Usage of integral representations for the surface current density when solving the problem on radiation of ultra wideband signals by unenclosed bent shields

Abstract

The solution of the problem of ultra wideband signal radiation by a TEM-horn, which is based an the solution of integral representation for a surface current density is proposed in view of the Meixner conditions on an edge.Keywords: ultra wideband signal, integral representation, surface current density, TEM-horn, condition on an edge.The theoretical analysis of the ultra wideband (UWB) signals diffraction is carried out using Fredholm integral equations of the I" and Znd kind. A TEM-horn, as well as the majority of the UWB radiators, represents a combination of unenclosed shields, for which, in most cases, the problem of the field diffraction is reduced to the first kind Fredholm integral equation [4], which fall into the class of illconditioned problem. When using up the second kind integral equations for the problems of diffraction on unenclosed shields with the Dirichlet and Neumann boundary conditions [I, 21, it is difficult to algorithm the obtained solutions of the three-dimensional problems in the class of special functions. This restricts feasibilities of the numerical method usage when calculating real unenclosed constructions. Therefore, the purpose of the given paper is the development of the iterative algorithm for defining the field emitted by unenclosed bent shields on the basis of intcgral representations for the surface current density. t y I . 7 Fig. 1. The calculation construction 0-7803-7881-4/03/$17.00 02003 IEEE.In the paper, an approach based on the refinement of physical optics approximation method [3] is used. To solve, the problem of UWB signal radiation by a TEM-horn, we shall consider a system consisting of two indefinitely thin bent unenclosed ideally conductive surfaces S = SI U S, with the exponential profiles (Fig. I), located in free space. Each of the surfaces SI, S, is a two-sided Lyapunov surface having no self-intersections.Let the system be excited by indirect sources of the electromagnetic field located at points Qo and representing a sct of equally oriented electrical dipoles, each having the distribution of the surfacc current density j ( Q , t ) . The vector-moment of the dipoles is directed along the Y-axis: ( Q , t ) = z J o s ( Q -Q O , s c t ) ,(1)where ZyJ0 is the dipole vector-moment; Ey is the ort of Oy -axis; Jo is the current amplitude: 6c.1 is the Dirac delta-function; Qo is a point of the dipole determination; Q is the variable point in the area of sources location.It is necessary tn determine the vectors of electrical E ( M , t ) and magnetic fields 2 ( M , t ) excited by the sources (1) located outside the surface S .In order to determine an electromagnetic field outside the surface S , it is necessary to solve a set of Maxwell equations satisfying zero initial conditions, boundary conditions executed on the both sides of the surface S , radiation conditions, electromagnetic field energy finiteness condition: