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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. [ABSTRACT FROM AUTHOR]

A permanent magnet with soft magnetic yokes has been widely adopted in the watt or joule balance for precisely measuring the Planck constant. A circularly symmetric structure is conducive to the alignment of the coil but is also an enormous challenge for machining and assembly. In this paper, we mathematically prove that one of the mechanical requirements—the misalignment of the inner and outer yoke centers—can be compensated by horizontally moving the coil in a 2D magnetic plane and the compensating displacement is analytically calculated. There is a strong linear relationship between the compensating displacement and misalignment of yoke centers. The scaling factor is obtained by reasonable simplification. Then, the method for designing the tolerance for the misalignment of yoke centers is proposed. Although a new equilibrium position can be found when the inner and outer yokes are not concentrically aligned, torque is generated when the coil radially expands with heat and the torque is proportional to the increment of the radius of the coil and the misalignment of the yoke centers. [ABSTRACT FROM AUTHOR]

Measurement of the mutual inductance is one of the key techniques in the joule balance to determine the Planck constant h, where a standard-square-wave compensation method was proposed to accurately measure the dc value of the mutual inductance. With this method, analog switches are used to compose an analog-switch signal generator to synthesize the excitation and compensation voltages. However, the accuracy of the compensation voltage is influenced by the non-ideal behaviors of analog-switches. In this paper, the effect from these non-ideal switches is analyzed in detail and evaluated with the equivalent circuits. A programmable Josephson voltage standard (PJVS) is used to generate a reference compensation voltage to measure the time integration of the voltage waveform generated by the analog-switch signal generator. Moreover, the effect is also evaluated experimentally by comparing the difference between the mutual inductance measured with the analog-switch signal generator and the value determined by the PJVS-analog-switch generator alternately in the same mutual inductance measurement system. The result shows that the impact of analog switches is 1.97  ×  10−7 with an uncertainty of 1.83  ×  10−7 (k  =  1) and confirms that the analog switch method can be used regularly instead of the PJVS in the mutual inductance measurement for the joule balance experiment. [ABSTRACT FROM AUTHOR]

The ordinary least-square fitting with polynomial is used in both the dynamic phase of the watt balance method and the weighting phase of joule balance method but few researches have been conducted to evaluate the uncertainty of the fitting data in the electrical balance methods. In this paper, a matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation. Based on this, another two derived methods are proposed. One is used to find the optimal fitting order for the watt or joule balance methods. Accuracy and effective factors of this method are experimented with simulations. The other is used to evaluate the uncertainty of the integral of the fitting data for joule balance, which is demonstrated with an experiment from the NIM-1 joule balance. [ABSTRACT FROM AUTHOR]

A programmable Josephson voltage standard (PJVS) can be used to generate a precision square wave for induced voltage compensation to measure the mutual inductance between the coils in a joule balance. In this paper, the influence of the transitions between quantized voltages in the synthesized square waves is analyzed in detail. The ratio of the time-integrated value of the transitions to the total waveform is reduced to several parts in 104 to improve the measurement accuracy. The influence of different configurations of the integrating digitizer is discussed. The result shows that when the voltages are in a quantum state, the time-integrated agreement between the measured and theoretical differences for two PJVS systems is within 4  ×  10−9 V s V−1 s−1. For the total time integration of a voltage waveform larger than 2 V s, the combined relative uncertainty is less than 5.9  ×  10−8 V s V−1 s−1. The result confirms the capability of the PJVS to generate a precision square wave for the joule balance. [ABSTRACT FROM AUTHOR]