High-Precision Capacitance Bridge for Dielectric-Constant Gas Thermometry

A high-resolution and high-precision autotransformer ratio capacitance bridge is described that has been built and tested at the Physikalisch-Technische Bundesanstalt for dielectric-constant gas thermometry. Its main component is a homemade high-precision 1 : 1 inductive voltage divider used in a autotransformer configuration. For balancing the bridge, adjustable in-phase and quadrature currents can be injected. A detailed uncertainty budget is presented for measuring small capacitance changes. Considering correlations between main terms in the mathematical model, it is shown that it is possible to measure capacitance changes of at most a few 0.1% with a relative standard uncertainty below one part per million, i.e., with an uncertainty relative to the capacitance value of order one part per billion.