A Volume Integral Formulation for Electromagnetic Scattering from Homogeneous Dielectric Bodies

In recent years, printed circuit antennas have become very useful in conformal and planar phased array antenna systems. Of particular interest is the radiation and scattering performance of stripline and microstrip printed circuit antenna array-elements used in these systems. These ele­ments are generally made up of a complex three-dimensional distribution of dielectrics and con­ductors, which can include microstrip or stripline feed circuitry on a dielectric substrate. Figure 1 shows the geometry of a typical multilayer printed circuit stripline-fed flared slot antenna, used as an array-element in a multioctave planar phased array antenna. This antenna element design also incorporates a stripline to slotline coupling transition through the dielectric layers which further increases the intricacy of the near fields. An explicit model of these types of complicated printed circuit geometries is needed for predicting their radiation and scattering characteristics. A numeri­cal method that utilizes a digital computer to subdivide the composite three-dimensional geometry and to organize the associated computations would be beneficial. This is especially important when one considers the larger problem of modeling arrays of multiple antenna elements and the environment surrounding the antenna (i.e., radomes, ground planes, and absorbers). In this work, a numerical technique is developed to solve for the electromagnetic field scattered from the dielectric substrate portion of the printed circuit problem. The near electric field of a dielectric body is primarily produced by the bound charge residing on the surface. An accurate model of the near field is obtained through the use of this bound charge density in an integral formulation. A method of moments solution technique is used to numerically solve for the scat­tered field [1]. This solution approach should also yield a reliable prediction of the radiated fields for the antenna problem when extended to modeling the full problem of conductors on the dielec­tric substrate