Calculation of Microstrip Lines by Means of Singular Integral Equations

In case of homogeneous filling the electromagnetic field of the lowest mode in a microstrip line is transverse and can be described by harmonic functions. If the filling is piecewise homogeneous the longitudinal components of electric and magnetic fields arise for lower frequencies being much less than transverse ones. This allows one to use the approximation of transverse electromagnetic waves. The idea of the proposed method is to represent the potential in the form of a Cauchy type integral. Thus the differential equations are satisfied. Then the boundaryr conditions lead to singular integral equations [ I]. We used to solve the equations numerically. In some simplest cases it is possible to get a solution in an analytical form. The main advantages of a method are: I. The method reduces the solution of a two-dimensional problem to one-dimensional one drasticadly shortening computer time. 2. The algorithm of the solution and the form of the equations don't depend on the shape of the line cross section. 3. The conduct of the solution in angular points rigorously corresponds to the static one. 4. From the computational point of view it appeared to be more convenient to apply the method to the line having real geometrical sizes (say finite thickness of a strip). If one considers a line having infinitely thin strips it is convenient to use the representation by Muskhelishvili