Graduate Thesis Or Dissertation
 

Computational methods for the quasi-TEM characteristics of fundamental MIC planar structures

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  • Accurate and efficient computational methods to evaluate the quasi-TEM parameters of various planar structures such as microstrips, coplanar lines and coplanar waveguides are developed. The characteristic parameters of all these structures which are used extensively in microwave integrated circuits for applications as transmission lines and other circuit elements are computed for the general case of single, symmetrical and nonsymmetrical multiple coupled lines. For the case of microstrip lines, the existing Green's function integral equation method used for single and identical coupled lines is completely reexamined to devise a much improved efficient version. In addition, new methods which are based on similar principles are developed for the case of coplanar striplines and waveguides. The quasi-TEM parameters of these structures are evaluated by utilizing the spectral domain Green's function. The kernel functions in the resulting Fredholm integral equations are found to be singular for coplanar structures without ground planes and numerical techniques to solve such equations are formulated. In many instances, it is shown that the use of basic physical laws can be quite effective in resolving the problems due to such singularities. The solution procedure adopted is the general Galerkin method employing the local basis approximation schemes with a piecewise constant (gate) function for basis functions. The local basis approximation scheme is readily adaptable to the case of multiple coupled line structures. A novel decomposition concept for the quasi-static spectral Green's function is introduced. This decomposition of the Green's function into a homogeneous part with singularities and the remainder leads to the formulation of efficient schemes for evaluating the needed numerical quadratures and to the analytical integrations of many terms with the singularity problem. The quasi-TEM normal mode parameters such as the characteristic impedances of all the lines and phase velocities for all the normal modes for various structures have been computed for typical range of several parameters. The accuracy of these computations is examined by comparing the computed results with exact analytical solutions for the special case of the homogeneous medium problems. A simple extrapolation scheme to improve the accuracy of the results is also included. It is shown, that the techniques developed can be applied to several Pther useful structures. In addition, the limitations and weakness of the numerical schemes adopted are also examined together with possible improvement schemes and alternatives.
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