Measurement of the frequency dependence of four terminal-pair air capacitors with a vector network analyzer

Four terminal-pair air capacitors are important transfer standards to calibrate LCR meters up to a frequency of 10 MHz. We report a simple and new method to obtain the frequency dependence of the four terminal-pair capacitance of these standards using a four-channel vector network analyzer (VNA). The frequency dependence of the capacitance of an air capacitor and its uncertainty can be obtained from a single set of measurements without changing connections between the standard and the VNA, as has been the case in previously published work. The calculation of the frequency dependency is straightforward and model-independent. Nevertheless, an elementary model is provided to explain the observed frequency dependence. This article allows every laboratory with a four-channel VNA to measure the frequency dependence of these capacitors. Hence, a significant shortening of the traceability chain is achieved.