Quadrature Bridge for $R$ – $C$ Comparisons Based on Polyphase Digital Synthesis

A coaxial quadrature bridge based on digital synthesis has been developed. The bridge compares two resistance standards (having nominal resistance R) with two capacitance standards (nominal capacitance C) at an angular frequency omega (such that omegaRC ap 1). All standards are defined as two terminal-pair impedances. All voltages and currents employed in the bridge are generated by a multiphase direct digital synthesizer constructed around a personal computer digital-to-analog converter (DAC) board and a set of buffer amplifiers; the number of electromagnetic devices has been kept to a minimum. The purpose of the bridge is to be employed in the realization of the farad unit, starting from the representation of ohm given by the quantum Hall effect. The relative bridge accuracy during the calibration of 1000-pF capacitors in terms of 100-kOmega resistors at omega = 10 krad ldr s^-1 has been verified to be less than 10^-6; preliminary uncertainty assignments give a transfer uncertainty of a few parts in 10⁸.