Even and odd mode cut-off parameters of pairs of ridges in rectangular waveguide using a mode matching solver A. Mediavilla, J.A. Pereda, A. Casanueva, M. McKay and J. Helszajn Abstract: A waveguide geometry of some interest consists of a symmetrical pair of ridges in a rectangular waveguide. The paper gives the even and odd mode cut-off spaces of such a structure in addition to its corresponding standing wave patterns. The classic power-voltage, power-current and voltage-current definitions of impedance of the two solutions are also evaluated. The calculations are based on a mode matching procedure and are verified separately using a finite element solver. A knowledge of these parameters is sufficient for the design of a proximity, reverse, directional coupler. 1 Introduction The cut-off space and impedance levels of rectangular waveguides with single and double ridge inserts have, by now, been investigated thoroughly in the open literature [1–9] . The parameters of rectangular waveguides with triple ridges have been described also [10]. Circular waveguides with triple, quadruple and multiple ridges have been dealt with separately [11, 12]. Another ridge waveguide is one consisting of either a pair of single or double ridges symmetrically displaced from the symmetry plane of a regular rectangular waveguide. A feature of this waveguide is that it has, with two of the ridges suitably terminated, the properties of a 4-port directional coupler between the other two ridges. The purpose of this paper is to evaluate the dominant and first order even and odd mode cut-off spaces of the double ridge arrangement. The corresponding voltage-current, power-voltage and power-current defini- tions of impedance at infinite frequency are calculated separately and the standing wave patterns of the two types of solution are also drawn. The impedance levels of single, double, triple and quadruple ridge waveguides are evaluated separately and compared. The procedure adopted in this paper is based on the mode matching (MM) method and the results are verified separately by having recourse to a finite element (FE) solver. The structure under considera- tion is illustrated in Fig. 1. Other papers of note on ridge waveguides are to be found in [13–17] . 2 Even and odd mode cut-off spaces An important quantity in the description of any waveguide is its cut-off space. The purpose of this Section is to summarise some calculations on the cut-off spaces of the even and odd mode geometries of two pairs of ridges symmetrically placed in a regular rectangular waveguide. The two circuits under consideration are illustrated in Figs. 2a and 2b. Each arrangement is defined by the spacing between the pairs of ridges ð‘=aÞ, the gap between the ridges ðd =bÞ and the width of the ridges ðs=aÞ. Figures 3a and 3b depict the relationship between the dominant even mode cut-off space and the normalised spacing between the ridges for parametric values of the normalised gap and two different values of s/a. The corresponding results for the odd mode solution are indicated in Figs. 4a and 4b respectively. The results were obtained by introducing a suitable electric or magnetic wall along the H-plane symmetry of the waveguide and modelling one quarter of the original topology. The onset of the first higher order even and odd modes are also of some interest in any design. These fix the dominant mode bandwidths in any waveguide. In d a s b l Fig. 1 Schematic diagram of ridge waveguide loaded by doublets of ridges A. Mediavilla, J.A. Pereda and A. Casanueva are with Dpto. Ingenier ! ıa de Comunicaciones, Universidad de Cantabria, Spain M. McKay is with Filtronic Comtek (UK) Ltd., 8 Redwood Crescent, Peel Park, East Kilbride, G74 5PA, UK J. Helszajn is with the Department of Computing and Electrical Engineering, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK E-mail: mmckay@filtronic.com r IEE, 2005 IEE Proceedings online no. 20045053 doi:10.1049/ip-map:20045053 Paper first received 9th July and in revised form 23rd November 2004 IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 4, August 2005 231