8. zyxwvutsrqponm C. Veyres and V. Fouad-Hanna, “Extension of the Application of Conformal Mapping Techniques to Coplanar Lines with Finite Dimensions,” zyxwvutsrqpo Int. J. Electron., Vol. 48, 1980, pp. 47-56. 9. T. Kitazawa and R. Mittra, “Quasi-Static Characteristics of Asym- metrical and Coupled Coplanar-Type Transmission Lines,” ZEEE Trans. Microwave Theory Tech., Vol. MTT-33, 1985, pp. 771-778. Received 9-14-94 Microwave and Optical Technology Letters, 8/3, 160-164 zyxwvutsr 0 1995 John Wiley zyxwvutsrqp & Sons, Inc. CCC 0895-2477/95 zyxwvutsrqp NOVEL APPROACH TO CONTIGUOUS BAND MULTIPLEXER DESIGN FOR SATELLITE APPLICATIONS Mohamed Khaled Chahine and Gdrard Carrer France Telecom, CNET lssy les Moulineaux 92131, France KEY TERMS Satellite multiplexer, microwave filter, circuit analysis, optimization zyxwvut ABSTRACT A novel and general technique for the optimization of contiguous band multiplexers using sensitivity analysis is presented. The method utilizes exact partial derivatives of circuit responses with respect to all design parameters. The equivalent circuit includes channel jlters, waveguide spacings, and three-port waveguide junctions. A ILchannel contiguous multiplexer at zyxwvutsrqp Ku band hus been designed. Utilizatwn of an eficient modelization and automatic decomposition approaches resulted in an excellent simulation performance of the presented multiplexer. 0 I995 John W i l q & Sons, Inc. INTRODUCTION Satellite transponders have traditionally employed odd-even channel configurations in order to simpllfy output multiplexer construction, which requires the use of a more complex antenna array and a duplication of components, and also increases individual filter rejection requirements in order to reduce adjacent channel interference. A solution to this problem is the use of a contiguous band multiplexer to cover a large number of channels. Practical design and manufacture of contiguous band mul- tiplexers having a significant number of channels have been presented previously [l-41 using optimization techniques in design procedures. This article extends these techniques by proposing a fast semianalytic network analysis method and an efficient itera- tive optimization procedure to determine the best multiplexer parameters. New techniques are introduced in order to be able to achieve an automatic decomposition of the multi- plexer circuit elements and channel parameters. zyxwvutsr Also we have introduced equality constraints on couplings realized by apertures, which is of significant interest to manufacturers. EQUIVALENT CIRCUIT AND SIMULATION METHOD Figure 1 illustrates the block diagram of the multiplexer. Channels are distributed along a common waveguide, a chan- nel filter is connected to this waveguide by a T junction, and each filter is shifted from the junction by a waveguide stub. The narrow-band lumped model of a standard multicou- pled cavity filter with synchronous resonators coupled via apertures has [5] a symmetrical nodal impedance matrix Z. As only input and output responses are of interest here, we construct a two-port equivalent circuit of the filter using an approach that reduces the problem to the inversion of the Z matrix. This inversion is done by a semianalytic method [6]. The inverse of Z is not computed numerically at each fie- quency point, but it is calculated in the form of matrix coefficient polynomials in the s, normalized frequency. This procedure allows us to obtain the responses of the circuit as rational functions in s and provides an important accelera- tion of the simulation process. The values of the equivalent circuit elements of the E plane T junction shown in Figure 2 are calculated as a function of frequency by cubic interpolation based on 156 values determined by a finite-element electromagnetic simu- lation of the junction. The four S parameters obtained by simulation are very close to the measured ones. Figure 3 shows the computed result and the measured data from an HP8510B network analyzer, showing the S,, magnitude of a Ku-band E-plane T junction over the frequency band from 8-15 GHz. Agreement between the computed and measured data is remarkable. The responses and sensitivity analysis of multiplexer cir- cuits is based on the use of a cascaded analysis approach utilizing transmission matrices [7]. The equivalent transmis- sion matrix Qij between two reference planes i and j is calculated by cascading transmission matrices of elements located between these two planes. Sensitivities of Q,, w.r.t. any variable x located between planes zyx i and j are evaluated as where f, is an index set whose elements identify the trans- mission matrices containing x; dQ:i/ax is the network trans- mission matrix located between planes i and j, where the Eth matrix is replaced by its derivative w.r.t. x. OPTIMIZATION This accurate model has been programmed on a digital computer in order to constitute the heart of a computer program for the design of contiguous band multiplexers, with all the multiplexer parameters: waveguide spacings, filter input and output couplings, cavity resonant frequencies, and intercavity couplings being treated as variables. The com- puter optimization program utilizes a modified Marquardt algorithm for nonlinear least squares proposed by Fletcher 181, which requires rcsponse sensitivities. A decomposition approach based on many different case studies has been developed, and provides good convergence features. Hence, the optimization program is the result of the combination of two main techniques. The first is based on a subdivision of the multiplexer is submultiplexers of lower order. Once a submultiplexer is optimized with equality con- straints between similar channel parameters, we integrate an additional channel. The operation is repeated until all chan- nels can be integrated. Then we perform a global optimiza- tion with equality constraints maintained only on the varying couplings realized by coupling slots. 164 MICROWAVE AND OPTICAL TECHNOLOGY LEllERS / Vol. 8, No. 3, February 20 1995