A method for evaluating the force factor in oscillating Kibble balances with application to the Planck-Balance

Abstract

Abstract The Planck-Balance is a table-top version of a Kibble balance, developed in a collaboration between the PTB and TU Ilmenau. In contrast to most Kibble balances, where the motion range is of up to several centimeters in the velocity mode, in the Planck-Balance it is below 100 μm. For a reliable determination of the force factor, the voice coil is set into harmonic oscillation, resulting in an induced AC voltage. The amplitude of the first harmonic is then taken to determine the force factor. However, due to the non-linear magnetic field across the motion range, the first harmonic is subject to a bias, and higher harmonics are excited. Those higher harmonics contain the information about the relative magnitude of the bias in the first harmonic, and can be used for a correction. In this paper we present an analytical model and show its application with real measurements. The estimated relative bias amounts to − 6.3 ⋅ 10 − 6 , with a residual relative uncertainty of 6.3 ⋅ 10 − 7 , for an oscillation amplitude of 20 μm. This method is especially of importance for Kibble balances with short motion range and working with harmonic oscillation. After such a correction is applied, a table-top version of a Kibble balance can be used as a conventional balance calibrated by means of E2 mass standards in the whole E2 class mass range.