The complete set of Green&rsquo / s functions for cylindrically layered media is presented. The formulations reported in the previously published work by Tokg&ouml / z (M.S.Thesis, 1997) are recalculated, the missing components are added and a solution to the problem when (rho equals rhop) is proposed. A hybrid method to calculate mutual coupling of electric or magnetic current elements on a cylindrically layered structure using MoM is proposed. For the calculation of MoM matrix entries, when (rho equals rhop) and fi is not close to fip, the closed-form Green&rsquo / s functions are employed. When fi is close to fip, since the spectral-domain Green&rsquo / s functions do not converge, MoM matrix elements are calculated in the spectral domain. The technique is applied to both printed dipoles and slots placed on a layered cylindrical structure. The computational efficiency of the anaysis of mutual coupling of printed elements on a cylindrically layered structure is increased with the use of proposed hybrid method due to use of closed-form Green&rsquo / s functions.

Full wave analysis of microstrip lines at microwave frequencies is performed by using method of moments in conjunction with closed-form spatial domain Green&rsquo / s functions. The Green&rsquo / s functions are in general Sommerfeld-type integrals which are computationally expensive. To improve the efficiency of the technique, Green&rsquo / s functions are approximated by their closed-forms. Microstrip lines are excited by arbitrarily located current sources and are terminated by complex loads at both ends. Current distributions over microstrip lines are represented by rooftop basis functions. At first step, the current distribution over a single microstrip line is calculated. Next, the calculation of the current distributions over coupled microstrip lines is performed. The technique is then, applied to directional couplers. Using the current distributions obtained by the analysis, the scattering parameters of the structures are evaluated by using Prony&rsquo / s method. The results are compared with the ones gathered by using simulation software tools, CNL/2&trade / and Agilent Advanced Design System&trade / (ADS).

In the first part of the thesis, the 2-D structures in stratified media are analyzed using an efficient MoM technique. The method is used to optimize transmitted or reflected electric fields from the 2-D structures. The genetic algorithm is used in the optimization process. In the second part a 3-D MoM technique is implemented to analyze multilayered structures with periodically implanted material blocks. Using the method, the dispersion and reflection characteristics of the structure are calculated for different configurations. The results are compared with the results found in the literature and it is seen that they are in good agreement. Asymptotic Waveform Evaluation (AWE) technique is utilized to obtain the Pade approximation of the solution in terms of frequency. The high order derivatives that are required by the AWE technique are calculated through Automatic Differentiation technique. Using the AWE method, the dispersion diagram and reflection characteristics of the periodic structures are obtained in a shorter time. The results are compared with the ones obtained through direct calculation and it is seen that they are in perfect agreement. The reflection coefficients that are obtained from the 3-D MoM procedure are used to calculate Green&rsquo / s functions that approximate electric field of an infinitesimal dipole on the periodically implanted substrate. Using the calculated Green&rsquo / s functions and the spectral domain MoM procedure, dispersion characteristics of a microstrip line on the periodically implanted substrate are obtained.

Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green&rsquo / s function in layered media which is expressed as an infinite series in terms of the spectral domain Green&rsquo / s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green&rsquo / s function. First, the spectral domain Green&rsquo / s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald&rsquo / s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green&rsquo / s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.

Method of Moments (MoM)/Green&rsquo / s function formulation is developed for the analysis of electromagnetic radiation from planar rectangular microstrip antennas with different feeding techniques. Investigated structures are microstrip line fed patch antenna, proximity coupled patch antenna and slot coupled patch antenna. For all these structures equivalent problems are defined. Then, integral equations where currents are the unknowns are obtained from boundary conditions and by using spectral domain representation of Green&rsquo / s functions. Finally, MoM is applied to convert these integral equations to a system of linear equations. Currents on the conducting surfaces as well as equivalent magnetic currents on the apertures are modeled as a sum of piecewise sinusoidal subdomain basis functions with unknown coefficients which are calculated by solving the system of linear equations. Based on the formulations provided in this study, a Fortran code is developed. Numerical results calculated by using the code are presented in the form of patch and line currents and input impedances. Presented results are in good agreement with the results given in the literature.

In this thesis, an analysis technique for the slot coupled patch antennas using MoM in conjunction with the closed form Green&rsquo / s functions is presented. Slot coupled patch antennas are fed by a microstrip open stub which is coupled to the patch through an electrically small slot. Current distributions over the microstrip line, slot line and the patch are represented by rooftop basis functions. First, a relatively simple structure, microstrip coupled slot line is investigated using the proposed technique. Then the method is extended to the slot coupled patch antenna geometry. By using the method, current distributions on the feedline and the patch are calculated for a generic slot coupled patch antenna. Then by using the distributions, return scattering parameters of the antenna is approximated with complex exponentials using Prony&rsquo / s method. A parametric study is carried out to observe the effect of each antenna component on the antenna performance. Current distributions and return loss calculations are repeated for modified antennas to observe and demonstrate the performance differences. All simulations are verified using HFSS&reg / software and the results available in the literature.

_I The theory of impulsive di&reg / erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di&reg / erential equations. In this work, higher order linear impulsive equations at &macr / xed moments of impulses together with certain boundary conditions are investigated by making use of a Green&#039 / s formula, constructed for piecewise di&reg / erentiable functions. Existence and uniqueness of solutions of such boundary value problems are also addressed. Properties of Green&#039 / s functions for higher order impulsive boundary value prob- lems are introduced, showing a striking di&reg / erence when compared to classical bound- ary value problems of ordinary di&reg / erential equations. Necessarily, instead of an or- dinary Green&#039 / s function there corresponds a sequence of Green&#039 / s functions due to impulses. Finally, as a by-product of boundary value problems, eigenvalue problems for higher order linear impulsive di&reg / erential equations are studied. The conditions for the existence of eigenvalues of linear impulsive operators are presented. Basic properties of eigensolutions of self-adjoint operators are also investigated. In particular, a necessary and su&plusmn / cient condition for the self-adjointness of Sturm-Liouville opera- tors is given. The corresponding integral equations for boundary value and eigenvalue problems are also demonstrated in the present work.