Application of the moment method to the antenna problems

SUMMARY Application of the Moment Method :o the Antenna Problems To solve the antenna problems by an analytic method, some assumptions are considered. For example, the curent distribution on a dipol antenna is generally assumed either uniform or sinusoidal as dependent on its length. However, for all the antenna problems, the accurate results cannot be obtained by such assumptions, and their analytic solutions cannot be easy. Therefore, to remove such assumptions from problem and to simplify analytic solution of the problem, various numerical methods has been developed. Moment method is one of these numerical methods and is succesfully applied a number of antenna problems. Moment method essentially transforms the derived equation of the considered antenna problem into a matrix equation which can be solved easily on a computer. Since the current distribution is the assumed quantity in the antenna problems, it is the unknown in the moment method solution. Thus, one must primarily obtain the current distribution for the solution of the problem. Once the current distribution is obtained, the others can be computed easily. For simplicity, considering a dipol antenna problem can be described applying to antenna problems of the moment method. The unknown in the intiegral equation of the problem is the form of the current distribution on the dipol. The dipol antenna is divided into N segments. The form of the current on each segment can be approximated by a puis, triangle or sinusoidal function whose coefficient is a constant. Thus, the current on the dipol is approximated by a series of functions with the unknown coefficients must be primarily determined, lo accomplish this, N equations with N unknowns are produced. These equations are obtained by applying the derived integral equation of the problem at N segments. Finaly, it is obtained a matrix equation shown in the form of !z||l| ? IV I. In this equation, |Z| and |v| are called the generalized impedance and voltage matrices. |l| is a current matrix containing the unknown coefficients. But their units need not necesarrily be, except the current matrix, ohms and volts, respectively. From this equation, the current distribution can be obtained by using the known standart inverse matrix methods. The method described above, can be considered as the general moment method. Moment method has two particular method. These are point matching method is efficient numerical integrations to decrease but, does not raipdly converge the result. Piecewise sinusoidal Galerkin method is efficient numerical integrations to decrease and rapidly converges the result.In this study, the various antenna problems are solved by using the point matching and piecewlaa sinusoidal Galerkin methods. The input impedance of a dlpol antenna of 0.47 X length is computed by using both the methods. The results are compared with the measured values. The input impedance of a Yagi array of 15-elements is computed by varying the spacing between the reflector element and the driven element. The computed values are compared with the measured values.