A digital four-arm bridge for the comparison of resistance with capacitance

TL;DR

This paper presents a digital four-arm bridge that accurately compares resistance and capacitance by mimicking classical bridge balances digitally, achieving high precision with reduced voltage stability requirements.

Contribution

The authors introduce a novel digital four-arm bridge design that enhances resistance-capacitance comparison accuracy using digital balancing techniques.

Findings

Achieved a combined standard uncertainty of 5×10⁻⁹ for 100 kΩ resistor and 1 nF capacitor comparison.

Demonstrated the digital bridge's effectiveness near 1592 Hz frequency.

Reduced voltage stability requirements due to correlation in the digital balancing process.

Abstract

We have built and demonstrated a digital four-arm bridge for the comparison of resistance with capacitance. The digital four-arm bridge mimics the classical quad bridge in the digital domain with three balances: the source balance, the detector balance, as well as the main balance. Due to correlation, the required precision of the source voltages is only of the order of the square root of the ultimate bridge precision. For the comparison of a $100\,$k$\Omega$ resistor with a $1\,$nF capacitor near 1592 Hz, the combined standard uncertainty $(k = 1)$ is $5\times 10^{-9}$.