An Analysis of Certain Errors in Electronic Differential Analyzers II-Capacitor Dielectric Absorption

The permittivity or dielectric constant of the materials used in capacitors is not actually a constant but is a complex function of frequency and temperature. Consequently, the feedback capacitors used in the integrators of a differential analyzer cannot be considered ideal, but their capacitance must be considered a variable. Methods of representing the complex capacitance are discussed and a model is selected which is conveniently suited to the analysis. Experimental methods of measuring the complex capacitance are described. The phenomenon of dielectric absorption is interpreted in terms of the capacitor model and it is shown that an integrator having such a feedback capacitor will experience a change in effective initial conditions after a solution is started on the computer. It is also shown that when such integrators are used to solve linear differential equations with constant coefficients, the locations of the roots of the characteristic equation are changed slightly; these changes can be evaluated when the properties of the capacitor model are known.