Microwave Polarizers, Power Dividers, Phase Shifters, Circulators, and Switches

JOSEPH HELSZAJN, PHD, is an international authority on non-reciprocal microwave circuits and devices. He has made a significant contribution to the characterization of the complex gyrator circuits and gain-bandwidth products of planar gyromagnetic resonators and other gyromagnetic devices. Professor Helszajn is a Fellow of the Institute of Electrical and Electronic Engineers (FIEEE), the City and Guilds Institute (FGCI), the Royal Society of Edinburgh (FRSE), and the Royal Academy of Engineering (FREng). He previously authored thirteen books, nine of which were published by Wiley.

• Preface xiiiAcknowledgments xvList of Contributors xvii1 Microwave Switching Using Junction Circulators 1Joseph Helszajn1.1 Microwave Switching Using Circulators 11.2 The Operation of the Switched Junction Circulator 11.3 The Turnstile Circulator 41.4 Externally and Internally Latched Junction Circulators 71.5 Standing Wave Solution of Resonators with Threefold Symmetry 71.6 Magnetic Circuit Using Major Hysteresis Loop 81.7 Display of Hysteresis Loop 91.8 Switching Coefficient of Magnetization 111.9 Magnetostatic Problem 131.10 Multiwire Magnetostatic Problem 141.11 Shape Factor of Cylindrical Resonator 15Bibliography 162 The Operation of Nonreciprocal Microwave Faraday Rotation Devices and Circulators 19Joseph Helszajn2.1 Introduction 192.2 Faraday Rotation 202.3 Magnetic Variables of Faraday Rotation Devices 252.4 The Gyrator Network 272.5 Faraday Rotation Isolator 292.6 Four-port Faraday Rotation Circulator 302.7 Nonreciprocal Faraday Rotation-type Phase Shifter 312.8 Coupled Wave Theory of Faraday Rotation Section 322.9 The Partially Ferrite-filled Circular Waveguide 33Bibliography 343 Circular Polarization in Parallel Plate Waveguides 37Joseph Helszajn3.1 Circular Polarization in Rectangular Waveguide 373.2 Circular Polarization in Dielectric Loaded Parallel Plate Waveguide with Open Sidewalls 40Bibliography 474 Reciprocal Quarter-wave Plates in Circular Waveguides 49Joseph Helszajn4.1 Quarter-wave Plate 504.2 Coupled Mode Theory of Quarter-wave Plate 534.3 Effective Waveguide Model of Quarter-wave Plate 584.4 Phase Constants of Quarter-wave Plate Using the Cavity Method 594.5 Variable Rotor Power Divider 62Bibliography 635 Nonreciprocal Ferrite Quarter-wave Plates 65Joseph Helszajn5.1 Introduction 655.2 Birefringence 655.3 Nonreciprocal Quarter-wave Plate Using the Birefringence Effect 675.4 Circulator Representation of Nonreciprocal Quarter-wave Plates 715.5 Coupled and Normal Modes in Magnetized Ferrite Medium 725.6 Variable Phase-shifters Employing Birefringent, Faraday Rotation, and Dielectric Half-wave Plates 735.7 Circulators and Switches Using Nonreciprocal Quarter-wave Plates 765.8 Nonreciprocal Circular Polarizer Using Elliptical Gyromagnetic Waveguide 77Bibliography 796 Ridge, Coaxial, and Stripline Phase-shifters 81Joseph Helszajn6.1 Differential Phase-shift, Phase Deviation, and Figure of Merit of Ferrite Phase-shifter 826.2 Coaxial Differential Phase-shifter 826.3 Ridge Waveguide Differential Phase-shifter 886.4 The Stripline Edge Mode Phase-shifter 906.5 Latched Quasi-TEM Phase-shifters 91Bibliography 927 Finite Element Adjustment of the Rectangular Waveguide-latched Differential Phase-shifter 95Joseph Helszajn and Mark McKay7.1 Introduction 957.2 FE Discretization of Rectangular Waveguide Phase-shifters 977.3 LS Modes Limit Waveguide Bandwidths 987.4 Cutoff Numbers and Split Phase Constants of a Twin Slab Ferrite Phase-shifter 997.5 The Waveguide Toroidal Phase-shifter 1027.6 Industrial Practice 1037.7 Magnetic Circuits Using Major and Minor Hysteresis Loops 1037.8 Construction of Latching Circuits 1067.9 Temperature Compensation Using Composite Circuits 107Bibliography 1098 Edge Mode Phase-shifter 111Joseph Helszajn and Henry Downs8.1 Edge Mode Effect 1128.2 Edge Mode Characteristic Equation 1158.3 Fields and Power in Edge Mode Devices 1158.4 Circular Polarization and the Edge Mode Effect 1188.5 Edge Mode Phase-shifter 1208.6 Edge Mode Isolators, Phase-shifters, and Circulators 123Bibliography 1249 The Two-port On/Off H-plane Waveguide Turnstile Gyromagnetic Switch 127Joseph Helszajn, Mark McKay, Alicia Casanueva, and Angel Mediavilla Sánchez9.1 Introduction 1279.2 Two-port H-plane Turnstile On/Off Switch 1279.3 Even and Odd Eigenvectors of E-plane Waveguide Tee Junction 1299.4 Eigenvalue Adjustment of Turnstile Plane Switch 1309.5 Eigen-networks 1329.6 Numerical Adjustments of Passbands 1339.7 An Off/On H-plane Switch 134Bibliography 13610 Off/On and On/Off Two-port E-plane Waveguide Switches Using Turnstile Resonators 137Joseph Helszajn, Mark McKay, and John Sharp10.1 Introduction 13710.2 The Shunt E-plane Tee Junction 13810.3 Operation of Off/On and On/Off E-plane Switches 14010.4 Even and Odd Eigenvector of H-plane Waveguide Tee Junction 14110.5 Phenomenological Description of Two-port Off/On and On/Off Switches 14210.6 Eigenvalue Diagrams of Small- and Large-gap E-plane Waveguide Tee Junction 14410.7 Eigenvalue Diagrams of E-plane Waveguide Tee Junction 14510.8 Eigen-networks of E-plane Tee Junction 14610.9 Eigenvalue Algorithm 14710.10 Pass and Stop Bands in Demagnetized E-plane Waveguide Tee Junction 148Bibliography 15011 Operation of Two-port On/Off and Off/On Planar Switches Using the Mutual Energy–Finite Element Method 153Joseph Helszajn and David J. Lynch11.1 Introduction 15311.2 Impedance and Admittance Matrices from Mutual Energy Consideration 15411.3 Impedance and Admittance Matrices for Reciprocal Planar Circuits 15711.4 Immittance Matrices of n-Port Planar Circuits Using Finite Elements 16011.5 Frequency Response of Two-port Planar Circuits Using the Mutual Energy–Finite Element Method 16111.6 Stripline Switch Using Puck/Plug Half-spaces 166Bibliography 16912 Standing Wave Solutions and Cutoff Numbers of Planar WYE and Equilateral Triangle Resonators 171Joseph Helszajn12.1 Introduction 17112.2 Cutoff Space of WYE Resonator 17212.3 Standing Wave Circulation Solution of WYE Resonator 17412.4 Resonant Frequencies of Quasi-wye Magnetized Resonators 17512.5 The Gyromagnetic Cutoff Space 17912.6 TM Field Patterns of Triangular Planar Resonator 18012.7 TM1,0,−1 Field Components of Triangular Planar Resonator 18212.8 Circulation Solutions 182Bibliography 18413 The Turnstile Junction Circulator: First Circulation Condition 185Joseph Helszajn13.1 Introduction 18513.2 The Four-port Turnstile Junction Circulator 18613.3 The Turnstile Junction Circulator 18813.4 Scattering Matrix 19013.5 Frequencies of Cavity Resonators 19313.6 Effective Dielectric Constant of Open Dielectric Waveguide 19313.7 The Open Dielectric Cavity Resonator 19613.8 The In-phase Mode 19813.9 First Circulation Condition 200Bibliography 20014 The Turnstile Junction Circulator: Second Circulation Condition 203Joseph Helszajn and Mark McKay14.1 Introduction 20314.2 Complex Gyrator of Turnstile Circulator 20414.3 Susceptance Slope Parameter, Gyrator Conductance, and Quality Factor 20714.4 Propagation in Gyromagnetic Waveguides 20814.5 Eigen-network of Turnstile Circulator 20914.6 The Quality Factor of the Turnstile Circulator 21114.7 Susceptance Slope Parameter of Turnstile Junction 213Bibliography 21315 A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the H-plane Turnstile Waveguide Circulator 217Joseph Helszajn15.1 Introduction 21715.2 Bandpass Frequency of a Turnstile Junction 21915.3 In-phase and Counterrotating Modes of Turnstile Junction 22115.4 Reference Plane 22215.5 FE Algorithm 22215.6 FE Adjustment 22415.7 The Reentrant Turnstile Junction in Standard WR75 Waveguide 23015.8 Susceptance Slope Parameter of Degree-1 Junction 23015.9 Split Frequencies of Gyromagnetic Resonators 233References 23616 The E-plane Waveguide Wye Junction: First Circulation Conditions 239Joseph Helszajn and Marco Caplin16.1 Introduction 23916.2 Scattering Matrix of Reciprocal E-plane Three-port Y-junction 24016.3 Reflection Eigenvalue Diagrams of Three-port Junction Circulator 24216.4 Eigen-networks 24416.5 Pass Band and Stop Band Characteristic Planes 24616.6 The Dicke Eigenvalue Solution 24716.7 Stop Band Characteristic Plane 24816.8 The E-plane Geometry 24916.9 First Circulation Condition 25116.10 Calculations of Eigenvalues 253Bibliography 25417 Adjustment of Prism Turnstile Resonators Latched by Wire Loops 257Joseph Helszajn and William D’Orazio17.1 Introduction 25717.2 The Prism Resonator 25817.3 Split Frequency of Cavity Resonator with Up or Down Magnetization 26017.4 Quality Factor of Gyromagnetic Resonator with Up and Down Magnetization 26117.5 Shape Factor of Tri-toroidal Resonator 26217.6 Squareness Ratio 26417.7 The Complex Gyrator Circuit of the Three-port Junction Circulator 26517.8 The Alternate Line Transformer 26617.9 Effective Complex Gyrator Circuit 267Bibliography 26718 Numerical Adjustment of Waveguide Ferrite Switches Using Tri-toroidal Resonators 269Joseph Helszajn and Mark McKay18.1 Introduction 26918.2 The Tri-toroidal Resonator 27018.3 The Wire Carrying Slot Geometry 27218.4 The Magnetostatic Problem 27318.5 Quality Factor of Junction Circulators with Up and Down Magnetization 27418.6 Split Frequencies of Planar and Cavity Gyromagnetic Resonators 27518.7 The Split Frequencies of Prism Resonator with Up and Down Magnetization 27618.8 Exact Calculation of Split Frequencies in Tri-toroidal Cavity 27718.9 Calculation and Experiment 27818.10 Tri-toroidal Composite Prism Resonator 27918.11 Tri-toroidal Wye Resonator with Up and Down Magnetization 280Bibliography 28219 The Waveguide H-plane Tee Junction Circulator Using a Composite Gyromagnetic Resonator 285Joseph Helszajn19.1 Introduction 28519.2 Eigenvalue Problem of the H-plane Reciprocal Tee Junction 28619.3 Electrically Symmetric H-plane Junction at the Altman Planes 28919.4 Characteristic Planes 29019.5 The Septum-loaded H-plane Waveguide 29219.6 The Waveguide Tee Junction Using a Dielectric Post Resonator: First Circulation Condition 29419.7 The Waveguide Tee Junction Circulator Using a Gyromagnetic Post Resonator: Second Circulation Condition 29619.8 Composite Dielectric Resonator 297Bibliography 29920 0 , 90 , and 180 Passive Power Dividers 301Joseph Helszajn and Mark McKay20.1 Introduction 30120.2 Wilkinson Power Divider 30220.3 Even and Odd Mode Adjustment of the Wilkinson Power Divider 30220.4 Scattering Matrix of 90 Directional Coupler 30520.5 Even and Odd Mode Theory of Directional Couplers 30920.6 Power Divider Using 90 Hybrids 31120.7 Variable Power Dividers 31320.8 180 Waveguide Hybrid Network 314Bibliography 318Index 321