Novel Impedance Standards Based on Series-Connected Metal-Foil Resistors

In this article, we present novel impedance standards at a nominal value of 12.9 k $\Omega $ based on a series connection of four commercial, metallically encapsulated metal-foil resistors. Single metal-foil resistors have advantages that make them suitable for many applications, including as an impedance standard at kHz frequencies. Nevertheless, metrologists are seeking to achieve even better standards. Selecting single resistors whose deviation from the nominal dc resistance value and whose temperature dependence has opposite signs allows a reduction of these properties at the series-connected resistor. In addition, connecting four resistors in series reduces the dissipative parallel capacitance by a factor of four. To avoid limitation due to the capacitances between each metal foil and its metal encapsulation, voltage is supplied to the encapsulations in such a way that their capacitance contribution is not only greatly reduced but also that their residual capacitance cancels the residual parallel capacitance (at least partially). This reduces the total capacitance to a few tens of femtofarads and the corresponding frequency dependence to the range of (20 to 37) $\times 10^{-9}$ kHz−1. These properties are not accurately calculable but can be modeled with a remarkably low uncertainty by electrical quantities measured at each single resistor. As such, the series-connected metal-foil resistors represent excellent standards of impedance and time constant.