.[Z] Matrix
b.[Y] Matrix
c.ABCD or “Chain” Matrix
A3.2Scattering parameters and conversion formulas
a.Conversion from “[ABCD]” to “[s]”
b.Conversion from “[s]” to “[ABCD]”
c.Conversion from “[ABCD]” to “[Z]”
d.Conversion from “[Z]” to “[ABCD]”
e.Conversion from “[t]” to “[s]”
f.Conversion from “[s]” to “[t]”
A3.3Conditions on scattering matrix for reciprocal and lossless networks
A3.4Three port networks
A3.5Four port networks
A3.6Quality parameters for directional couplers
a.Coupling.
b.Isolation.
c.Directivity.
A3.7Scattering parameters in unmatched case
REFERENCES
Appendix A4: Resonant Elements, “Q,” Losses
A4.1The intrinsic losses of real elements
A4.2The quality factor “Q”
A4.3Elements of filter theory
A4.4Butterworth, Chebyshev, and Cauer low pass filters
1.Band Pass Region
2.Stop Band Region
3.Transition Band Region
A4.5Filter generation from a normalized low pass
a.High Pass Filters
b.Band Pass Filters
c.Band Stop Filters
A4.6Filters with lossy elements
REFERENCES
Appendix A5: Charges, Currents, Magnetic Fields, and Forces
A5.1Introduction
A5.2Some important relationships of classic mechanics
a.First Principle of Dynamics
b.Second Principle of Dynamics
c.Third Principle of Dynamics
1.Work of a Force
2.Momentum of Inertia of a Body with Respect to an Axis
3.“Vector Momentum” of a Vector
4.Couple and Momentum of a Couple
5. Vector “Quantity of Motion” and Vector “Angular Orbital Momentum of the Quantity of Motion”
6.Vector “Angular Intrinsic Momentum of the Quantity of Motion”
7.The Theorem of the Quantity of Motion
8.Centrifugal and Centripetal Force
9.Kinetics Energy
A5.3Forces working on lone electric charges
1.Coulomb Force
2.Couple Working on an Electric Dipole and Its Energy
3.Lorentz Force
4.Potential Energy of a Charge
A5.4Forces working on electrical currents
1.Electromotive Force
2.Magnetic Force on a Current
3.Vector “Magnetic Momentum” Produced by a Current in a Closed Wire
4.Couple on a Magnetic Momentum and Its Energy
5.Faraday, Neumann, Lenz Law
A5.5Magnetic induction generated by currents
1.Laplace Expression
2.Biot e Savart Expression
3.Ampere’s Expression
A5.6Two important relationships of quantum mechanics
1.Indetermination Principle
2.The Energy-Frequency Relationship
A5.7The foundations of atom theory
A5.8The atom structure in quantum mechanics
A5.9The precession motion of the atomic magnetic momentum
A5.10Principles of wave mechanics
REFERENCES
Appendix A6: The Magnetic Properties of Materials
A6.1Introduction
A6.2Fundamental relationships for static magnetic fields and materials
A6.3The definitions of materials in magnetism
a.Diamagnetic Materials
b.Paramagnetic Materials
c.Ferromagnetic Materials
d.Antiferromagetic Materials
e.Ferrimagnetic Materials
A6.4Statistics functions for particle distribution in energy levels
a.Boltzmann Function
b.Bose-Einstein Function
c.Fermi-Dirac Function
A6.5Statistic evaluation of atomic magnetic moments
A6.6AnIsotropy, magnetostriction, demagnetization in ferromagnetic materials
a.Magnetization Anisotropy
b.Magnetostriction
c.Demagnetizing Field
A6.7The Weiss domains in ferromagnetic materials
A6.8Application of Weiss’ theory to some ferromagnetic phenomena
a.Spontaneous Magnetization and Curie’s Temperature
b.Ferromagnetic Paramagnetism
c.First Magnetization Curve and Hysteresis Loop
A6.9The Heisenberg Theory for the Molecular Field
A6.10Ferromagnetic materials and their applications
1.“Soft” Materials
a.Hard Materials
A6.11Antiferromagnetism
A6.12Ferrimagnetism
REFERENCES
Appendix A7: The Electromagnetic Field and the Ferrite
A7.1Introduction
A7.2The chemical composition of ferrites
A7.3The ferrite inside a static magnetic field
a.Permanent Magnetization
b.First Magnetization Curve and Hysteresis Loop
c.Paramagnetism
d.Precession Motion
A7.4The Permeability Tensor of Ferrites
A7.5“TEM” wave inside an isodirectional magnetized ferrite
A7.6Linear polarized, uniform plane wave inside an isodirectional magnetized ferrite: The Farada...
A7.7Electromagnetic wave inside a transverse magnetized ferrite
A7.8Considerations on demagnetization and anisotropy
A7.9The behavior of not statically saturated ferrite
A7.10The quality factor of ferrites at resonance
A7.11Losses in ferrites
a.The Conduction Losses “Lc”
b.The Hysteresis Loop Losses “Li”
c.The Residual Losses “Lr”
A7.12Isolators, phase shifters, circulators in waveguide with isodirectional magnetization
a.Nonreciprocal Isolators
b.Nonreciprocal Phase Shifters
c.Circulators
A7.13Isolators, phase shifters, and circulators in waveguides with transverse magnetization
a.Nonreciprocal Isolators
b.Phase Shifters
c.Circulators
A7.14Field displacement isolators and phase shifters
a.Nonreciprocal Isolators
b.Phase Shifters
A7.15The ferrite in planar transmission lines
a.The Ferrite As Microstrip Substrate
b.Nonreciprocal Isolators
c.Phase Shifters
d.Three Port Circulators
A7.16Other Uses of Ferrite in the Microwave Region
a.Variable Frequency Oscillators “VFO”
b.Tunable Filters
A7.17Use of ferrite until UHF
A7.18Harmonic signal generation in ferrite
A7.19Main resonance reduction and secondary resonance in ferrite
a.Main Resonance Peak Reduction
b.Secondary Resonance
REFERENCES
Appendix A8: Symbols, Operator Definitions and Analytical Expressions
A8.1Introduction
A8.2Definitions of Symbols and abbreviations
A8.2.1Associated to Vectors
A8.2.2Mathematical
A8.2.3General
A8.3Operator definitions and associated identities
A8.3.1 : Vector Operator Nabla or Vector Operator Delta
A8.3.2 : Laplacian or Square Delta
A8.3.3Operator identities.
A8.4Delta operator functions in cartesian orthogonal coordinate system
A8.5Delta operator functions in a cylindrical coordinate system
A8.6Delta operator functions in a spherical coordinate system
A8.7The divergence and Stokes theorems and Green identities
a.Divergence, or Gauss’s Theorem
b.Stokes Theorem
c.Green First Identity
d.Green Second Identity
e.Green Two Dimensional First Identity
f.Green Two Dimensional Second Identity
A8.8Elliptic integrals and their approximations
REFERENCES
INDEX
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