Calculated Frequency Behavior of the PTB Calculable Capacitor in Audio Frequency Range

Abstract

A determination of the frequency behavior of the Physikalisch-Technische Bundesanstalt (PTB) calculable capacitor in the audio frequency range is carried out by applying an equivalent circuit model. The circuit model considers the influence of distributed admittances and impedances within the calculable capacitor and has been derived from the main currents flowing inside the calculable capacitor and the voltage drops caused by these currents. It has been found that the frequency dependence of the cross capacitance is proportional to the square of the frequency, whereby mutual inductances of opposite electrodes and capacitances to ground dominate the behavior at higher frequencies. At a frequency of 1592 Hz, the correction of the PTB calculable capacitor with a value of 1 pF amounts to 9.2 × 10 −8 pF with an expanded uncertainty (k = 2) of 3.1 × 10 −8 pF.