Abstract
The Planck-Balance is a table-top version of a Kibble balance. In contrast to many other Kibble balances, the coil is moved sinusoidally and an ac rather than a dc signal is generated in the velocity mode. The three-parameter sine fitting algorithm is applied to estimate the amplitudes of the induced voltage and the coil motion, which are used to determine the force factor Bl of the voice coil of the electromagnetic force compensation balance. However, the three-parameter sine fitting algorithm is not robust against some perturbations, e.g. additive Gaussian white noise, quantization error, harmonic distortion, frequency error and time jitter. These effects have influences on the accuracy of the amplitude estimation. Based on numerical simulations and correlation analyses, the effects of these perturbations are determined. By optimizing measurement and data processing approach, the bias and standard deviation of the estimated amplitude can be effectively reduced, and thus the accuracy of the force factor Bl in the velocity mode can be improved.
Highlights
After the redefinition of the kilogram, the Kibble balance is one possible approach to the calibration of mass standards in terms of the fixed value of the Planck constant with zero uncertainty [1]
The results show that those theoretically determined values have been validated by the Monte Carlo Method (MCM)
Perturbations in the signal can result in a bias of the amplitude estimation when using the three-parameter sine-fitting algorithm
Summary
After the redefinition of the kilogram, the Kibble balance is one possible approach to the calibration of mass standards in terms of the fixed value of the Planck constant with zero uncertainty [1]. In the velocity mode of other Kibble balance experiments, the coil is usually moved at a constant velocity [3][5] In contrast to these Kibble balances, the coil of the PB is sinusoidally moved through the magnetic (B-)field in an oscillatory manner, inducing an AC voltage across the coil ends. This voltage is digitised by means of a high-precision digital multimeter (Keysight 3458A). The measurements of voltage and position are synchronised by means of an external trigger source with a trigger frequency of 1 kHz. The three-parameter sine fitting algorithm is applied to determine the amplitudes of the induced voltage and the coil motion. The bias and standard deviation of the estimated amplitude provided by the three-parameter sine fit are investigated by the theoretical equations and a Monte Carlo simulation
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