Resonance frequency of four-terminal-pair air-dielectric capacitance standards and closing the metrological impedance triangle

A new technique for determining the resonance frequency (f(0)) of four-terminal-pair air-dielectric capacitance standards is discussed. The resonance frequency is determined by measuring four parameters of the capacitance standards over a range of frequencies near f(0). These parameters are the two-terminal-pair impedance coefficients as defined in an impedance matrix. From a knowledge of the four-terminal-pair resonance frequency of the standards it is possible to calculate their frequency dependence for f << f(0) using a simple electrical model. For air-dielectric capacitance standards it is also possible to determine their dissipation factor from the -3 dB width of the measured resonance curve. Ultimately, the validity of the technique described here would need to be verified by establishing closure of a proposed 'metrological impedance triangle' (MIT). This would involve measuring the frequency dependence of a four-terminal-pair air-dielectric capacitance and a calculable resistance standard in a 10: 1 bridge between a range of frequencies, for example 1.592 kHz and 1.592 MHz. The same standards are then compared in a quadrature bridge operating at the upper frequency of 1.592 MHz to enable closure of the MIT. Accurate closure of the MIT would be an important test for the validity of a number of high-frequency techniques and calculations for the first time.