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

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 $5\times 10^{-9}$.