Empirically-derived capacitor characteristic formulas from distributed modelling

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Diffusion equation modelling is used to develop formulas for the normally fixed values of capacitance and resistance of the traditional capacitor equivalent circuit. The formulas define the dependence of the equivalent circuit values on metal film resistivity, capacitance per unit area, areal dimensions of the metallisation and on frequency. A multilayer capacitor topology, having both capacitor plates connected at the same end, is used for the derivation, but it is shown that the results are also representative for the more standard double-end connected topologies with some restrictions above the typical self-resonance frequency of these capacitors. The formulas allow accurate prediction of dissipation factor and input impedance according to the design parameters used in constructing the capacitor, thus providing powerful tools in capacitor design. The algorithms also facilitate the determination of internal voltages, currents and power distribution within the capacitor, thus exposing the effects, for example, of partial edge disconnection. The formulas may potentially provide a better capacitor equivalent circuit with dependent variables for circuit emulation. In the paper, the derivation process is described and the formulas tested against experimental results. A simple addition to the equivalent circuit is also included to model dielectric loss which dominantly determines the dissipation factor at low frequency.