This paper presents a method for the calculation of the S-parameter of arbitrary shape and composition post or group of posts in a waveguide. The method segments the problem into regions that are characterized by their respective generalized admittance matrix (GAM). Analytic formulation as well as a boundary integral formulation based on the wave function are used in this characterization. Our method is specially suitable for its incorporation in real time CAD tools because only the changing parameters must be computed. This method also permits the simple combination of different numerical techniques.Peer ReviewedPostprint (published version

Ferrando Bataller, Miquel

This paper presents a method for the calculation of the S-parameter of arbitrary shape and composition post or group of posts in a waveguide. The method segments the problem into regions that are characterized by their respective generalized admittance matrix (GAM). Analytic formulation as well as a boundary integral formulation based on the wave function are used in this characterization. Our method is specially suitable for its incorporation in real time CAD tools because only the changing parameters must be computed. This method also permits the simple combination of different numerical techniques.Peer Reviewe

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Multimode equivalent network representation for multiple arbitrarily shaped posts in H-plane waveguide

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Multimode Equivalent Network Representation for Multiple Arbitrarily Shaped posts in H-Plane Waveguide Alejandro Valero', Miguel Ferrando Dept. Comunicaciones. Universidad PolitCcnica de Valencia 4607LVaIencia (Spain) ABSTRACT This paper presents a method for the calculation of the S-parameter of arbitrary shape and composition post or group of p o s t s  in guide. I h e  niethod segments the problem into regions that are characterized by their respective generalized admittance matrix (GAM). Analyitic formulation as well as a boundary integral formulation baaed on wave function are used in this characterization. Our nietliod is specially suitable for its incorporation to real time CAI) tools because only the changing parameters must be computed. This method also permits the simple combination of different numerical techniques. 1. INTRODUCTION ?lie rigorous study of the dielcctric posts in guide is of constant interest in the design of filters. A number of analysis have been performed in recent years facing more and more complex and interesting problems each time [ I -  41. In the methods applied tu date. the region containing the post is analysed together with the post itself. This implies that i n  case of any modification in fonn, position or electric characteristics of the post. the problem would need to be analysed from the beginning, thus limiting its systematic computation. The method that we propose segments the problem into regions. Each region is analysed independently by means of a generalized admittance matrix (CAM). This method has a double advantage. The first one is that one can use the technique that is best suited to the characteristics ol the post. The second one is that it avoids having to calculate once more those elements which were not modified. The problem we intend to solve is depicted in fig. I .  In a rectangular waveguide there is a post generally not centered and of is the one which establishes a circular contour around the post, because the scattered field can be better expressed in terms of cylindrical waves. On the other hand. the propagation of these waves i n  the waveguide can be expressed more adequately by means of the solution modes in i t .  I I .  INTEGRAL FORMULATION FOR THE ADMITTANCE OF TRASlTlON REGIONS I AND 111 A modified version of [he boundary integral equation based on the wave function proposed by Kishi and Okoshi (51 is used in the full-wave description of homogeneous regions by means of GAM. Regions I and 111 are homogeneous source free areas where Green's second identity can be erbitrury cruas-section and composition. The most convenient s e g m e n d o n  0-7803-4478-2/98/$10.M) Q 1998 IEEE 2270 applied on the auxiliar vector potencial A = cuf and the electric field E .  After some manipulations, the following identity i s  obtained ( jquy.,  + M , x V y ) . i d c = o  ( 1 )  P, being j ,  = A x fi, and Ms = E, x A .  The solution of the two-dimensional homogeneous wave equation in a waveguide i s  a linear combination of modes. Then identity ( I )  should be simultaneously valid to a l l  the solutions. We therefore have a group of N integral equations. Expanding the equivalent currents in the contour as a linear combination of orthogonal functions, the integral operator i s  transformed into a matricial one [HI Pf =PI IMF (2 )  being [Y]=(H]-'.[u] (3) 111. ANALYTICAL FORMULATION FOR THE ADMITTANCE IN THE CENTRAL REGION In region II two accesses can be observed, as depicted in figure 2. The post or the group of posts are generally not centered. Therefore the wave function that is  used to characterize the accesses 3 and 4 i s  U y,, = ~ [ o , J , ( k p )  + b..H!"(kp)~"* (4) I-- U where the spectrum of the incident and reflected waves are related by means of a reflection coefficient matrix. When the post i s  centered. [RJ represents i ts  reflection coefficient. However, when the post i s  not centered i t  is  necessary to transform the incident and reflected waves, and then a new reflection coefficient i s  obtained. (6)  where I T ~ I ]  and IT,] are translation matrices for Hankel and Bessel functions respectively. obtained from G a r s  Addition Theorem for Bessel functions. Now, we can establish a relationship between 2 and f i  in accesses 3 and 4 by means of [R, j =IT,, I IR, 1 IT, I As the wave function i s  separable for accesses 3 and 4. the four matrix elements [Vi,] in the generalized admittance matrix can be obtained independently. Then, expanding the electric and magnetic field and using the inner product. after some manipulations. self and mutual admittances can be expressed in matrix form as where 227 I IJ.1 and (H.1 are diagonal matrices containing Bessel and Wankel modes evaluated at p a  When a set of posts  is considered. the group can be characterized by a reflection coefficient. In this way, the previous formulation for the isolated post can be used. Enforcing the relationships among incident and reflccted espectra on each post, and after some manipulations, the following reflection coellicient for the whole set of posts  can be obtained l R ' l L [ [ r , v l  . . .  lrpl ... [r..] - [R, ]LI  ". 111 ... -IR,lr", l j  I , [ R , ~ L ] /  R " I C "  1 ;  -IR.Ic.I . .  -l%Ir-l ' . . I 1 1  where are traslation matrices, [ R , I  is  the reflection coefficient of each post and I[] is the identity matrix. When the three regions have been characterized by their GAMS. the next step is lo get the global admittance matrix. They can be connected by imposing the continuity conditions in the common surfaces. IV.  RESULTS Figure 3 shows a plot of the S parameten as a function of permittivity for a circular post of R = 0.75a. The frequency of work is fJ0.7. These values are compared with the ones calculated by Abdulnour 141 and show great agreement. A set of three dielectric posts has been computed to solve for the &I parameter. The values obtained by the generalized network model are compared against those obtained by Hsu and Auda 121 using FEM in figure 4. Both curves show the same tendency although they are slightly displaced. V. CONCLNSIONS A systematic method for the analysis of posts in waveguide has been proposed using the network theory and the concept of generalized admittance. REFERENCES Y. Leviatan. O.S. Sheaffer. "Analysis of Inductive Posh in Rectangular Waveguides". IEEE Trons. on Micmn'uve Thcorj ond Tech., vol. MTT-35,  pp. 48- 59. 1987. C.G. Hsu. Auda. "Mulliple dielectric posls in a reclangular waveguide". lEEE Trons. on Microwove Theoryand Tech.. vol MTT-34. pp. 883-891, 1986. K.L. Wu. et al. "Waveguide Discontinuity Analysis with a Coupled Finite- Boundary Element Mahod". IEEE Trans. on Micromavc Theory and Tcch.. vol. MTT-37. pp. 993-998. 1989. 1. Abdulnour. L. Marchildon. "Boundary Elements and Analytic Expansions applied to H-Plane Waveguide Funclions", lEEE Trans. on Microwve  73eory and Tech.. vol. MTT-42. pp. 1038-1045. 1994. N. Kishi. T. Okoshi, "Vectorial wave analysis of uniform-core optical fibers using a novel boundary integral method". IEEE Tronr. on Microm,uve Theory and Tech., vol. MTT-37. pp. 526-533. Mar 1989. 2272 Figure 1. Description of h e  prohlem. Flgurc 2. Region surrounding the posts to be characterized analytically. 1. /I = 0.7 0' Abluln?uI1I 0 m U Lo s no 110 I* I- 1s U.*<YI' a"- Flgurc 3. S paranleterr for a crntcred cylindrical dielectric port vs. dielectric constant. 0 9  0 1  07 I I  I1 a 111. Vigurc 4. SI, parameter for a set of three cylindical dielectric posts VI. normalized lrequency. 2213 

Multimode equivalent network representation for multiple arbitrarily shaped posts in H-plane waveguide

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