General Coupling Matrix Research Articles

On Iterative Solutions of General Coupled Matrix Equations

In this paper we study coupled matrix equations, which are encountered in many systems and control applications. First, we extend the well-known Jacobi and Gauss--Seidel iterations and present a large family of iterative methods, which are then applied to develop iterative solutions to coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle. Next, we generalize the Sylvester equations to general coupled matrix equations, and propose a gradient-based iterative algorithm for the solutions, using a block-matrix inner product---the star $(\star)$ product; we prove that the iterative algorithm always converges to the (unique) solutions for any initial values. One advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods. Finally, we test the algorithms and show their effectiveness using numerical examples.

Rapid coupling matrix reduction for longitudinal and cascaded-quadruplet microwave filters

To realize standard microwave filter structures, it is necessary to zero some of the elements in a general even-mode coupling matrix. The zeroing process involves solving a nonlinear set of equations, performed here by using the Newton-Raphson method. Thus, intelligence is added to the numerical iteration procedure, to ensure rapid convergence. The reproduced transmission coefficient S/sub 21/ from the reduced matrix agrees well with the one synthesized.

Design of band pass filter by coupling matrix and conformal mapping algorithm

We design band pass filter using general coupling matrix synthesis methods with Chebyshev filtering function. The band pass filters with low return loss and efficient high performance can be synthesized in the form of coupling resonators. The transfer polynomials with canonical network can create the coupling which determine the performance of a microwave filter. On the other hand, the coupling coefficients in the matrix, between the resonators are strongly faction of the geometry of resonators that were modeled of distributed elements. In this paper, the inter-resonator coupling will be modeled using conformal mapping algorithm and the coupling matrix synthesis procedure will be discussed.

Design of Multilayer Microwave Devices by Coupling Matrix Algorithm for LTCC Process

We design multilayer microwave devices using general coupling matrix synthesis algorithm with Chebyshev filtering function. Multilayer structure can reduces the size and return loss of bandpass filters. High performance bandpass filters can be synthesized by using multiple u /2-resonators. The multilayer filter, including 4 or more resonators, exhibites markedly improved performance, as compared with that of the single layer ones. In this paper, the inter-resonator coupling will be modeled and a prototype band pass filter based on low temperature cofired multilayered ceramics will be demonstrated.

General coupling matrix synthesis methods for Chebyshev filtering functions

Methods are presented for the generation of the transfer polynomials, and then the direct synthesis of the corresponding canonical network coupling matrices for Chebyshev (i.e., prescribed-equiripple) filtering functions of the most general kind. A simple recursion technique is described for the generation of the polynomials for even- or odd-degree Chebyshev filtering functions with symmetrically or asymmetrically prescribed transmission zeros and/or group delay equalization zero pairs. The method for the synthesis of the coupling matrix for the corresponding single- or double-terminated network is then given. Finally, a novel direct technique, not involving optimization, for reconfiguring the matrix into a practical form suitable for realization with microwave resonator technology is introduced. These universal methods will be useful for the design of efficient high-performance microwave filters in a wide variety of technologies for application in space and terrestrial communication systems.