A NEW APPROACH TO NUMERICAL FIELD AND POTENTIAL CALCULATIONS

Abstract

A. Conformal Transformation Methods A standard analytic method for the determination of field and potential distributions uses the Schwarz‐Christoffel (SC) conformal transformation integral. When applied to configurations such as the capacitor with fringing accounted for or a metal stripe separated by a dielectric from a ground plane, it leads to complicated expressions containing elliptic integrals, and when applied to a metal disc separated from a ground plane, Hankel transforms are also involved. Since elliptic integrals must be evaluated numerically in practice, it is desirable to replace these complicated analytic processes with one that is numerical from the start. Such a method has been published by Foster, Anderson, and Warner. It is based on the standardization of a two‐step conformal transform; Step 1 takes the original geometry and lays it out along the real axis and Step 2 converts this arrangement—using a reverse Schwarz‐Christoffel transform—into a rectangular structure from which the field lines and equipotentials can be determined by inspection. Step 1 is different for each problem but Step 2 is common to all problems, and represents one of several advantages of this procedure. The simplest example given by the originators is the tri‐plate strip line of Figure 1, which—by symmetry—can be reduced to the quadrant of Figure 2. The SC

Citation

Nussbaum, A. (1994), "A NEW APPROACH TO NUMERICAL FIELD AND POTENTIAL CALCULATIONS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 13 No. 1, pp. 47-50. https://doi.org/10.1108/eb051837