An AC-bridge for low-frequency measurements of the quantized Hall resistance

A simple circuit which makes possible the use of a resistance-ratio bridge based on a cryogenic current comparator (CCC) with both AC and DC is described. The different sources of uncertainty associated with the use of AC in a CCC bridge are discussed. It is shown that they should have an effect which does not exceed a few parts in 10 ⁹ of the resistance-ratio being measured, if the frequency is limited to a few hertz. This analysis is confirmed by experimental results of resistance-ratio measurements between the quantized Hall resistance (QHR) and a 100 Ω resistance standard carried out at DC, 1, 2, and 4 Hz. These measurements are, to the author´s knowledge, the first accurate DC measurements of the QHR. They demonstrate that the quantization of the Hall resistance, observed with AC and for the frequency range studied here, remains complete to within a few parts in 10⁹ or better