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, now widely used in commercial electronics and communications devices. A definitive reference source on this topic, this book will enable the reader to have direct access to this subject without need for exhaustive search of research papers.
Inspec keywords: finite element analysis; fin line components; dielectricloaded waveguides; mode matching; microwave isolators; waveguide filters; ridge waveguides; variational techniques; coupled circuits; Faraday effect; phase shifters; polarisation; directional couplers
Other keywords: mode matching; circular polarisation; gyromagnetic quadruple ridge waveguide; nonreciprocal ridge isolators; transverse resonance; dielectric loaded ridge waveguides; finite element method; finline waveguide; rectangular waveguides; Faraday rotation; ridge crossguide directional coupler; inverted turnstile finline junction circulator; ridge waveguide filter; semitracking ridge circulator; RayleighRitz procedure; passive microwave components; directly coupled filter circuits; variational calculus; immittance inverters; phaseshifters
Subjects: Waveguide and microwave transmission line components; Finite element analysis; Mathematical analysis; Filters and other networks; Other analogue circuits; Waveguides and microwave transmission lines
 Book DOI: 10.1049/PBEW049E
 Chapter DOI: 10.1049/PBEW049E
 ISBN: 9780852967942
 eISBN: 9781849190213
 Page count: 344
 Format: PDF

Front Matter
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1 The ridge waveguide
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A waveguide used in many broadband microwave equipments is the ridge geometry. An important feature of this sort of waveguide compared to the conventional rectangular waveguide is the wider separation between the cutoff numbers of its dominant and first higher order mode. Another is the fact that its impedance is bracketed between that of the regular rect angular waveguide (377 Ω) and those of coaxial and stripline structures (50 Ω). The original ridge waveguide consisted of a regular rectangular waveguide with one or two ridge inserts. Most passive components that may be realised in conventional rectangular waveguides are also available in ridge geometry. This chapter includes some typical arrangements by way of introduction.
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2 Propagation and impedance in rectangular waveguides
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The description of any waveguide includes its cutoff number, its propagation constant, one or more definitions of impedance, power flow and attenuation and a description of its field pattern. Since the rectangular wave guide embodies all the salient properties of the ridge waveguide it is apt to review some of its more important features before tackling the ridge structure. The chapter is restricted to a description of the dominant mode in the geometry but the existence of higher order modes is understood. The orthogonal property of any two modes of the waveguide is separately established.
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3 Impedance and propagation in ridge waveguides using the transverse resonance method
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Important quantities in the description of any waveguide are the definition of its propagation constant and the voltagecurrent, powervoltage and powercurrent definitions of its characteristic impedance. One purpose of this chapter is to summarise some closed form descriptions of propagation, power flow and impedance in the ridge waveguide based on the transverse resonance method (TRM). Since the different notations introduced in its characterisation are on occasion difficult to follow readily, another purpose of this chapter is to reproduce the existing literature in a single nomenclature. Still another is to summarise graphically its voltagecurrent, power voltage and powercurrent definitions of impedance in a unified way.
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4 Fields, propagation and attenuation in double ridge waveguide
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A knowledge of the fields in any waveguide is necessary in order to calculate its power flow, its attenuation and its impedance. The purpose of this chapter is to summarise some approximate closed form relationships for the fields in this type of waveguide and present some calculations based on the finite element method (FEM) procedure. The TE family of solutions is obtained by calculating H_{z} of the related planar problem region with top and bottom magnetic walls and forming the other components of the field by using Maxwell's equations. The TM family of solutions is obtained by solving the dual planar circuit with top and bottom electric walls. Comparison between the closed form and FEM procedures suggests that the closed form representation is adequate for engineering purposes. Some results on the standing wave solutions of the dominant and higher order modes of this sort of waveguide based on a magnetic field integral equation (MFIE) are also included. The power flow and attenuation are separately summarised.
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5 Impedance of double ridge waveguide using the finite element method
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One means of calculating the cutoff space and impedance of a ridge wave guide which avoids the need to describe the fringing fields at the edges of the ridges is the finite element method (FEM). One way of obtaining any of the definitions of impedance at any frequency in such a waveguide is to make use of the relationship between that at finite and infinite frequencies. The impedance at infinite frequency is readily deduced by recognising that the electric field distribution is invariant at cutoff and at infinite frequency and that the magnetic field at infinite frequency is simply related to the electric field there by the impedance of free space. This suggests that a knowledge of the electric field at infinite frequency or at the cutoff space is in practice sufficient for calculation.
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6 Characterisation of single ridge waveguide using the finite element method
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The various definitions of impedance in a single ridge waveguide are also of some interest. The purpose of this chapter is to summarise some calculations. The description of this problem region follows closely that introduced in connection with the double ridge arrangement except that the limits of the integral used to define the current in the waveguide walls are in this instance different. It corresponds, instead, with the position at which the polarity of the electric field on the boundary contour on either side of the symmetric plane reverses. This condition ensures that the magnitude of the total currents flowing in the equivalent top and bottom walls of the waveguide are equal. A careful scrutiny of this problem suggests that the interior contour of the waveguide breaks up in every instance into one interval consisting of the top and sidewalls of the structure and a second interval comprising the remaining walls. The calculation undertaken here suggests that the error resulting in approximating the discontinuity at a typical ridge edge by a shunt capacitance and retaining the contributions from the top and side walls of the ridge and bottom waveguide wall is negligible. This observation may be understood by recognising that the field is concentrated between the ridge and upper wall of the waveguide. This difficulty does not arise in the powervoltage definition of impedance. The powercurrent definition is simply obtained by using the relationship between the three classic definitions of impedance. The analysis of the field distribution and power voltage definition of impedance in various nonsymmetrical ridge structures has included mode matching techniques, a variational method and a surface integral approach. The work outlined here is based on the nodal FEM.
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7 Propagation constant and impedance of dielectric loaded ridge waveguide using a hybrid finite element solver
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The finite element method (FEM) has been widely utilised in the analysis of the cutoff space and propagation constant of dielectric loaded waveguides containing isotropic and anisotropic media.The purpose of this chapter is to give some calculations on the cutoff space, the propagation constant and the impedance of the ridge waveguide with a dielectric filler between its ridges based on a hybrid finite element calculation.
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8 Circular polarisation in ridge and dielectric loaded ridge waveguides
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An important concept in microwave engineering is that of circular polarisation. The two possibilities correspond to two equal vectors in space quadrature with one or the other advanced or retarded in time quadrature. Counterrotating magnetic fields occur naturally on either side of the symmetry plane of an ordinary rectangular waveguide propagating the dominant TE mode; and at the interface and everywhere outside two different dielectric regions. Furthermore, in each instance, the hand of rotation is interchanged if the direction of propagation is reversed. Situations in which the rotation of these waves are different in the two directions of propagation are, of course, of special interest.
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9 Quadruple ridge waveguide
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The ridge waveguide is not in practice restricted to the rectangular waveguide with one or two ridges. One or more ridges have by now been introduced into circular, square and triangular waveguides. A property of the round or square waveguide symmetrically loaded by four ridges is that its dominant mode can be decomposed into counterrotating circular polarised waves on its axis. This sort of ridge waveguide supports Faraday rotation provided it is perturbed by a gyromagnetic material along its axis. Since the dominant mode solution of this structure has twofold symmetry it is sufficient, insofar as it is concerned, to investigate the problem regions revealed by introducing suitable orthogonal magnetic and electric walls in all combinations. Its mode nomenclature coincides with that of the round or square waveguide obtained by removing the ridges. The nodal finite element method (FEM) again provides one means of investigating this sort of isotropic waveguide. The effect of depositing dielectric tiles on the ridges is also given some attention.
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10 Faraday rotation in gyromagnetic quadruple ridge waveguide
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One unique property of Faraday rotation is that it is nonreciprocal. This means that a wave propagating in one direction which is rotated by an angle θ does not rotate back to its original position when it is returned to its starting point. It is therefore a suitable structure for the construction of nonreciprocal Faraday rotation devices such as circulators, phase shifters and isolators. It is also an appropriate prototype for a host of reciprocal power dividers and other components. Propagation in a dual mode triple ridge gyromagnetic waveguide is handled separately. One model of a Faraday rotation bit is a nonreciprocal 4port directional coupler. The chapter includes the scattering matrix of the arrangement. A threecomponent magnetic field formulation of the sort of functional met in the RayleighRitz calculation of propagation in this type of waveguide is included separately. It is employed in the calculations of propagation of a number of the gyromagnetic waveguides addressed in this chapter. The descriptions of some typical nonreciprocal components are also given.
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11 Characterisation of discontinuity effects in single ridge waveguide
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The transition between any two different waveguides is of some interest in the design of filters and other waveguide components. One canonical representation of such a discontinuity is a lumped element susceptance in cascade with an ideal transformer. The purpose of this chapter is to summarise some experimental data on a transition between an ordinary waveguide and a single ridge one. This sort of data may be experimentally extracted by making separate measurements on the external quality factor and resonant frequency of a halfwave long prototype. The network variables of the over all arrangement are separately established by using the ABCD notation. The chapter includes a careful characterisation of this problem region for each possible definition of impedance in the waveguide. The work outlined here omits, in keeping with some prior art, the effect of the lumped element susceptance of the discontinuity on the description of the external quality factor but, in keeping with some previous work, retains it in that of the midband frequency.
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12 Ridge crossguide directional coupler
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The object of this chapter is to present some calculations on the coupling and directivity of a number of crossguide couplers in a ridge waveguide. The four possibilities consist of one arrangement with both the primary and secondary waveguides in a double ridge, a similar arrange ment with primary and secondary waveguides in a single ridge, and configurations with the primary and secondary waveguides in either single and double ridge or double and single ridge, respectively. The coupling geometry usually consists of either a circular or crossslot aperture. Apart from discrepancies in the vicinity of the ridge discontinuities these agree well with some Finite Element Method (FEM) calculations in the same chapter. The closedform formulations may therefore be utilised for engineering purposes.
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13 Directly coupled filter circuits using immittance inverters
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The design of 2port microwave filters relies either on an exact synthesis procedure in the tplane involving one kind of element separated by UEs or on an approximate splane technique involving one kind of element separated by immitance inverters. This sort of topology enters in the realisation of directly coupled bandpass filters using halfwave long cavities connected by metal or inductive posts. The circuit is not canonical since the impedance inverters do not contribute to the overall amplitude response of the filter but only provide a practical layout of the circuit elements. The design is completed by physically realising the impedance inverters. The original immittance inverter took the form of a simple quarterwave impedance transformer. Such filters are known as quarterwave coupled. The modern version, in which the inverter is realised by a step discontinuity, is known as a directly coupled arrangement. Since the notion of the immittance inverter is central to the design it is given special attention notwithstanding that it is a classic topic in the literature.
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14 Ridge waveguide filter design using mode matching method
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The specification of a conventional waveguide filter is usually incorporated in a ladder lumped element network which is then realised in terms of immittance inverters and one kind of element. The synthesis of this type of topology is a standard problem in the literature. A typical inverter is realised by introducing a suitable discontinuity into the waveguide and embedding it into negative line lengths. This is usually achieved by foreshortening the lengths of each cavity. To proceed with the design, it is necessary to have some representation of the discontinuities involved. One means of characterising discontinuities in waveguides is the MMM (mode matching method). To overcome the effects of interaction between discrete discontinuities on the overall filter performance a global transmission matrix is constructed and its overall specification is optimised by resorting to a suitable optimisation subroutine. The chapter includes the layout of one lowpass filter which relies on cutoff waveguide sections for its inverters. It separately includes the design of one bandpass filter using cutoff waveguide sections for its inverters and another employing inductive septa for the realisation of the inverters.
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15 Nonreciprocal ridge isolators and phaseshifters
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One important class of ridge waveguide hardware is the nonreciprocal 2port one. Two classic devices are the nonreciprocal phase shifter and the resonance isolator. Each device relies on the two different interactions between a spinning electron with a clockwise or anticlockwise circularly polarised alternating radio frequency magnetic field in a suitably magnetised ferrite medium. If the alternating magnetic field rotates in the same direction as that of the electron spin then the medium exhibits a scalar permeability with one distinct value; if, however, it rotates in the oppposite direction it again behaves as a scalar medium but with a different value. This property of a magnetised ferrite medium is the basis of a number of important non reciprocal devices. One means of realising such components in a ridge wave guide is to recognise that such polarisation always exists at the interface between any two different semiinfinite dielectric regions and everywhere outside and that its hand is determined by the direction of propagation. Another significant property of this sort of arrangement is that the senses of rotations are in opposite directions on either side of a dielectric rib. Such dielectric inserts are therefore suitable for the construction of non reciprocal ferrite devices such as phase shifters and isolators. It is assumed, for simplicity, throughout, that the introduction of thin H or Eplane ferrite or garnet tiles in the vicinity of the dielectric wall does not in the first instance disturb the polarisation in its neighbourhood. While the double ridge waveguide does not have natural planes of circular polarisation in its trough regions it does have such planes at its electric symmetry wall. An Hplane bifurcation produces one possible carrier for the design of nonreciprocal phase shifters and isolators.
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16 Finline waveguide
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A waveguide arrangement whose topology has many of the features of the ridge one is the finline structure. It consists of a dielectric sheet across the waveguide metallised on either one or both sides in a number of different ways. Four typical arrangements are the unilateral geometry, the bilateral one, the insulated finline and the antipodal structures. The bilateral arrangement may be visualised as a quasiridge waveguide. One benefit of this family of waveguides is that quite complicated circuits can be fabricated using planar techniques. A complete description of a typical finline wave guide includes its cutoff space, its impedance, its attenuation, its propagation constant and a description of its field pattern. It also requires an understanding of the location of the planes of circular polarisation in the waveguide. The solution of this class of waveguide has been the object of a host of numerical descriptions. The approach used here relies, in each instance, on an approximate closed form formulation of the field in each region of the structure. The effects of finite metallisation on both the propagation constant and the impedance in these sorts of waveguides are outside the remit of this chapter. The chapter includes the description of one resonance isolator.
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17 Inverted turnstile finline junction circulator
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The 3port circulator is a unique nonreciprocal symmetrical junction having one typical input port, one output port and one decoupled port. The fundamental definition of the junction circulator has its origin in energy conservation. It states that the only matched symmetrical 3port junction corresponds to the definition of the circulator. One possible model of a circulator is a magnetised ferrite or garnet gyromagnetic resonator having threefold symmetry connected or coupled to three transmission lines or waveguides.
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18 Semitracking ridge circulator
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Ridge or finline circulators may be realised by introducing a suitable gyro magnetic resonator at the junction of three E or Hplane waveguides. The arrangement met in connection with the finline waveguide is an Eplane junction embodying one or two reentrant quarterwave long gyromagnetic resonators opencircuited at one end and shortcircuited at the other. The purpose of this chapter is to describe an Hplane ridge structure which relies for its operation on a planar resonator.
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19 Variational calculus, functionals and the RayleighRitz procedure
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A number of the calculations on the ridge waveguide described in this book amount to obtaining the eigenvalues and eigenvectors of the related planar problem region by using the finite element method. It is therefore appropriate to include a chapter on this technique. A property of a typical eigen solution of any problem region is that it must satisfy both the wave equation and the boundary conditions of the region. Solutions of the wave equation based on a separation of variables technique, however, only exist for regular geometries such as rectangular and circular structures. For irregular structures, a variational approach based on the fact that the stationary values of the energy functional of the problem region also satisfy the related scalar homogeneous Helmholtz differential equation must be employed. The stored energy of the circuit when integrated over the problem region is known as the functional of the problem region. If the region consists of top and bottom electrical walls then this quantity automatically satisfies a magnetic boundary condition on the sidewall of the problem region. If the problem region has top and bottom magnetic walls then it automatically satisfies an electric wall at its sidewalls. If the former structure contains an electric wall or segments of such walls then these have to be separately catered for. A dual statement applies to the latter problem region. The process of obtaining a solution to a Helmholtz differential equation by extremising a functional is called a variational method. The use of the word 'functional' in this context serves as a reminder that it is not in itself a function but rather a function of functions. The stationary values obtained in this way satisfy, as will be demonstrated, the homogeneous Helmholtz differential equation.
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Back Matter
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