reading

Cover
Preface
1 Microwave Switching Using Junction Circulators
1. 1.1 Microwave Switching Using Circulators
2. 1.2 The Operation of the Switched Junction Circulator
3. 1.3 The Turnstile Circulator
4. 1.4 Externally and Internally Latched Junction Circulators
5. 1.5 Standing Wave Solution of Resonators with Threefold Symmetry
6. 1.6 Magnetic Circuit Using Major Hysteresis Loop
7. 1.7 Display of Hysteresis Loop
8. 1.8 Switching Coefficient of Magnetization
9. 1.9 Magnetostatic Problem
10. 1.10 Multiwire Magnetostatic Problem
11. 1.11 Shape Factor of Cylindrical Resonator
12. Bibliography
2 The Operation of Nonreciprocal Microwave Faraday Rotation Devices and Circulators
1. 2.1 Introduction
2. 2.2 Faraday Rotation
3. 2.3 Magnetic Variables of Faraday Rotation Devices
4. 2.4 The Gyrator Network
5. 2.5 Faraday Rotation Isolator
6. 2.6 Four‐port Faraday Rotation Circulator
7. 2.7 Nonreciprocal Faraday Rotation‐type Phase Shifter
8. 2.8 Coupled Wave Theory of Faraday Rotation Section
9. 2.9 The Partially Ferrite‐filled Circular Waveguide
10. Bibliography
3 Circular Polarization in Parallel Plate Waveguides
1. 3.1 Circular Polarization in Rectangular Waveguide
2. 3.2 Circular Polarization in Dielectric Loaded Parallel Plate Waveguide with Open Sidewalls
3. Bibliography
4 Reciprocal Quarter‐wave Plates in Circular Waveguides
1. 4.1 Quarter‐wave Plate
2. 4.2 Coupled Mode Theory of Quarter‐wave Plate
3. 4.3 Effective Waveguide Model of Quarter‐wave Plate
4. 4.4 Phase Constants of Quarter‐wave Plate Using the Cavity Method
5. 4.5 Variable Rotor Power Divider
6. Bibliography
5 Nonreciprocal Ferrite Quarter‐wave Plates
1. 5.1 Introduction
2. 5.2 Birefringence
3. 5.3 Nonreciprocal Quarter‐wave Plate Using the Birefringence Effect
4. 5.4 Circulator Representation of Nonreciprocal Quarter‐wave Plates
5. 5.5 Coupled and Normal Modes in Magnetized Ferrite Medium
6. 5.6 Variable Phase‐shifters Employing Birefringent, Faraday Rotation, and Dielectric Half‐wave Plates
7. 5.7 Circulators and Switches Using Nonreciprocal Quarter‐wave Plates
8. 5.8 Nonreciprocal Circular Polarizer Using Elliptical Gyromagnetic Waveguide
9. Bibliography
6 Ridge, Coaxial, and Stripline Phase‐shifters¹
1. 6.1 Differential Phase‐shift, Phase Deviation, and Figure of Merit of Ferrite Phase‐shifter
2. 6.2 Coaxial Differential Phase‐shifter
3. 6.3 Ridge Waveguide Differential Phase‐shifter
4. 6.4 The Stripline Edge Mode Phase‐shifter
5. 6.5 Latched Quasi‐TEM Phase‐shifters
6. Bibliography
7 Finite Element Adjustment of the Rectangular Waveguide‐latched Differential Phase‐shifter
1. 7.1 Introduction
2. 7.2 FE Discretization of Rectangular Waveguide Phase‐shifters
3. 7.3 LS Modes Limit Waveguide Bandwidths
4. 7.4 Cutoff Numbers and Split Phase Constants of a Twin Slab Ferrite Phase‐shifter
5. 7.5 The Waveguide Toroidal Phase‐shifter
6. 7.6 Industrial Practice
7. 7.7 Magnetic Circuits Using Major and Minor Hysteresis Loops
8. 7.8 Construction of Latching Circuits
9. 7.9 Temperature Compensation Using Composite Circuits
10. Bibliography
8 Edge Mode Phase‐shifter
1. 8.1 Edge Mode Effect
2. 8.2 Edge Mode Characteristic Equation
3. 8.3 Fields and Power in Edge Mode Devices
4. 8.4 Circular Polarization and the Edge Mode Effect
5. 8.5 Edge Mode Phase‐shifter
6. 8.6 Edge Mode Isolators, Phase‐shifters, and Circulators
7. Bibliography
9 The Two‐port On/Off H‐plane Waveguide Turnstile Gyromagnetic Switch
1. 9.1 Introduction
2. 9.2 Two‐port H‐plane Turnstile On/Off Switch
3. 9.3 Even and Odd Eigenvectors of E‐plane Waveguide Tee Junction
4. 9.4 Eigenvalue Adjustment of Turnstile Plane Switch
5. 9.5 Eigen‐networks
6. 9.6 Numerical Adjustments of Passbands
7. 9.7 An Off/On H‐plane Switch
8. Bibliography
10 Off/On and On/Off Two‐port E‐plane Waveguide Switches Using Turnstile Resonators
1. 10.1 Introduction
2. 10.2 The Shunt E‐plane Tee Junction
3. 10.3 Operation of Off/On and On/Off E‐plane Switches
4. 10.4 Even and Odd Eigenvector of H‐plane Waveguide Tee Junction
5. 10.5 Phenomenological Description of Two‐port Off/On and On/Off Switches
6. 10.6 Eigenvalue Diagrams of Small‐ and Large‐gap E‐plane Waveguide Tee Junction
7. 10.7 Eigenvalue Diagrams of E‐plane Waveguide Tee Junction
8. 10.8 Eigen‐networks of E‐plane Tee Junction
9. 10.9 Eigenvalue Algorithm
10. 10.10 Pass and Stop Bands in Demagnetized E‐plane Waveguide Tee Junction
11. Bibliography
11 Operation of Two‐port On/Off and Off/On Planar Switches Using the Mutual Energy–Finite Element Method*
1. 11.1 Introduction
2. 11.2 Impedance and Admittance Matrices from Mutual Energy Consideration
3. 11.3 Impedance and Admittance Matrices for Reciprocal Planar Circuits
4. 11.4 Immittance Matrices of n‐Port Planar Circuits Using Finite Elements
5. 11.5 Frequency Response of Two‐port Planar Circuits Using the Mutual Energy–Finite Element Method
6. 11.6 Stripline Switch Using Puck/Plug Half‐spaces
7. Bibliography
12 Standing Wave Solutions and Cutoff Numbers of Planar WYE and Equilateral Triangle Resonators
1. 12.1 Introduction
2. 12.2 Cutoff Space of WYE Resonator
3. 12.3 Standing Wave Circulation Solution of WYE Resonator
4. 12.4 Resonant Frequencies of Quasi‐wye Magnetized Resonators
5. 12.5 The Gyromagnetic Cutoff Space
6. 12.6 TM Field Patterns of Triangular Planar Resonator
7. 12.7 TM _1,0,−1 Field Components of Triangular Planar Resonator
8. 12.8 Circulation Solutions
9. Bibliography
13 The Turnstile Junction Circulator: First Circulation Condition
1. 13.1 Introduction
2. 13.2 The Four‐port Turnstile Junction Circulator
3. 13.3 The Turnstile Junction Circulator
4. 13.4 Scattering Matrix
5. 13.5 Frequencies of Cavity Resonators
6. 13.6 Effective Dielectric Constant of Open Dielectric Waveguide
7. 13.7 The Open Dielectric Cavity Resonator
8. 13.8 The In‐phase Mode
9. 13.9 First Circulation Condition
10. Bibliography
14 The Turnstile Junction Circulator: Second Circulation Condition
1. 14.1 Introduction
2. 14.2 Complex Gyrator of Turnstile Circulator
3. 14.3 Susceptance Slope Parameter, Gyrator Conductance, and Quality Factor
4. 14.4 Propagation in Gyromagnetic Waveguides
5. 14.5 Eigen‐network of Turnstile Circulator
6. 14.6 The Quality Factor of the Turnstile Circulator
7. 14.7 Susceptance Slope Parameter of Turnstile Junction
8. Bibliography
15 A Finite‐Element Algorithm for the Adjustment of the First Circulation Condition of the H‐plane Turnstile Waveguide Circulator
1. 15.1 Introduction
2. 15.2 Bandpass Frequency of a Turnstile Junction
3. 15.3 In‐phase and Counterrotating Modes of Turnstile Junction
4. 15.4 Reference Plane
5. 15.5 FE Algorithm
6. 15.6 FE Adjustment
7. 15.7 The Reentrant Turnstile Junction in Standard WR75 Waveguide
8. 15.8 Susceptance Slope Parameter of Degree‐1 Junction
9. 15.9 Split Frequencies of Gyromagnetic Resonators
10. References
16 The E‐plane Waveguide Wye Junction: First Circulation Conditions
1. 16.1 Introduction
2. 16.2 Scattering Matrix of Reciprocal E‐plane Three‐port Y‐junction
3. 16.3 Reflection Eigenvalue Diagrams of Three‐port Junction Circulator
4. 16.4 Eigen‐networks
5. 16.5 Pass Band and Stop Band Characteristic Planes
6. 16.6 The Dicke Eigenvalue Solution
7. 16.7 Stop Band Characteristic Plane
8. 16.8 The E‐plane Geometry
9. 16.9 First Circulation Condition
10. 16.10 Calculations of Eigenvalues
11. Bibliography
17 Adjustment of Prism Turnstile Resonators Latched by Wire Loops
1. 17.1 Introduction
2. 17.2 The Prism Resonator
3. 17.3 Split Frequency of Cavity Resonator with Up or Down Magnetization
4. 17.4 Quality Factor of Gyromagnetic Resonator with Up and Down Magnetization
5. 17.5 Shape Factor of Tri‐toroidal Resonator
6. 17.6 Squareness Ratio
7. 17.7 The Complex Gyrator Circuit of the Three‐port Junction Circulator
8. 17.8 The Alternate Line Transformer
9. 17.9 Effective Complex Gyrator Circuit
10. Bibliography
18 Numerical Adjustment of Waveguide Ferrite Switches Using Tri‐toroidal Resonators
1. 18.1 Introduction
2. 18.2 The Tri‐toroidal Resonator
3. 18.3 The Wire Carrying Slot Geometry
4. 18.4 The Magnetostatic Problem
5. 18.5 Quality Factor of Junction Circulators with Up and Down Magnetization
6. 18.6 Split Frequencies of Planar and Cavity Gyromagnetic Resonators
7. 18.7 The Split Frequencies of Prism Resonator with Up and Down Magnetization
8. 18.8 Exact Calculation of Split Frequencies in Tri‐toroidal Cavity
9. 18.9 Calculation and Experiment
10. 18.10 Tri‐toroidal Composite Prism Resonator
11. 18.11 Tri‐toroidal Wye Resonator with Up and Down Magnetization
12. Bibliography
19 The Waveguide H‐plane Tee Junction Circulator Using a Composite Gyromagnetic Resonator
1. 19.1 Introduction
2. 19.2 Eigenvalue Problem of the H‐plane Reciprocal Tee Junction
3. 19.3 Electrically Symmetric H‐plane Junction at the Altman Planes
4. 19.4 Characteristic Planes
5. 19.5 The Septum‐loaded H‐plane Waveguide
6. 19.6 The Waveguide Tee Junction Using a Dielectric Post Resonator: First Circulation Condition
7. 19.7 The Waveguide Tee Junction Circulator Using a Gyromagnetic Post Resonator: Second Circulation Condition
8. 19.8 Composite Dielectric Resonator
9. Bibliography
20 0°, 90°, and 180° Passive Power Dividers
1. 20.1 Introduction
2. 20.2 Wilkinson Power Divider
3. 20.3 Even and Odd Mode Adjustment of the Wilkinson Power Divider
4. 20.4 Scattering Matrix of 90° Directional Coupler
5. 20.5 Even and Odd Mode Theory of Directional Couplers
6. 20.6 Power Divider Using 90° Hybrids
7. 20.7 Variable Power Dividers
8. 20.8 180° Waveguide Hybrid Network
9. Bibliography
Index
End User License Agreement

List of Illustrations

Chapter 01
1. Figure 1.1 Microwave phase shifter using (a) schematic of circulator switch, (b) SP4T Butler switch using circulators, (c) pin dioded switch and fixed circulator, and (d) switched circulator.
2. Figure 1.2 Standing wave patterns in (a) demagnetized stripline junction and (b) magnetized stripline junction.
3. Figure 1.3 Current and magnetic field in ferrite disc.
4. Figure 1.4 (a) Ferrite unmagnetized; first circulation condition. (b) Ferrite magnetized; second circulation condition.
5. Figure 1.5 Schematic diagram of externally latched circulator using a post‐resonator waveguide junction.
6. Figure 1.6 Schematic diagram of waveguide junction circulator using a partial height: (a) triangular and (b) circular resonator with a wire loop.
7. Figure 1.7 Schematic diagrams of waveguide circulators showing different switching wire configurations.
8. Figure 1.8 Standing wave solution of three‐port circulators using (a) triangular resonator and (b) WYE resonator.
9. Figure 1.9 Typical hysteresis loop of a latching phase shifter operating with a major hysteresis loop switching.
10. Figure 1.10 Schematic diagram of hysteresis display.
11. Figure 1.11 Hysteresis loops showing the effect of gaps in a magnetic circuit. (a) No gap, (b) gap of 2½ thou, (c) gap of 5 thou, and (d) gap of 10 thou.
12. Figure 1.12 Ferrite core with two windings for measuring switching time.
13. Figure 1.13 Reciprocal reversal time 1/T as a function of direct magnetic field H for ferroxcube.
14. Figure 1.14 Up and down direct magnetic field strength in a cylindrical resonator using a single wire loop using a magnetostatic solver (r/R = 0.5, r/R = 0.6, r/R = 0.707) (Helszajn and Sharp 2012).
15. Figure 1.15 Plan view of a cylindrical resonator subdivided in concentric rings.
16. Figure 1.16 Up and down direct magnetic field strength in a cylindrical resonator using a pair of wire loops using a magnetostatic solver (r/R = 0.5, r/R = 0.6, r/R = 0.707) (Helszajn and Sharp 2012).
17. Figure 1.17 Uniform partial gyrotropy in the inner region of a composite gyromagnetic resonator against factor q (ratio of up and down surfaces) with κ_pi = 0.5 (κ₀ = 0.7).
Chapter 02
1. Figure 2.1 Schematic diagrams of normal modes of propagation in longitudinally magnetized ferrite medium.
2. Figure 2.2 Schematic diagrams of Faraday rotation in positive and negative directions of propagation.
3. Figure 2.3 Some waveguides with required symmetry for use in Faraday rotation devices.
4. Figure 2.4 Variation of κ/μ as a function of direct field.
5. Figure 2.5 Schematic diagram of a gyrator network.
6. Figure 2.6 Four‐port differential circulator employing a Faraday gyrator network.
7. Figure 2.7 Equivalent circuit of four‐port circulator.
8. Figure 2.8 Schematic diagram of Faraday rotator isolator.
9. Figure 2.9 Four‐port Faraday rotator circulator.
10. Figure 2.10 Nonreciprocal Faraday rotator phase shifter.
11. Figure 2.11 Circular waveguide containing a coaxial ferrite cylinder.
12. Figure 2.12 Normalized values of propagation constants for TM₁₁ limit mode for ε_r/ε_d = 5, a/λ_d = 0.40 and parametric values of κ.
Chapter 03
1. Figure 3.1 Schematic diagram of a rectangular waveguide.
2. Figure 3.2 Planes of circular polarization in rectangular waveguide for forward direction of propagation.
3. Figure 3.3 Planes of circular polarization in rectangular waveguide for backward direction of propagation.
4. Figure 3.4 Schematic diagram of dielectric loaded parallel plate waveguide with open sidewalls.
5. Figure 3.5 (a–c) Electric and magnetic fields of dielectric‐loaded parallel plate waveguide with open sidewalls (dominant even mode solution) (Cohn 1959).
6. Figure 3.6 Relationship between β/k and (Anderson and Hines 1961).
7. Figure 3.7 (a–c) Electric and magnetic fields of dielectric‐loaded parallel plate waveguide with open sidewalls (dominant odd mode solution) (Cohn 1959).
Chapter 04
1. Figure 4.1 Schematic diagram of quarter‐wave plates using partially filled circular waveguides.
2. Figure 4.2 Schematic diagram of quarter‐wave plate showing port nomenclature.
3. Figure 4.3 Construction of normal modes of a quarter‐wave plate.
4. Figure 4.4 Equivalence between inhomogenous and homogenous circular waveguides.
5. Figure 4.5 Sketch of power absorbed versus resonant frequency for undercoupled critically coupler and overcoupled cavity resonator.
6. Figure 4.6 Effective dielectric constants of round waveguide with polarization perpendicular to dielectric vane versus ε_r for parametric values of H/R.
7. Figure 4.7 Effective dielectric constants of round waveguide with polarization parallel to dielectric vane versus ε_r for parametric values of H/R.
8. Figure 4.8 Input and output waves on half‐wave plate with θ = π/4.
9. Figure 4.9 Rotary vane phase‐shifter.
Chapter 05
1. Figure 5.1 Variation of μ_eff as a function of the direct magnetic field intensity.
2. Figure 5.2 Schematic diagram of square birefringent waveguide showing quadrature magnetic coil arrangement.
3. Figure 5.3 Linear combination of TE₁₀ and TE₀₁ in square waveguide.
4. Figure 5.4 Schematic diagram of round birefringent waveguide showing quadrature magnetic coil arrangement.
5. Figure 5.5 Schematic diagrams of round birefringent waveguides using ferrite slabs.
6. Figure 5.6 (a–d) Equivalent circuits of nonreciprocal quarter‐wave plate.
7. Figure 5.7 (a–d) Equivalent circuits of nonreciprocal quarter‐wave plate (direct magnetic field conditions reversed).
8. Figure 5.8 Nonreciprocal ferrite phase‐shifter using reciprocal and nonreciprocal quarter‐wave plates and birefringent bits.
9. Figure 5.9 Reciprocal ferrite phase‐shifter using reciprocal and nonreciprocal birefringent quarter‐wave and half‐wave birefringent bits.
10. Figure 5.10 Equivalent circuit of nonreciprocal ferrite phase‐shifter.
11. Figure 5.11 Schematic diagram of a switchable circular polarizer.
12. Figure 5.12 Circulator network using 2 two‐mode transducers, a ferrite quarter‐wave plate and a reciprocal quarter‐wave plate.
13. Figure 5.13 Two‐mode transducer and 90° rotator.
14. Figure 5.14 Elliptical Faraday rotator.
15. Figure 5.15 Wave amplitude in two polarizations in elliptical Faraday rotator for (β_x − β_y)/c = 2 and (β_x − β_y)/c = 0.
Chapter 06
1. Figure 6.1 Schematic diagram of nonreciprocal coaxial transmission line.
2. Figure 6.2 Equivalent parallel plate waveguide of partially dielectric‐filled coaxial transmission line.
3. Figure 6.3 Schematic diagram of nonreciprocal coaxial transmission line loaded with metal septum.
4. Figure 6.4 Equivalent parallel waveguides of partially filled coaxial line using conformal mappings.
5. Figure 6.5 Phase constants versus direct magnetic for 100 mm × 2.99 mm × 2 mm long ferrite sheet (M₀ 0.0800 T) (Helszajn 1982).
6. Figure 6.6 Ferrimagnetic resonance in a half dielectric‐filled coaxial line loaded by garnet sheets (70 mm long by 0.80 mm × 2.0 mm) (Helszajn 1982).
7. Figure 6.7 Schematic diagram of ridge waveguide phase‐shifter.
8. Figure 6.8 Differential phase‐shift in WRD200 ridge waveguide (Hastings and Helszajn 1987).
9. Figure 6.9 Photograph of ridge waveguide differential phase‐shift circulator.
10. Figure 6.10 Schematic diagram of edge mode stripline phase‐shifter.
11. Figure 6.11 Schematic diagram of nonreciprocal ridge waveguide using closed ferrite magnetic circuits.
12. Figure 6.12 Schematic diagram of nonreciprocal stripline using closed ferrite magnetic circuits.
Chapter 07
1. Figure 7.1 Rectangular waveguide phase‐shifters: (a) loaded with a ferrite slab and (b) symmetrically loaded with two oppositely magnetized ferrite slabs.
2. Figure 7.2 Toroidal phase‐shifter in rectangular waveguide.
3. Figure 7.3 Typical tetrahedral finite element.
4. Figure 7.4 Discretization of waveguide loaded with a ferrite slab.
5. Figure 7.5 Dielectric‐loaded rectangular waveguide.
6. Figure 7.6 LS modes in dielectric‐loaded rectangular waveguide: (a) ε_d = 6.5 and (b) ε_d = 16.0.
7. Figure 7.7 Cutoff numbers of twin slab ferrite phase‐shifter ε_f = 16: (a) ε_d = 6.5 and (b) ε_d = 11.
8. Figure 7.8 Split phase constants of a twin slab ferrite phase‐shifter (ε_d = 1).
9. Figure 7.9 Coordinate system of rectangular waveguide loaded with two ferrite slabs.
10. Figure 7.10 Differential phase in twin slab ferrite phase‐shifter versus gyrotropy (ε_d = 1).
11. Figure 7.11 Differential phase in toroidal phase‐shifter versus gyrotropy.
12. Figure 7.12 Matching between dielectric loaded and regular waveguides.
13. Figure 7.13 A practical approach for avoidance of the propagation of higher‐order modes in a ferrite phase‐shifter.
14. Figure 7.14 Plan view of a 4‐bit toroidal phase‐shifter in undersized waveguide.
15. Figure 7.15 Block diagram of a typical electronic driver circuit for a multi‐toroid latching waveguide phase‐shifter.
16. Figure 7.16 Typical hysteresis loop of a latching phase‐shifter operating with a major loop switching.
17. Figure 7.17 Major B–H loop characteristics of YIG at several temperatures.
18. Figure 7.18 Major and minor B–H loops of nickel–cobalt ferrite at 25 °C.
19. Figure 7.19 Maximum flux composite circuit versus temperature.
Chapter 08
1. Figure 8.1 Schematic diagram of (a) an air–ferrite–air parallel edge mode prototype with magnetic sidewalls and (b) a four‐region edge mode parallel plate waveguide with magnetic sidewalls.
2. Figure 8.2 Field and power distribution in an air–ferrite–air edge mode prototype with magnetic sidewalls for propagation in (a) the forward direction and (b) the reverse direction with k₀a = 0.50, c/a = 2, ε_f = 15, and κ = − 0.40.
3. Figure 8.3 Quality of circular polarization versus frequency and k₀ for an air–ferrite–air edge mode prototype with c/a = 2.
4. Figure 8.4 Normalized differential phase‐shift for an air–ferrite–dielectric–air parallel plate edge mode waveguide with magnetic sidewalls with ε_f = 15, ε_d = 25, a/b = 4, c/(a + b) = 2, and parametric values of κ.
5. Figure 8.5 Frequency response of air–ferrite–dielectric–air edge mode differential phase‐shifter with magnetic sidewalls with ε_f = 15, ε_d = 25, a/b = 4, c/(a + b) = 2, and parametric values of ε_d.
6. Figure 8.6 Field and power distributions in an air–ferrite–dielectric–air parallel plate edge mode waveguide with magnetic sidewalls for propagation in (a) the forward direction and (b) the reverse direction with k₀a = 0.40, k₀b = 0.10, c/(a + b) = 2, ε_f = 15, ε_d = 25, and κ = − 0.40.
7. Figure 8.7 Differential phase‐shift for an air–ferrite–dielectric–air parallel plate edge mode waveguide with magnetic sidewalls with ε = 15, ε_d = 15, k₀a = 2.5, a/b = 4, and c/(a + b) = 2.
8. Figure 8.8 Edge mode (a) isolator, (b) phase‐shifter, (c) three‐port circulator, and (d) four‐port circulator.
Chapter 09
1. Figure 9.1 Two‐port H‐plane waveguide reflection switches using reentrant (a) and inverted reentrant (b) single quarter‐wave‐long gyromagnetic resonators.
2. Figure 9.2 H‐plane series tee junction.
3. Figure 9.3 Lumped element models of H‐plane switches: (a) demagnetized and (b) magnetized resonators.
4. Figure 9.4 E‐plane waveguide tee junction: (a) odd eigenvector and (b) even eigenvector.
5. Figure 9.5 Plan view of even and odd eigen‐networks of an H‐plane two‐port reflection switch.
6. Figure 9.6 (a) Even mode demagnetized eigen‐network. (b) Odd mode demagnetized eigen‐network.
7. Figure 9.7 (a) Even mode magnetized eigen‐network. (b) Odd mode magnetized eigen‐network.
8. Figure 9.8 (a) Comparison between calculated and experimental passband return loss and insertion loss (R/L = 2.0, k₀R = 0.807, q_eff = 0.5364) (Helszajn et al. 2010). (b) Experimental stopband frequency response of two‐port on–off gyromagnetic switch (B₀/μ₀M₀ = 0.34) (Helszajn et al. 2010).
9. Figure 9.9 Off and On circuits of H‐plane switches using 180° long (a) demagnetized and (b) magnetized resonators.
Chapter 10
1. Figure 10.1 Schematic diagrams of reentrant and inverted reentrant ferrite switches using (a) E‐plane tee junctions and (b) H‐plane tee junctions.
2. Figure 10.2 Shunt E‐plane tee junction.
3. Figure 10.3 (a) E‐plane stop band (demagnetized). (b) E‐plane pass band (magnetized).
4. Figure 10.4 (a) E‐plane pass band (demagnetized). (b) E‐plane stop band (magnetized).
5. Figure 10.5 H‐plane waveguide tee junction: (a) odd eigenvector and (b) even eigenvector.
6. Figure 10.6 (a–d) Operation of the two‐port off/on E‐plane switch.
7. Figure 10.7 (a–d) Operation of the two‐port on/off E‐plane switch.
8. Figure 10.8 (a–d) Even and odd eigenvalue diagrams of two‐port E‐plane switches at a reflection plane 90° away from the symmetry plane.
9. Figure 10.9 (a) Schematic diagram of reentrant switch using E‐plane tee junction. (b) Symmetry plane of reentrant switch using E‐plane tee junction. (c) Odd mode eigen‐network. (d) Even mode eigen‐network.
10. Figure 10.10 Eigen‐networks of demagnetized E‐plane junction.
11. Figure 10.11 Eigen‐networks of magnetized E‐plane junction.
12. Figure 10.12 (a) Stop band frequency response of demagnetized large‐gap E‐plane junction (Helszajn et al. unpublished). (b) Pass band frequency response of demagnetized small gap H‐plane junction (Helszajn et al. unpublished).
Chapter 11
1. Figure 11.1 Mutual impedance (Z_ij) in two‐port planar circuit with magnetic sidewalls.
2. Figure 11.2 Problem region defined by (a) and (b)
3. Figure 11.3 Mutual admittance (Y_ij) in two‐port planar circuit with magnetic sidewalls.
4. Figure 11.4 Problem region defined by (a) and (b)
5. Figure 11.5 n‐Port problem region defined by
6. Figure 11.6 Topology of two‐port isotropic stripline band elimination filter.
7. Figure 11.7 Decomposition of band elimination filter into 2 one‐port circuits for evaluation of admittance matrix.
8. Figure 11.8 Transmission coefficient of stripline band elimination filter (R = 19.06 mm, H = 3.2 mm, W = 7.78 mm, ε_f = 2.4).
9. Figure 11.9 Finite element mesh used in solution of stripline band elimination filter.
10. Figure 11.10 Topology of two‐port gyromagnetic dipolar switch.
11. Figure 11.11 Decomposition of band elimination filter into 2 one‐port circuits for evaluation of admittance matrix.
12. Figure 11.12 Finite element mesh used in solution of stripline dipolar switch.
13. Figure 11.13 Reflection coefficient for two‐port dipolar switch for κ/μ = 1 using mutual energy and mode‐matching formulations.
14. Figure 11.14 Transmission coefficient for two‐port dipolar switch for κ/μ = 1 using mutual energy and mode‐matching formulations.
15. Figure 11.15 Schematic diagram of two‐port stripline on/off switch using puck and plug half‐spaces.
16. Figure 11.16 (a) Reflection and transmission parameters of the demagnetized switch, (b) magnitude of even and odd eigenvalues, (c) phase of even and odd eigenvalues, and (d) eigenvalue diagram.
Chapter 12
1. Figure 12.1 Schematic diagram of wye resonator.
2. Figure 12.2 Segmentation of wye resonator into finite elements.
3. Figure 12.3 Equipotential lines of dominant mode in wye resonator.
4. Figure 12.4 (a) First symmetric mode in wye resonator and (b) first higher‐order dominant mode in wye resonator.
5. Figure 12.5 Equipotential lines of dominant mode in wye circulator.
6. Figure 12.6 Circulation terminals of wye resonator for (a) “aa” terminals and (b) “bb” terminals.
7. Figure 12.7 Schematic diagram of quasi‐wye resonator using a circular disc loaded with UEs.
8. Figure 12.8 Cutoff wavenumber of the fundamental mode in a demagnetized wye resonator.
9. Figure 12.9 Comparison between closed form and FEM calculations of cutoff space of wye resonator.
10. Figure 12.10 Split frequencies of planar gyromagnetic wye resonator in kR space using closed‐form formulation (ψ = 0.20 rad, R_i/R₀ = 0.20, 0.40, and 0.60).
11. Figure 12.11 Split frequencies of planar gyromagnetic wye resonator in kR space using closed‐form formulation (ψ = 0.20 rad, R_i/R₀ = 0.20, 0.40, and 0.60).
12. Figure 12.12 Schematic of microstrip triangular resonator.
13. Figure 12.13 (a) Magnetic field pattern for dominant mode and (b) lines of equipotential (A_1,0,−1 = 1).
14. Figure 12.14 Schematic diagrams of waveguide circulators using quarter‐wave‐coupled triangular resonators.
15. Figure 12.15 Standing wave solutions of waveguide circulator using a triangular resonator.
Chapter 13
1. Figure 13.1 Reciprocal four‐port turnstile junction.
2. Figure 13.2 Nonreciprocal four‐port turnstile junction.
3. Figure 13.3 H‐plane turnstile junction circulator.
4. Figure 13.4 Schematic diagram of three‐port E‐plane turnstile circulator using single turnstile resonator.
5. Figure 13.5 Eigen‐solutions of the three‐port circulator.
6. Figure 13.6 Eigenvalue diagram of reciprocal three‐port junction for maximum power transfer.
7. Figure 13.7 Eigenvalue diagram of ideal three‐port junction circulator.
8. Figure 13.8 Equivalence between open dielectric waveguide with imperfect magnetic walls and equivalent waveguide model with idealized walls.
9. Figure 13.9 Effective dielectric constant of open dielectric waveguide.
10. Figure 13.10 Schematic diagram of a practical gyromagnetic resonator.
11. Figure 13.11 (a) Schematic diagram of half‐wave long open ferrite or dielectric resonator loaded by image wall. (b) Schematic diagram of coupled quarter‐wave long ferrite or dielectric resonators loaded by image wall.
12. Figure 13.12 Circuit topology of closed composite gyromagnetic resonator.
13. Figure 13.13 Quarter‐wave coupled turnstile junctions using single (a) and pair (b) of quarter‐wave long resonators.
14. Figure 13.14 In‐phase eigen‐network of the three‐port junction circulator.
Chapter 14
1. Figure 14.1 (a) Schematic diagram of waveguide junction circulators using single turnstile resonators. (b) Reentrant turnstile junction using a quarter‐wave long resonator. (c) Inverted reentrant turnstile junction using a quarter‐wave long resonator. (d) Reentrant turnstile junction using a pair of quarter‐wave long resonators. (e) Inverted turnstile junction using a pair of quarter‐wave long resonators.
2. Figure 14.2 Definition of complex gyrator circuit.
3. Figure 14.3 Eigenvalue diagram of reciprocal three‐port junction for maximum power transfer.
4. Figure 14.4 Eigenvalue diagram of ideal three‐port junction circulator.
5. Figure 14.5 Comparison between perturbation and numerical solutions in the case of a circular gyromagnetic waveguide with an ideal magnetic wall.
6. Figure 14.6 Eigen‐networks of reentrant and inverted reentrant turnstile circulators using (a) single quarter‐wave long resonator and (b) doublets of quarter‐wave long resonators.
Chapter 15
1. Figure 15.1 Schematic diagrams of waveguide junction circulators using single turnstile resonators.
2. Figure 15.2 Schematic diagram of integrated substrate waveguide circulator using turnstile resonators.
3. Figure 15.3 (a–c) Eigenvalue diagrams of reciprocal three‐port junction.
4. Figure 15.4 Construction of reference terminals of resonator: (a) reflection coefficient and (b) transmission coefficient.
5. Figure 15.5 k ₀ R versus q_± of inverted reentrant turnstile junction in half‐height WR75 waveguide for counterrotating mode (f₀/f_c = 1.683, R/L = 2.0).
6. Figure 15.6 k ₀ R versus q₀ of inverted reentrant turnstile junction in half‐height WR75 waveguide for in‐phase mode (f₀/f_c = 1.683, R/L = 2.0).
7. Figure 15.7 Flowchart for the solution of either s₀ = −1 or s_± = 1 at the resonator edge.
8. Figure 15.8 First circulation condition of inverted reentrant turnstile junction in half‐height WR75 waveguide (f₀/f_c = 1.683, R/L = 2.0).
9. Figure 15.9 Flowchart algorithm for first circulation condition.
10. Figure 15.10 Smith chart of the first circulation condition of inverted reentrant turnstile junction in half‐height WR75 waveguide (f₀/f_c = 1.683, R/L = 2.0).
11. Figure 15.11 Smith chart of reentrant turnstile junction in standard WR75 waveguide (f₀/f_c = 1.683, R/L = 2.0).
12. Figure 15.12 Comparison between calculated (‐‐‐) and experimental (––) frequency response of reentrant turnstile junction in WR75 waveguide at each port.
13. Figure 15.13 Frequency response of first circulation condition of inverted reentrant turnstile junction in half‐height WR75 waveguide (f₀/f_c = 1.683, R/L = 2.0).
14. Figure 15.14 Eigenvalue diagrams associated with scalar counterrotating permeabilities.
15. Figure 15.15 9½ dB frequencies corresponding to μ_d = 1.0 and μ_± = 0.7, 1.3.
16. Figure 15.16 Return loss at port 1 of inverted reentrant turnstile circulator in half‐height WR75 waveguide for parametric values of normalized magnetization in saturated magnetic insulator.
Chapter 16
1. Figure 16.1 Schematic diagram of E‐plane junction.
2. Figure 16.2 (a–c) Electrical field pattern across the narrow dimension of an E‐plane waveguide wye junction with the generator sitting at port 3.
3. Figure 16.3 (a–d) Eigenvalue diagrams of the three‐port symmetrical junction circulator (90° away from axis of junction).
4. Figure 16.4 Eigen‐networks of the H‐plane circulator (a, b), and that of the E‐plane circulator (c, d).
5. Figure 16.5 Schematic diagram of E‐plane wye junction showing the positions of the characteristic planes.
6. Figure 16.6 Schematic diagram of E‐plane prism circulator using (a) coupled quarter‐wave long resonators and (b) single quarter‐wave long resonator.
7. Figure 16.7 Schematic diagram of E‐plane cylindrical circulator using (a) coupled quarter‐wave long resonators and (b) single quarter‐wave long resonator.
8. Figure 16.8 Schematic diagram of (a) the in‐phase eigen‐network and (b) the counterrotating eigen‐network.
9. Figure 16.9 Smith chart of small gap in‐phase reflection eigenvalue ρ₁.
Chapter 17
1. Figure 17.1 Schematic diagram of a junction circulator using a latched prism resonator.
2. Figure 17.2 Geometry of tri‐toroidal prism resonator.
3. Figure 17.3 Experimental split frequencies of prism resonators (μ₀M₀ = 0.0800 T and 0.1200 T).
4. Figure 17.4 Experimental connection between q and k_f in prism resonator with up and down magnetization.
5. Figure 17.5 Photograph of switch resonator.
6. Figure 17.6 Experimental split frequencies of wire‐operated half‐wave long prism resonator with up and down magnetization (μ₀M_s = 0.1200 T).
7. Figure 17.7 One‐port complex gyrator circuit of junction circulator.
8. Figure 17.8 Normalized conductance of wired junction.
9. Figure 17.9 Quality factor of wired junction.
10. Figure 17.10 Topology of alternate line‐matched complex gyrator of junction circulator.
Chapter 18
1. Figure 18.1 Topologies of two half‐wave long gyromagnetic resonators.
2. Figure 18.2 (a–c) Schematic diagrams of waveguide circulators showing different switching wire configurations.
3. Figure 18.3 Practical configurations met in the design of latched prism cavities.
4. Figure 18.4 Tri‐toroidal gyromagnetic cavity.
5. Figure 18.5 Split frequencies of up and down magnetized tri‐toroidal prism resonator for parametric values of shape factor (q = 1, 3, 6 and ∞).
6. Figure 18.6 Uniform up and down magnetizations in a planar resonator with top and bottom electric walls, and a magnetic sidewall, for q = 1 and q = 6.
7. Figure 18.7 Discretization of prism resonator.
8. Figure 18.8 Magnetic flux density in prism resonator latched by wire loops: (a) q = 1, (b) q = 3, and (c) q = 6.
9. Figure 18.9 Exact split frequencies versus q in latched prism resonator.
10. Figure 18.10 k _f versus q in latched prism resonator (simulation: ▴ up/down magnetization, ● exact; ■ experiment).
11. Figure 18.11 Q_eff versus q in latched composite prism resonator (M₂ = 0).
12. Figure 18.12 Tri‐toroidal wye resonator.
13. Figure 18.13 First wire configuration.
Chapter 19
1. Figure 19.1 H‐plane waveguide tee junction indicating the position of Dicke’s planes.
2. Figure 19.2 Standing wave solutions produced by eigenvectors of waveguide tee junction (arbitrary plane).
3. Figure 19.3 Eigenvalue diagram of electrically symmetrical H‐plane waveguide tee junction at its characteristic planes.
4. Figure 19.4 Definition of characteristic planes.
5. Figure 19.5 Standing wave patterns produced by pistons at the characteristic planes of the junction.
6. Figure 19.6 Inductive vane‐loaded H‐plane tee junction.
7. Figure 19.7 Standing wave solution of H‐plane waveguide tee junction with symmetry vane (s/a = 0.25).
8. Figure 19.8 Experimental results of fabricated H‐plane tee junction.
9. Figure 19.9 Topology of H‐plane waveguide tee junction using a dielectric post resonator.
10. Figure 19.10 Return loss at port 3 versus frequency for parametric values of d₀/a.
11. Figure 19.11 Return loss at ports 1 and 2 versus frequency for parametric values of d₀/a.
12. Figure 19.12 Experimental frequency response of tee junction circulator.
13. Figure 19.13 Standing wave solution of turnstile circulator with a gyromagnetic resonator.
14. Figure 19.14 Radial composite resonator.
15. Figure 19.15 Split frequencies for ring stripline junction circulator.
Chapter 20
1. Figure 20.1 Ideal Wilkinson two‐way power divider.
2. Figure 20.2 Circuit diagram of Wilkinson two‐way power divider.
3. Figure 20.3 (a) In‐phase and (b) out‐of‐phase circuits of Wilkinson two‐way power divider.
4. Figure 20.4 Schematic diagram of microstrip branch line coupler.
5. Figure 20.5 Schematic diagram of microstrip multi‐branch coupler.
6. Figure 20.6 (a) Even and (b) odd mode circuits for branch line coupler.
7. Figure 20.7 Butler network.
8. Figure 20.8 Use of Butler networks in phased array equipment: (a) nondistributed (passive), (b) semidistributed and (c) fully distributed (active).
9. Figure 20.9 (a) Four‐channel Butler switch. (b) Phase setting for n = 4 Butler switch.
10. Figure 20.10 (a) Four‐channel hybrid matrix switch. (b) Phase setting for n = 4 hybrid network switch.
11. Figure 20.11 Symmetry plane of Magic‐Tee.
12. Figure 20.12 Power divider using 3 dB hybrids and variable phase‐shifter.