Measuring Non-linearity in AH 2700A Capacitance Bridges with sub-ppm level uncertainty

The stability and non-linearity of a commercial AH 2700A capacitance bridge were studied beyond its specified capabilities using the Thompson-Lampard Calculable Capacitor (TLCC) at LNE. The TLCC allows for continuous variation of measured capacitance between 0.4 pF and 1.2 pF with a resolution of 2 parts in $10^{7}$ and stability better than 1 part in $10^{9}$ over 2 days. The study aimed to determine root cause of the saw-tooth non-linearity pattern observed in the AH 2700A capacitance bridge. This pattern becomes apparent when the internal calibration is no longer valid, indicating deviations in the bridge circuit. Additionally, the dependence of capacitance non-linearity on various factors such as frequency and capacitance value are described. This work enables automatic calibration of the commercial bridge with an uncertainty of sub-ppm level and allows for quick evaluation of TLCC's non-linearity and monitoring of any changes over time through in-situ measurements.