The magnet system is one of the key elements of a watt balance. For the new watt balance currently under construction at the National Institute of Standards and Technology, a permanent magnet system was chosen. We describe the detailed construction of the magnet system, first measurements of the field profile, and shimming techniques that were used to achieve a flat field profile. The relative change of the radial magnetic flux density is less than 10 −4 over a range of 5 cm. We further characterize the most important aspects of the magnet and give order of magnitude estimates for several systematic effects that originate from the magnet system.

The watt balance is operated in two asynchronous measurement modes to obtain the voltage–velocity ratio U/v and the force–current ratio mg/I, respectively. The magnetic flux density will change between the two modes when the effect due to the coil current is taken into account, particularly for watt balances using a soft magnetic material in the magnetic circuit. Normally, the linear component of the magnetic flux density change can be easily eliminated by reversing the coil current; however, the quadratic component remains as a systematic error, i.e. a non-linear error. In this paper, we use a theoretical analysis and a differential finite element method to investigate the behaviour of the quadratic dependence in a typical magnetic circuit. Several strategies are discussed to minimize this error in the magnetic system design for the watt balance.

The joule balance experiment has been carried out at the National Institute of Metrology, China (NIM) since 2007. By the end of 2013 the first generation of the joule balance (NIM-1) achieved a measurement uncertainty of 7.2 × 10 −6 (k = 1). To reduce the measurement uncertainty further, the next generation of the joule balance apparatus (NIM-2) system is under construction. A new coil system using ferromagnetic material is being adopted in NIM-2 to reduce self-heating in the coils. However, the effects on the measurement of the mutual inductance from the nonlinearity and hysteresis of the ferromagnetic material will bring a considerable measurement uncertainty. Inspired by the watt balance, the measurement of the mutual inductance is replaced by an equivalent measurement of the magnetic flux linkage difference. The nonlinearity and hysteresis will not be a problem in the measurement of the magnetic flux linkage difference. This technique comes from the watt balance method. It is called the generalized joule balance method, which is actually a modification of the watt balance method. However, it still represents a valid change that can reduce the difficulty of dynamic measurement experienced using the watt balance. Permanent magnets can also be adopted in the generalized joule balance. To check the feasibility of the generalized joule balance method, some preliminary experiments have been performed on NIM-1. A yokeless permanent magnet system has been designed and used to replace the exciting coils in NIM-1. In this paper, the structure of the yokeless permanent magnet system is introduced. Furthermore, a determination of the Planck constant with the permanent magnet system is presented. The value of the Planck constant h we obtained is 6.626 069(17) × 10 −34 J s with a relative standard uncertainty of 2.6 × 10 −6 .

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Abstract-In the joule balance developed at National Institute of Metrology (NIM), the dynamic phase of a watt balance is replaced by the mutual inductance measurement in an attempt to provide an alternative method for the kg redefinition. But for this method a rather large current in the exciting coil, is needed to offer the necessary magnetic field in the force weighing phase, and the coil heating becomes an important uncertainty source. To reduce coil heating, a new coil system, in which a ferromagnetic material is used to increase the magnetic field was designed recently. But adopting the ferromagnetic material brings the difficulty from the nonlinear characteristic of material. This problem can be removed by measuring the magnetic flux linkage difference of the suspended coil at two vertical positions directly to replace the mutual inductance parameter. Some systematic effects of this magnet are discussed.

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The advantage of the joule balance over the classic watt balance is that the dynamic measurement in the watt balance is replaced by a static measurement, which makes the whole measurement procedure easier. The main problems in the joule balance are the precise measurement of mutual inductance and coil heating. These problems and recent progress in the development of the joule balance are described and discussed in this paper. The whole system is at the stage of being adjusted and improved. The principle of the joule balance has been demonstrated by a measurement of the Planck constant, h = 6.626 104(59) × 10 −34 J s with an 8.9 ppm measurement uncertainty.

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