Comparison of a 100-pF Capacitor With a 12 906-Ω Resistor Using a Digital Impedance Bridge

We tested a digital impedance bridge in a hybrid structure for comparison of a capacitor with a resistor where the impedance ratio was measured in two separate parts. The modulus of the impedance ratio was matched arbitrarily close to the input-to-output ratio, in magnitude, of a two-stage inductive voltage divider by adjusting the operating frequency of the bridge; the residual deviation between the two together with the phase factor of the impedance ratio was measured using a custom detection system based on a four-channel 24-bit digitizer. The ratio of the inductive voltage divider was calibrated, <italic>in situ</italic>, using a conventional four-arm bridge with two known capacitors. Fluctuations of the source voltages were largely removed through postprocessing of the digitized data, and the measurement results were limited by the digitizer error. We have achieved an overall bridge resolution and stability of <inline-formula> <tex-math notation="LaTeX">$0.02~{\mu }\text{F}$ </tex-math></inline-formula>/F in 2 h for measuring a 100-pF capacitor relative to a 12 906-<inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> resistor at 1233 Hz. The relative combined standard uncertainty (<inline-formula> <tex-math notation="LaTeX">$k $ </tex-math></inline-formula> = 1) is <inline-formula> <tex-math notation="LaTeX">$0.13~{\mu }\text{F}$ </tex-math></inline-formula>/F, dominated by the digitizer error.