Frequency dependence of 100-Ohm standard resistors measured with a CCC-based AC resistance bridge

This paper describes the frequency dependence of three 100-Ohm standard resistors in the frequency range from 0.1 Hz to 1 Hz. The measurements were carried out with an automated AC bridge based on the cryogenic current comparator (CCC) and a DC SQUID null detector. A GaAs Quantum-Hall resistance (QHR) cooled down to 1.4-1.8 K was used as a reference. The error sources related to the AC bridge and the quantum-Hall component are analyzed in detail. The kinetic inductance in the QHR is found to have an important role in ac measurements. The ac bridge has a very high sensitivity, providing a resolution of 1 ppb for a current of 40 µA at 1 Hz, with a 5 min averaging time. The plateau i=2 was obtained at 7.4 T. Some resistors, such as an NBS type 100 Ohm (L&N), reveal a strong frequency dependence below 1 Hz. The frequency dependence of the Wilkins type 100 Ohm (Tinsley) is reasonably small, and a film resistor (ZIP) shows no significant frequency dependence. Thus the frequency dependence of the standard resistors cannot, in general, be neglected, and an accurate measurement of the dependence is necessary for the determination of the value of the resistance. In addition, all the precise resistance measurements should be performed with a sinusoidal current in order to make the interpretation of the results less ambiguous.