Networks and Devices Using Planar Transmissions Lines

Description

A single text that incorporates all of the theoretical principles and practical aspects of planar transmission line devices - since the early development of striplines, it has been sought by countless microwave engineers, researchers, and students. With the publication of Networks and Devices Using Planar Transmission Lines, the search for that one authoritative resource is over. This is more than just a handbook, much more than a theoretical treatment. It's the ideal integration of the theory and applications of planar transmission lines and devices. Striplines, microstrips, slot lines, coplanar waveguides and strips, phase shifters, hybrids, and more - the author examines them all. For each type of structure, his treatment is complete and self-contained, including: Geometric characteristics Electric and magnetic field lines Solution techniques for the electromagnetic problem Quasi-static, coupled modes, and full wave analysis methods Design equations Attenuation Practical considerations Of particular interest is the author's comprehensive treatment of planar ferrimagnetic devices, such as phase shifters, isolators, and circulators, and three appendices dedicated to the theoretical aspects of ferrimagetism. Five other appendices provide thorough reviews of various theoretical concepts implicit in the body of the work, such as wave theory, the external properties of networks, and resonant circuits. 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 Back cover