Stepwise compensation waveform generation by using Josephson voltage standards for joule balance

Abstract

Flux linkage difference in the new joule balance can be obtained by the time integration of the induced voltage u(t) from the suspended coil relative to a moving magnet driven by a dc motor translation platform. Due to the finite acceleration of the dc motor, the transition and waveform of u(t) are finite and not regular. To accurately measure the time integration of u(t), a compensation waveform with precision time integration should be synthesized. In this paper, a stepwise compensation waveform is synthesized by a programmable Josephson voltage standard (PJVS) according to u(t). The accuracy of measuring the stepwise waveform with multiple transitions can be improved by reducing the ratio of the time integrated value of the total transitions to the total waveform less than one part in 102 in the joule balance. The time integration of the rise/fall transition is measured by a synchronized reference square wave generated by another PJVS system. With the total time integration more than 20 Vs, the uncertainty of the generated stepwise waveform is within 5.2 × 10−8 VsV−1s−1. The result confirms that the PJVS has the capability to generate a stepwise compensation voltage for flux linkage difference measurement.

The first determination of the Planck constant with the joule balance NIM-2

“…When the PJVS is switching between quantized voltage levels, it produces transient voltages which can add uncertainty to the calculation of the voltage integral. The uncertainty from the transitions has been accurately determined by a simultaneously generated square wave [16] and its value is within 2 × 10 -7 V s. With the total time integration value is more than 10 V s, the relative uncertainty contribution will be within 2 × 10 -8 .…”

“…To measure the flux linkage difference, the time integration of the compensation waveform should be determined in advance. The time integration of the transitions of the stepwise compensation is accurately determined by a simultaneous square wave generated by another PJVS [16]. The stable voltage integral is calculated by the duration and quantized voltage value.…”

“…The stable voltage integral is calculated by the duration and quantized voltage value. The uncertainty of the duration of the stable voltage is about several parts in 10 11 [16]. To eliminate the undesired offset voltage, which includes both the voltmeter offset and thermal electromotive forces (EMFs) in the measurement loop, with a fixed and a linear drift component, the time integration measurement procedure follows a '+ − + − + −' sequence, where '+' and '−' respectively represent waveforms biased positively and negatively.…”

“…The uncertainty of flux linkage difference measurement is listed in table 5, and its value is 1.6 × 10 -8 V s V −1 s −1 . When the total time integration values of the waveforms are more than 10 V s, the difference between the uncertainty contribution of the transition to stepwise waveform and that to the square wave is less than 4 × 10 −10 V s V −1 s −1 [16], which is neglected in this section. With the standard deviation of the time integration of the stepwise waveform listed in table 4 is 2.1 × 10 -9 V s V −1 s −1 , the uncertainty of the time integration of stepwise compensation waveform is calculated as √2 × 2.1 × 10 -9 V s V −1 s −1 ≈ 2.9 × 10 -9 V s V −1 s −1 .…”

The upgrade of NIM-2 joule balance since 2017

“…Due to the effect of the magnet motion repeatability, the measurement interval fluctuation will lead to a relative uncertainty of 6.1 × 10 −9 . Finally, the compensation voltage waveform may deviate from the ideal square waveform because of the transient characteristics of level conversion and the leakage resistance of the PJVS system, which yield the relative uncertainties of around 2.9 × 10 −9 and 7.2 × 10 −9 , respectively [17]. The different uncertainty sources of flux linkage difference measurement have been listed in table 1, and the relative uncertainty contribution is 1.1 × 10 −8 .…”