Analysis and design of polygonal resistors by conformal mapping

To compute the electrical resistance ( ~ conformal modulus) of a polygonally shaped resistorcut from a sheet of uniform resistivity, it suffices to find a conformal map of the polygon onto arectangle. Constructing such a map requires the solution of a Schwarz-Christoffel parameter prob-lem. First we show by examples that this is practical numerically. Then we consider an inverse 704Lloyd N. Trefethen ZAMP "resistor trimming" problem in which the aim is to cut a slit in a given polygon just long enoughto increase its resistance to a prescribed value. We show that here the solution can be obtained bysolving a "generalized parameter problem." The idea of a generalized parameter problem is applica-ble also in many other Schwarz-Christoffel computations.