Ridge waveguides and passive microwave components
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Contents
Preface xiii
1 The ridge waveguide 1
1.1 Introduction 1
1.2 Cut-off space of ridge waveguide 1
1.3 Impedance of ridge waveguide 3
1.4 Attenuation of ridge waveguide 4
1.5 Ridge waveguide junctions 5
1.6 Waveguide transitions 10
1.7 Filter circuits . 11
1.8 Turnstile junction circulator 11
2 Propagation and impedance in rectangular waveguides 13
2.1 Introduction 13
2.2 The wave equation 13
2.3 Dominant mode in rectangular waveguides 14
2.4 Impedance in waveguides 15
2.5 Power transmission through rectangular waveguides 17
2.6 Impedance in rectangular waveguides 18
2.7 Circular polarisation in rectangular waveguides 19
2.8 Calculation of impedance based on a mathematical
technique 22
2.9 Orthogonal properties of waveguide modes 24
3 Impedance and propagation in ridge waveguides using the
transverse resonance method 26
J. Helszajn and M. Caplin
3.1 Introduction 26
3.2 Cut-off space of ridge waveguide 26
3.3 Power flow in ridge waveguide
3.4 Voltage-current definition of impedance in ridge waveguide
3.5 Power-voltage definition of impedance in ridge waveguide
3.6 Power-current definition of impedance in ridge waveguide
3.7 Admittances of double ridge waveguide
3.8 Closed form polynomials for single and double ridge waveguides
3.9 Synthesis of quarter-wave ridge transformers
4 Fields, propagation and attenuation in double ridge waveguide
4.1 Introduction
4.2 Finite element calculation (TE modes)
4.3 Finite element method (TM modes)
4.4 Cut-off space (TE mode)
4.5 Standing wave solution in double ridge waveguide
4.6 TE fields in double ridge waveguide
4.7 TM fields in double ridge waveguide
4.8 MFIE
4.9 The Poynting vector
4.10 Attenuation in waveguides
5 Impedance of double ridge waveguide using the finite element method
J. Helszajn and M. McKay
5.1 Introduction
5.2 Voltage-current definition of impedance
5.3 Calculation of voltage-current definition of impedance
5.4 Power-current and power-voltage definitions of impedance
5.5 Impedance of ridge waveguide using trapezoidal ribs
6 Characterisation of single ridge waveguide using the finite element method
M. McKay and J. Helszajn
6.1 Introduction
6.2 Cut-off space of single ridge waveguide
6.3 Fields in single ridge waveguide
6.4 Impedance of single ridge waveguide
6.5 Insertion loss in single ridge waveguide
6.6 Higher order modes
7 Propagation constant and impedance of dielectric loaded ridge
waveguide using a hybrid finite element solver 83
M. McKay and J. Helszajn
7.1 Introduction 83
7.2 Hybrid functional 84
7.3 Cut-off space of dielectric loaded rectangular ridge
waveguide 88
7.4 Propagation constant in dielectric loaded rectangular ridge
waveguide 90
7.5 Propagation constant in dielectric loaded square waveguide 91
7.6 Voltage-current definition of impedance 92
8 Circular polarisation in ridge and dielectric loaded ridge waveguides 99
8.1 Introduction 99
8.2 Circular polarisation 100
8.3 Open half-space of asymmetrically dielectric loaded ridge
waveguide 100
8.4 Circular polarisation in dielectric-loaded parallel plate
waveguides with open side-walls 102
8.5 Circular polarisation in dielectric loaded ridge waveguide 105
8.6 Circular polarisation in homogeneous ridge waveguide 107
9 Quadruple ridge waveguide 11 7
9.1 Introduction ' 117
9.2 Quadruple ridge waveguide 117
9.3 Cut-off space in quadruple ridge waveguide using MFIE
method 119
9.4 Cut-off space of ridge waveguide using MMM 121
9.5 Cut-off space of quadruple ridge waveguide using FEM 121
9.6 Fields in quadruple ridge waveguide 126
9.7 Cut-off space of dielectric loaded quadruple ridge
waveguide 127
9.8 Impedance in quadruple ridge circular waveguide using
conical ridges 132
10 Faraday rotation in gyromagnetic quadruple ridge waveguide 134
10.1 Introduction 134
10.2 Faraday rotation section 135
10.3 Scattering matrix of Faraday rotation section 138
Ю.4 Gyrator network 139
10.5 Gyromagnetic waveguide functional 141
10.6 Ridge waveguide using gyromagnetic ring 144
10.7 Quadruple ridge waveguide using gyromagnetic tiles 144
10.8 Faraday rotation isolator 145
10.9 Four-port Faraday rotation circulator 148
10.10 Nonreciprocal Faraday rotation-type phase shifter 148
10.11 Faraday rotation in dual-mode triple ridge waveguide 149
11 Characterisation of discontinuity effects in single ridge waveguide 153
11.1 Introduction 153
11.2 ABCD parameters of 2-port step discontinuity 154
11.3 Frequency response 157
11.4 Characterisation of half-wave long ridge waveguide test-set 157
11.5 Experimental characterisation 160
11.6 Symmetrical short section 163
12 Ridge cross-guide directional coupler 170
M. McKay and J. Helszajn
12.1 Introduction 170
12.2 Operation of cross-guide directional coupler 170
12.3 Bethe’s small-hole coupling theory 173
12.4 The 0-degree crossed-slot aperture 175
12.5 The 0-degree crossed-slot aperture in rectangular waveguide 177
12.6 The 0-degree crossed-slot aperture in single ridge waveguide 178
12.7 The 45-degree crossed-slot aperture 179
12.8 Circular polarisation in rectangular and ridge waveguides 181
12.9 Rectangular and ridge waveguide cross-guide couplers
using 45-degree crossed-slot apertures 182
12.10 Coupling via waveguide walls of finite thickness 184
13 Directly coupled filter circuits using immittance inverters 189
13.1 Introduction 189
13.2 Immittance inverters 189
13.3 Lowpass filters using immittance inverters 190
13.4 Bandpass filters using immittance inverters 193
13.5 Immittance inverters 195
13.6 Practical inverter 198
13.7 Immittance inverters using evanescent mode waveguide 200
13.8 E-plane filter 201
13.9 Element values of lowpass prototypes 204
13.10 Frequency response of microwave filters 205
14 Ridge waveguide filter design using mode matching method 207
M. McKay and J. Helszajn
14.1 Introduction 207
14.2 Mode matching method 207
14.3 MMM characterisation of 1-port networks 212
14.4 Double septa and thick septum problem regions 215
14.5 MMM characterisation of symmetrical waveguide
discontinuities 216
14.6 Eigensolutions of waveguide sections 218
14.7 Immittance inverters 221
14.8 E-plane bandpass filters using metal inverters 221
14.9 Lowpass ridge filters using immittance inverters 222
15 Nonreciprocal ridge isolators and phase-shifters 226
15.1 Introduction 226
15.2 Nonreciprocal ferrite devices in rectangular waveguide 227
15.3 Differential phase shift, phase deviation and figure of merit
of ferrite phase shifter 230
15.4 90-degree phase shifter in dielectric loaded WRD 200 ridge
waveguide 231
15.5 Isolation, insertion loss and figure of merit of resonance
isolator 233
15.6 Resonance isolator in dielectric loaded WRD 750 ridge
waveguide 234
15.7 Resonance isolator in bifurcated ridge waveguide 236
15.8 Differential phase shift circulator 238
16 Finline waveguide 241
16.1 Introduction 241
16.2 Finline waveguide topologies 241
16.3 Normalised wavelength and impedance in finline 242
16.4 Empirical expressions for propagation in bilateral and
unilateral finline 245
16.5 Fields in unilateral finline waveguide 247
16.6 Bilateral finline 250
16.7 Empirical formulation of impedance in bilateral finline
waveguide 251
16.8 Circular polarisation in bilateral and unilateral finline
waveguides 251
16.9 Finline isolator using hexagonal ferrite substrate 251
17 Inverted turnstile finline junction circulator 256
17.1 Introduction 256
17.2 Turnstile junction circulator 256
17.3 Re-entrant H-plane waveguide circulator 261
17.4 Re-entrant E-plane waveguide circulator 262
17.5 Closed gyromagnetic resonator 262
17.6 Perturbation theory of closed cylindrical gyromagnetic
resonator 264
17.7 Quality factor of closed gyromagnetic x-esonator 266
17.8 E-plane finline circulator using coupled H-plane turnstile
resonators 266
17.9 Experimental adjustment of finline turnstile circulator 268
18 Semi-tracking ridge circulator 270
18.1 Introduction 270
18.2 Phenomenological adjustment 271
18.3 Impedance matrix 272
18.4 Complex gyrator circuit 277
18.5 Semi-tracking complex gyrator circuit 278
18.6 Direct magnetic field and magnetisation of semi-tracking
circulators 281
18.7 Physical variables of semi-tracking circulators 285
18.8 Network problem 285
18.9 Frequency response 287
18.10 Design of octave-band semi-tracking circulators 294
19 V ariational calculus, functionals and the Rayleigh-Ritz procedure 296
19.1 Introduction 296
19.2 Stationary value of functional 297
19.3 Electrical and magnetic energies in planar circuits 298
19.4 Electric and magnetic fields in planar circuits with top and
bottom electric walls 299
19.5 Derivation of functional for planar isotropic circuits 301
19.6 Rayleigh-Ritz procedure 303
19.7 Field patterns 305
19.8 Derivation of energy functional based on a mathematical
technique 306
Bibliography 308
Index 322
