NUMERICALLY EFFICIENT TECHNIQUES FOR THE ANALYSIS OF MICROWAVE ANTENNAS, CIRCUITS AND SCATTERING PROBLEMS
Open Access
- Author:
- Yeo, Junho
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 10, 2003
- Committee Members:
- Raj Mittra, Committee Chair/Co-Chair
Kultegin Aydin, Committee Member
Douglas Henry Werner, Committee Member
Vijay Krishna Varadan, Committee Member
Eugene Edmund Clothiaux, Committee Member - Keywords:
- Impedance Matrix Interpolation
Method of Moments (MoM)
Characteristic Basis Function (CBF)
Microwave antennas and Circuits
Scattering Problems - Abstract:
- In this thesis, three approaches to alleviating the problem of large computation times arising in the Method of Moments (MoM) analysis of electromagnetic (EM) problems are presented. First, a new impedance matrix interpolation algorithm is proposed to speed up the time for matrix generation over a wide frequency range for planar microstrip structures. We extend the free space impedance matrix interpolation method to planar microstrip structures by using the properties of the associated Green¡¯s function over the frequency range of interest. We do this by first computing and storing the impedance matrix elements at three selected frequencies, and then generating them at intermediate frequencies within the band via interpolation. The present interpolation scheme differs from those employed previously in a rather significant way, because it uses ¡°different¡± interpolating functions in three different regions, viz., near, intermediate and far, defined on the basis of the distance between the source and the testing functions. We also investigate the problem of deriving an optimum interpolation step size for microstrip structures that depends on the largest distance between the source and testing functions, and the upper limit of the frequency band. Second, a novel method for efficient MoM analysis of large and/or complex planar array antennas using Characteristic Basis Functions (CBFs) is proposed to reduce the matrix solution time. The CBFs are special types of high-level basis functions, defined over domains that encompass a relatively large number of conventional subdomain bases, e.g., triangular patches or rooftops. For instance, for a microstrip array, the original antenna geometry is divided into N blocks, where each block contains an individual array element, and the primary and secondary CBFs are constructed for each block. The primary CBF for a particular block is associated with the solution for the isolated block, while the secondary ones account for the mutual coupling effects between it and the other blocks. This technique differs from other similar approaches, developed previously, in several aspects. First, it includes mutual coupling effects directly by using primary and secondary CBFs, which are then used to represent the unknown induced currents on the blocks, and solved for via the Galerkin method rather than by using iterative refinements. Second, the Characteristic Basis Function Method (CBFM) is more general, and can be applied to a wide class of electromagnetic problems. Finally, we present an efficient method for computing the matrix elements directly for distances greater than 0.15¥ë that bypasses the Green¡¯s function calculation and the evaluation of the double integrals needed to generate the matrix elements for scattering problems of perfectly conducting objects. In the conventional MoM using the sub-sectional basis functions, and a l/10 or l/20 discretization, the computation of the MoM impedance matrix elements consumes a considerable portion of the total solution time as the problem dimensions become large in terms of the wavelength, because the matrix generation requires O(N2) operations, where N is the number of unknowns. In the proposed method, we investigate the number of Degrees of Freedom (DoFs) of the MoM matrix elements, and show that they can be represented in terms of a very small number of Characteristic Functions. The coefficients of the Characteristic Functions are pre-determined by interpolating several directly-calculated impedance matrix elements along two principal directions. Thus, we can generate the MoM matrix elements without having to perform the usual integration involving the basis, testing and Green¡¯s functions, except for a few entries that are computed directly.