A Capacitance Build-Up Method to Determine LCR Meter Errors and Capacitance Transfer

We present a capacitance build-up method suitable for the determination of the measurement error of a capacitance meter. The method requires only a small number of uncalibrated base capacitors, to be connected in parallel in various combinations, and a single calibrated capacitor, which provides measurement traceability. The outcome of the method is both the determination of the meter error and the calibration of all the base capacitors; it can therefore be also considered a capacitance scaling method. The method's equations, cast in matrix form, express estimates and uncertainties for all the quantities of interest. As an example of application, a commercial $\mathit {LCR}$ meter is calibrated in the ranges of (100-1000) pF and (1-10) nF at 1.6 and 10 kHz, with an accuracy at the level of a few parts in 106. The calibration is validated by comparison with an ultrahigh accuracy capacitance bridge.