Influences on amplitude estimation using three-parameter sine fitting algorithm in the velocity mode of the Planck-Balance

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.

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

“…The bias, which we derived above, does not depend on the sampling strategy employed. In [16] it was shown that if coherent sampling is applied, i.e. when only full cycles of the oscillation are analyzed, then the bias due to higher harmonics is zero.…”

Adaptation of metrology-grade ac current source in velocity mode of Planck-Balance 2: direct referencing induced voltages with ac quantum voltage standard

“…The resulting voltage induced in the measurement coil in each case was measured with the same voltmeter under the same parameter configurations (aperture time 700 µs, sampling time 1 ms, voltage range 1 V). The comparison of all three measured signals shows no obvious difference (see figure 5(a), however when subtracting the first harmonics obtained by a sine fit [18] from each measured signal it is possible to distinguish from the remaining noise of the amplitude spectral densities a substantial characteristic differences. In particular, as expected, it is seen that the higher order harmonics (2nd, 3rd,...) apparent in each signal from which the highest magnitude distortions (including the noise) demonstrate the low-grade dSpace system.…”

Measuring the Induced Ac Voltage in the Planck-Balance With an Ac Quantum Voltmeter

“…For this sampling frequency the aperture time is set to 2.27 × 10 -4 s. The sampling lasts 10 s for each measurement cycle, thus including 40 oscillation cycles. By means of a three-parameter sine fitting we obtain the voltage amplitude of the coil [6]. The model function contains the first four higher harmonics of the fundamental oscillation frequency.…”

“…Those amplitudes are obtained by a three-parameter sine fit to the sampled data, where the frequency 𝑓 is known very accurately, since the oscillation is driven with a stable frequency generator. A more 2 of 5 detailed description of the analysis can be found in [6].…”