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

Abstract

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 inputto-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, in situ, 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 0.02 μF/F in 2 hours for measuring a 100 pF capacitor relative to a 12906 Ω resistor at 1233 Hz. The relative combined standard uncertainty (k = 1) is 0.13 μF/F, dominated by the digitizer error.

Measurement of the Frequency Dependence of Four Terminal-Pair Air Capacitors With a Vector Network Analyzer

“…Understanding the weak frequency dependence of the air capacitors at very low frequencies is an important stepping stone for impedance metrology at audio frequencies. At this frequency range, the air capacitors can be used as stable transfer standards, see, for example, [22].…”

Improving the Accuracy of Digital Unbalanced Impedance Bridges

“…To determine the measurement errors of the real part E and the imaginary part F of the impedance ratio, the complex errors occurring in relation (15)-the impedance ratio (16), the ratio of the measured voltages reproduced by digital voltage sources (17)(18) and the unbalanced voltages (19)(20)-are presented in the form of the sum of their real and imaginary parts:…”

“…Considering the relations (16)(17)(18)(19)(20) in (15), the following form of the expressions defining the measurement error, respectively, of the real and imaginary parts of the ratio of the compared impedances Z 1 and Z 2 are obtained:…”

“…Currently, automatic fully digital bridges allow comparisons of impedance standards with an uncertainty of 10 −6 -10 −5 in the audio frequency range [15][16][17][18][19][20][21]. Achieving such measurement uncertainties requires the use of systems based on DAC and ADC converters with extremely high resolutions and appropriate, often advanced, digital signal processing algorithms.…”