Frequency Dependence of Primary Capacitance Standard in Audio Frequency Range

Beschreibung

The Thompson-Lampard theorem is a theorem of electrostatics which describes a so-called cross capacitance independent of its cross sectional dimensions. It is therefore best suited to be used as a capacitance standard for the absolute determination of the unit of capacitance, the farad. As this cross capacitance is defined for DC but must be operated at AC, a frequency correction must be applied the uncertainty of which is one of the largest contributions to the uncertainty budget. The frequency correction can be calculated with a sufficient accuracy using an equivalent circuit model which describes the behaviour of the calculable cross capacitor at AC. Calculable cross capacitors are mostly operated at a frequency of 1592 Hz (ϖ = 104 rad/s) which is convenient for the link between the farad and the ohm. The determination of the frequency behavior of the PTB calculable cross capacitor in the audio frequency range is carried out by applying an equivalent circuit model which considers the influence of distributed admittances and impedances within the calculable cross capacitor. It has been derived taking into account the main currents flowing inside the calculable cross capacitor and the voltage drops caused by these currents. Most of the circuit parameters of the model were directly measured in the actual configuration of the electrode system with a commercial autobalancing bridge in a frequency range between 1 kHz and 10 kHz. Owing to the uncertainty of the bridge which is 0.1 % for capacitance measurements and 2 % for inductance measurements, the calculated uncertainty of the frequency correction amounts to a few parts in 108. The capacitances on the calculable cross capacitor were found to be frequency independent, but self-inductances and mutual inductances of the electrodes are frequency dependent and linearly proportional to the inverse square root of the frequency in the examined frequency range. The frequency dependence of the calculable cross capacitor has been calculated based on the measured circuit parameters. It has been found that the frequency dependence of the cross capacitance is proportional to the square of the frequency, and that the influence of mutual inductances of opposite electrodes dominate the behavior at higher frequencies. At a frequency of 1592 Hz, the correction of the PTB calculable cross 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.
The Thompson-Lampard theorem is a theorem of electrostatics which describes a so-called cross capacitance independent of its cross sectional dimensions. It is therefore best suited to be used as a capacitance standard for the absolute determination of the unit of capacitance, the farad. As this cross capacitance is defined for DC but must be operated at AC, a frequency correction must be applied the uncertainty of which is one of the largest contributions to the uncertainty budget. The frequency correction can be calculated with a sufficient accuracy using an equivalent circuit model which describes the behaviour of the calculable cross capacitor at AC. Calculable cross capacitors are mostly operated at a frequency of 1592 Hz (ϖ = 104 rad/s) which is convenient for the link between the farad and the ohm. The determination of the frequency behavior of the PTB calculable cross capacitor in the audio frequency range is carried out by applying an equivalent circuit model which considers the influence of distributed admittances and impedances within the calculable cross capacitor. It has been derived taking into account the main currents flowing inside the calculable cross capacitor and the voltage drops caused by these currents. Most of the circuit parameters of the model were directly measured in the actual configuration of the electrode system with a commercial autobalancing bridge in a frequency range between 1 kHz and 10 kHz. Owing to the uncertainty of the bridge which is 0.1 % for capacitance measurements and 2 % for inductance measurements, the calculated uncertainty of the frequency correction amounts to a few parts in 108. The capacitances on the calculable cross capacitor were found to be frequency independent, but self-inductances and mutual inductances of the electrodes are frequency dependent and linearly proportional to the inverse square root of the frequency in the examined frequency range. The frequency dependence of the calculable cross capacitor has been calculated based on the measured circuit parameters. It has been found that the frequency dependence of the cross capacitance is proportional to the square of the frequency, and that the influence of mutual inductances of opposite electrodes dominate the behavior at higher frequencies. At a frequency of 1592 Hz, the correction of the PTB calculable cross 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.

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Monthol Homklintian

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