диафрагмированные волноводные фильтры / 1951d0c1-ab43-4317-89b5-7f2f32a4fc6a

Efficient CAD Tool for Inductively Coupled Rectangular Waveguide Filters with Rounded Corners

S. Cogollos(1), V.E. Boria(1), P. Soto(1), B. Gimeno(2), M. Guglielmi(3)

(1)Dpto. Comunicaciones, Univ. Politécnica de Valencia Camino de Vera s/n, E-46022, Valencia (Spain)

(2)Dpto Física Aplicada - I.C.M.U.V., Univ. de Valencia Dr. Moliner 50, E-46100 Burjassot, Valencia (Spain)

(3)European Space Research and Technology Centre P.O. Box 299, 2200 AG Noordwijk (The Netherlands)

Tel: +34 96 3879718 Fax: +34 96 3877309 E-mail: vboria@dcom.upv.es

Abstract

The ‘rounded corners’ effect is commonly introduced during the fabrication step of passive devices in rectangular waveguide technology. Recently, several methods have been proposed for considering such effect in the H- and E-plane of cavity filters. In this paper, the presence of rounded corners in the cross-sections of inductively coupled filters is successfully solved following a novel hybrid technique. Furthermore, a complete automated design procedure based on this new analysis technique is fully detailed. Following this new design technique, a WR-90 waveguide filter considering rounded corners in the cross-section of the cavities and coupling windows has been obtained.

I. INTRODUCTION

Modern fabrication techniques, such as computer-controlled milling, spark-eroding, electro-forming, or die casting, usually introduce internal rounded corners when applied to the low-cost production of passive devices in rectangular waveguide technology, Arndt et al. (1). If this mechanisation effect could be rigorously taken into account during the analysis stage of computer-aided design (CAD) tools, the production of the aforementioned devices would be highly improved in terms of accuracy, cost and development times. The presence of rounded corners in H- and E-plane rectangular waveguide cavity filters has been widely studied in the technical literature, Page (2) - Bressan et al. (4), following different analysis techniques. In Page (2), a first approach based on classic mode-matching techniques applied to a ladder model of the rounded corners is proposed. To improve the accuracy of such approach, adequate hybrid methods which combine numerical (space discretization) and modal techniques can be employed. For instance, the rigorous boundary contour mode-matching method described in Reiter and Arndt (3), or the boundary integral-resonant mode expansion (BI-RME) method recently formulated for 3D cavities in Bressan et al. (4) are hybrid solutions.

In this paper, we focus on the study of inductively coupled rectangular waveguide filters with rounded corners in the cross-section of the waveguides (see Fig. 1), which is a practical case of mechanisation effects that has not been considered yet. For the analysis of these devices, a novel and efficient hybrid technique based on the solution of an integral equation, Gerini et al. (5), and the BI-RME method proposed in Conciauro et al. (6) - Arcioni (7) for arbitrarily shaped 2D contours has been implemented. An improved version of the cited BI-RME method has been developed in order to obtain the modal chart of the waveguides with rounded corners in a very accurate way. The new analysis technique proposed has been first verified with several step discontinuities and irises involving waveguides with rounded corners. Next, the effect of varying the radius of the rounded corners in a WR-75 inductively coupled rectangular waveguide filter has also been successfully considered. Finally, the analysis method proposed has been integrated into a CAD tool for the filters considered in this paper. A complete automated design procedure based on the aggressive space mapping technique, Bandler et al. (8), has been applied to a practical design case.

II. ANALYSIS METHOD

An inductively coupled rectangular waveguide filter with rounded corners (see Fig. 1) can be considered as the cascade of discontinuity junctions between waveguides with an arbitrary cross-section. The electrical behaviour of such discontinuities can be characterised through Generalized Impedance Matrix (GIM) representations obtained by the integral equation method described in Gerini et al. (5). The practical implementation of this method requires the knowledge of the modal chart of the waveguides with rounded corners in their cross-section, as well as the coupling coefficients between the modal sets of such waveguides.

To obtain the modes of the waveguides with rounded corners, we have developed an improved version of the BI-RME method described in Conciauro et al. (6), which gives more accurate results by using curved elements to segment the rounded corners of the waveguide.

For computing the required coupling coefficients between two arbitrarily shaped waveguides, efficient and accurate two-fold summations have been derived

a′ . The modes of the arbitrarily shaped waveguides have been expanded in series of well-known vector mode functions related to the standard rectangular waveguides of sections r and r ′ that enclose, respectively, the arbitrary contours a and a′ . For the bigger arbitrarily shaped waveguide of section a, we can write

Expression (1) requires the knowledge of three kinds of coupling integrals (inner products). The first and the last kind of coupling integrals in (1), that involve waveguides with an arbitrary cross-section and their corresponding external rectangular contours, are provided in Arcioni (7). The second kind of integrals represent coupling levels between rectangular waveguides, which can be easily computed.

Once the coupling integrals required are computed, the GIM representations of all discontinuities are easily deduced. Then, in order to analyze the complete device, the aforementioned GIMs must be properly connected thus giving place to a banded linear system. This system can be efficiently solved following the procedure described in Boria et al. (9).

In order to validate the new analysis method proposed in the paper, we have considered two application examples that involve junctions between arbitrarily shaped waveguides. The first case is a thick circular iris which consists of two step discontinuities between circular waveguides of radius R1 = 12.74445 mm and R2 = 9.525 mm. The modal characterisation of these circular waveguides has been obtained assuming external resonators with a square crosssection of size equal to 2R1 and 2R2, respectively, which are perturbed by 4 rounded corners of 90° and radius R1 and R2. The simulated results for this case are successfully compared in Fig. 2(a) with the numerical data provided in Shen and MacPhie (10). The next example considered is a transition between two rectangular waveguides with rounded corners in their cross-sections. In Fig. 2(b), results for a small radius (R = 0.1 mm) are successfully compared with those obtained for the same transition without rounded corners. Results for a bigger radius of the rounded corners (R = 2 mm) are also included in Fig. 2(b). Once the accuracy of the analysis method has been fully tested, the effect of introducing rounded corners in the cross-sections of the resonators and coupling windows of an inductive rectangular waveguide filter (see Fig. 1) has been studied. For this purpose, a band-pass response of 300 MHz centred at 11 GHz has been first derived considering right corners in the filter. This result, as well as those corresponding to bigger curvature radii of the rounded corners, can be seen in Fig. 3.

III. DESIGN STRATEGY

Next, a CAD tool for inductively coupled rectangular waveguide filters with rounded corners (Fig. 1) based on the aggressive space mapping technique has been developed. For the coarse and fine models of such design technique the new analysis method described before has been selected, although with a different number of modes in the GIM representations (15 and 5 accessible modes have been considered in the fine and coarse model, respectively). Due to computational efficiency reasons, the length of the cavities (l) and the thickness of the coupling windows (t) are chosen as the design parameters (see Fig. 1). With regard to the coupling aperture widths of the structure (w), they are properly determined before the optimisation procedure in order to cope with the required bandwidth of the filter. A key point for the success of any space mapping design procedure relies on a very accurate determination of the optimal solution in the coarse model space.

With the aim of reducing the complexity related to the initial optimisation stage, a novel procedure for determining a good starting point based on single-mode equivalent circuits has also been derived. An equivalent network representation based on impedance inverters and resonators has been used to obtain an ideal response verifying the electrical specifications. In the real structure, the impedance inverters are replaced by coupling windows terminated with waveguide sections of suitable lengths. The initial thickness of each coupling window is determined in order to recover the inversion constant of the corresponding impedance inverter. With regard to the ideal resonators, they are finally replaced with half-wavelength sections of uniform waveguide.