Abstract
Semi-infinite resistive grounded grids are countably infinite electrical networks that arise from the discretization of the partial differential equation governing the minority-carrier density in a doped semiconductor. If the doping varies with depth from the surface of the semiconductor, the grid’s resistances also vary with distance from the inputs to the grid. This nonuniformity prevents the use of the characteristic-resistance method for determining currents and voltages. A computational method for making such a determination is presented herein. It is based upon the theory of infinite continued fractions whose entries are positive operators on a Hilbert space. It is also know that the solution given by the method is precisely that solution for which the power dissipated in the network is finite. Finally, the method is extended to RLC networks, and this allows the computation of transient responses in semi-infinite grounded grids of positive-real impedances.
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