Ridge waveguides and passive microwave components

The ridge waveguide, which is a rectangular waveguide with one or more metal inserts (ridges), is an important transmission line in microwave engineering, through which many passive components can be achieved. As such it is a well-established and widely used element in commercial electronics and communications devices. This book collects together much of the work of Professor Helszajn, an international authoriy in the field, and will enable the reader to have direct access to this material without need for exhaustive search of research papers. Generously illustrated, it is likely to become the definitive reference source on this topic. The book includes closed-form and finite element calculations of the propagation constant, attenuation and mode spectrum for the ridge waveguide, as well as power-current and power-voltage definitions of impedance. Circular polarisation is also treated. Propagation properties where the waveguide has a dielectric filler are calculated. The treatment is then extended to more complex designs, including quadruple ridge waveguides with and without a gyromagnetic filler. The text includes descriptions of many of the passive devices which can be realised using these waveguides, including isolators, phase shifters and circulators. A treatment of the finline waveguide is included as its geometry is closely related to that of the ridge waveguide, leading to components such as the 3-port finline calculator.

ended to more complex designs, including quadruple ridge waveguides with and without a gyromagnetic filler. The text includes descriptions of many of the passive devices which can be realised using these waveguides, including isolators, phase shifters and circulators. A treatment of the finline waveguide is included as its geometry is closely related to that of the ridge waveguide, leading to components such as the 3-port finline calculator.ended to more complex designs, including quadruple ridge waveguides with and without a gyromagnetic filler. The text includes descriptions of many of the passive devices which can be realised using these waveguides, including isolators, phase shifters and circulators. A treatment of the finline waveguide is included as its geometry is closely related to that of the ridge waveguide, leading to components such as the 3-port finline calculator.ended to more complex designs, including quadruple ridge waveguides with and without a gyromagnetic filler. The text includes descriptions of many of the passive devices which can be realised using these waveguides, including isolators, phase shifters and circulators. A treatment of the finline waveguide is included as its geometry is closely related to that of the ridge waveguide, leading to components such as the 3-port finline calculator.

Author Notes

Professor Joseph Helszajn OBE is an international authority on non-reciprocal microwave circuits and devices. After industrial experience in the USA he obtained his PhD from the University of Leeds and spent much of his academic career at Heriot-Watt University, where he founded its microwave laboratory. A Fellow of the IEE and IEEE, he acted as an Honorary Editor of the IEE Proceedings for 18 years and has published 11 books. In 1995 he was awarded the IEE JJ Thomson Medal.

J. Helszajn and M. CaplinJ. Helszajn and M. McKayM. McKay and J. HelszajnM. McKay and J. HelszajnM. McKay and J. HelszajnM. McKay and J. Helszajn

Preface	p. xiii
1 The ridge waveguide	p. 1
1.1 Introduction	p. 1
1.2 Cut-off space of ridge waveguide	p. 1
1.3 Impedance of ridge waveguide	p. 3
1.4 Attenuation of ridge waveguide	p. 4
1.5 Ridge waveguide junctions	p. 5
1.6 Waveguide transitions	p. 10
1.7 Filter circuits	p. 11
1.8 Turnstile junction circulator	p. 11
2 Propagation and impedance in rectangular waveguides	p. 13
2.1 Introduction	p. 13
2.2 The wave equation	p. 13
2.3 Dominant mode in rectangular waveguides	p. 14
2.4 Impedance in waveguides	p. 15
2.5 Power transmission through rectangular waveguides	p. 17
2.6 Impedance in rectangular waveguides	p. 18
2.7 Circular polarisation in rectangular waveguides	p. 19
2.8 Calculation of impedance based on a mathematical technique	p. 22
2.9 Orthogonal properties of waveguide modes	p. 24
3 Impedance and propagation in ridge waveguides using the transverse resonance method	p. 26
3.1 Introduction	p. 26
3.2 Cut-off space of ridge waveguide	p. 26
3.3 Power flow in ridge waveguide	p. 31
3.4 Voltage-current definition of impedance in ridge waveguide	p. 31
3.5 Power-voltage definition of impedance in ridge waveguide	p. 32
3.6 Power-current definition of impedance in ridge waveguide	p. 33
3.7 Admittances of double ridge waveguide	p. 34
3.8 Closed form polynomials for single and double ridge waveguides	p. 35
3.9 Synthesis of quarter-wave ridge transformers	p. 38
4 Fields, propagation and attenuation in double ridge waveguide	p. 47
4.1 Introduction	p. 47
4.2 Finite element calculation (TE modes)	p. 47
4.3 Finite element method (TM modes)	p. 50
4.4 Cut-off space (TE mode)	p. 50
4.5 Standing wave solution in double ridge waveguide	p. 52
4.6 TE fields in double ridge waveguide	p. 54
4.7 TM fields in double ridge waveguide	p. 56
4.8 MFIE	p. 59
4.9 The Poynting vector	p. 61
4.10 Attenuation in waveguides	p. 61
5 Impedance of double ridge waveguide using the finite element method	p. 63
5.1 Introduction	p. 63
5.2 Voltage-current definition of impedance	p. 64
5.3 Calculation of voltage-current definition of impedance	p. 66
5.4 Power-current and power-voltage definitions of impedance	p. 67
5.5 Impedance of ridge waveguide using trapezoidal ribs	p. 71
6 Characterisation of single ridge waveguide using the finite element method	p. 73
6.1 Introduction	p. 73
6.2 Cut-off space of single ridge waveguide	p. 74
6.3 Fields in single ridge waveguide	p. 75
6.4 Impedance of single ridge waveguide	p. 78
6.5 Insertion loss in single ridge waveguide	p. 79
6.6 Higher order modes	p. 80
7 Propagation constant and impedance of dielectric loaded ridge waveguide using a hybrid finite element solver	p. 83
7.1 Introduction	p. 83
7.2 Hybrid functional	p. 84
7.3 Cut-off space of dielectric loaded rectangular ridge waveguide	p. 88
7.4 Propagation constant in dielectric loaded rectangular ridge waveguide	p. 90
7.5 Propagation constant in dielectric loaded square waveguide	p. 91
7.6 Voltage-current definition of impedance	p. 92
8 Circular polarisation in ridge and dielectric loaded ridge waveguides	p. 99
8.1 Introduction	p. 99
8.2 Circular polarisation	p. 100
8.3 Open half-space of asymmetrically dielectric loaded ridge waveguide	p. 100
8.4 Circular polarisation in dielectric-loaded parallel plate waveguides with open side-walls	p. 102
8.5 Circular polarisation in dielectric loaded ridge waveguide	p. 105
8.6 Circular polarisation in homogeneous ridge waveguide	p. 107
9 Quadruple ridge waveguide	p. 117
9.1 Introduction	p. 117
9.2 Quadruple ridge waveguide	p. 117
9.3 Cut-off space in quadruple ridge waveguide using MFIE method	p. 119
9.4 Cut-off space of ridge waveguide using MMM	p. 121
9.5 Cut-off space of quadruple ridge waveguide using FEM	p. 121
9.6 Fields in quadruple ridge waveguide	p. 126
9.7 Cut-off space of dielectric loaded quadruple ridge waveguide	p. 127
9.8 Impedance in quadruple ridge circular waveguide using conical ridges	p. 132
10 Faraday rotation in gyromagnetic quadruple ridge waveguide	p. 134
10.1 Introduction	p. 134
10.2 Faraday rotation section	p. 135
10.3 Scattering matrix of Faraday rotation section	p. 138
10.4 Gyrator network	p. 139
10.5 Gyromagnetic waveguide functional	p. 141
10.6 Ridge waveguide using gyromagnetic ring	p. 144
10.7 Quadruple ridge waveguide using gyromagnetic tiles	p. 144
10.8 Faraday rotation isolator	p. 145
10.9 Four-port Faraday rotation circulator	p. 148
10.10 Nonreciprocal Faraday rotation-type phase shifter	p. 148
10.11 Faraday rotation in dual-mode triple ridge waveguide	p. 149
11 Characterisation of discontinuity effects in single ridge waveguide	p. 153
11.1 Introduction	p. 153
11.2 ABCD parameters of 2-port step discontinuity	p. 154
11.3 Frequency response	p. 157
11.4 Characterisation of half-wave long ridge waveguide test-set	p. 157
11.5 Experimental characterisation	p. 160
11.6 Symmetrical short section	p. 163
12 Ridge cross-guide directional coupler	p. 170
12.1 Introduction	p. 170
12.2 Operation of cross-guide directional coupler	p. 170
12.3 Bethe's small-hole coupling theory	p. 173
12.4 The 0-degree crossed-slot aperture	p. 175
12.5 The 0-degree crossed-slot aperture in rectangular waveguide	p. 177
12.6 The 0-degree crossed-slot aperture in single ridge waveguide	p. 178
12.7 The 45-degree crossed-slot aperture	p. 179
12.8 Circular polarisation in rectangular and ridge waveguides	p. 181
12.9 Rectangular and ridge waveguide cross-guide couplers using 45-degree crossed-slot apertures	p. 182
12.10 Coupling via waveguide walls of finite thickness	p. 184
13 Directly coupled filter circuits using immittance inverters	p. 189
13.1 Introduction	p. 189
13.2 Immittance inverters	p. 189
13.3 Lowpass filters using immittance inverters	p. 190
13.4 Bandpass filters using immittance inverters	p. 193
13.5 Immittance inverters	p. 195
13.6 Practical inverter	p. 198
13.7 Immittance inverters using evanescent mode waveguide	p. 200
13.8 E-plane filter	p. 201
13.9 Element values of lowpass prototypes	p. 204
13.10 Frequency response of microwave filters	p. 205
14 Ridge waveguide filter design using mode matching method	p. 207
14.1 Introduction	p. 207
14.2 Mode matching method	p. 207
14.3 MMM characterisation of 1-port networks	p. 212
14.4 Double septa and thick septum problem regions	p. 215
14.5 MMM characterisation of symmetrical waveguide discontinuities	p. 216
14.6 Eigensolutions of waveguide sections	p. 218
14.7 Immittance inverters	p. 221
14.8 E-plane bandpass filters using metal inverters	p. 221
14.9 Lowpass ridge filters using immittance inverters	p. 222
15 Nonreciprocal ridge isolators and phase-shifters	p. 226
15.1 Introduction	p. 226
15.2 Nonreciprocal ferrite devices in rectangular waveguide	p. 227
15.3 Differential phase shift, phase deviation and figure of merit of ferrite phase shifter	p. 230
15.4 90-degree phase shifter in dielectric loaded WRD 200 ridge waveguide	p. 231
15.5 Isolation, insertion loss and figure of merit of resonance isolator	p. 233
15.6 Resonance isolator in dielectric loaded WRD 750 ridge waveguide	p. 234
15.7 Resonance isolator in bifurcated ridge waveguide	p. 236
15.8 Differential phase shift circulator	p. 238
16 Finline waveguide	p. 241
16.1 Introduction	p. 241
16.2 Finline waveguide topologies	p. 241
16.3 Normalised wavelength and impedance in finline	p. 242
16.4 Empirical expressions for propagation in bilateral and unilateral finline	p. 245
16.5 Fields in unilateral finline waveguide	p. 247
16.6 Bilateral finline	p. 250
16.7 Empirical formulation of impedance in bilateral finline waveguide	p. 251
16.8 Circular polarisation in bilateral and unilateral finline waveguides	p. 251
16.9 Finline isolator using hexagonal ferrite substrate	p. 251
17 Inverted turnstile finline junction circulator	p. 256
17.1 Introduction	p. 256
17.2 Turnstile junction circulator	p. 256
17.3 Re-entrant H-plane waveguide circulator	p. 261
17.4 Re-entrant E-plane waveguide circulator	p. 262
17.5 Closed gyromagnetic resonator	p. 262
17.6 Perturbation theory of closed cyclindrical gyromagnetic resonator	p. 264
17.7 Quality factor of closed gyromagnetic resonator	p. 266
17.8 E-plane finline circulator using coupled H-plane turnstile resonators	p. 266
17.9 Experimental adjustment of finline turnstile circulator	p. 268
18 Semi-tracking ridge circulator	p. 270
18.1 Introduction	p. 270
18.2 Phenomenological adjustment	p. 271
18.3 Impedance matrix	p. 272
18.4 Complex gyrator circuit	p. 277
18.5 Semi-tracking complex gyrator circuit	p. 278
18.6 Direct magnetic field and magnetisation of semi-tracking circulators	p. 281
18.7 Physical variables of semi-tracking circulators	p. 285
18.8 Network problem	p. 285
18.9 Frequency response	p. 287
18.10 Design of octave-band semi-tracking circulators	p. 294
19 Variational calculus, functionals and the Rayleigh-Ritz procedure	p. 296
19.1 Introduction	p. 296
19.2 Stationary value of functional	p. 297
19.3 Electrical and magnetic energies in planar circuits	p. 298
19.4 Electric and magnetic fields in planar circuits with top and bottom electric walls	p. 299
19.5 Derivation of functional for planar isotropic circuits	p. 301
19.6 Rayleigh-Ritz procedure	p. 303
19.7 Field patterns	p. 305
19.8 Derivation of energy functional based on a mathematical technique	p. 306
Bibliography	p. 308
Index	p. 322

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Table of Contents