# Vol.3 No.3 2010 32/60

Research paper : National electrical standards supporting international competition of Japanese manufacturing industries (Y. Nakamura et al.)−217−Synthesiology - English edition Vol.3 No.3 (2010) Fig. 4 Quadrature bridgeof the cross capacitance. Also, the capacitance measurement by cross capacitor requires experience and skill, and it is not easy to realize the standard of 0.1 ppm or less using this method. While the leading countries of cross capacitor, NMIA (Australia), NIST (USA), PTB (Germany), and LNE (France) have realized the standard for 0.1 ppm or less using this method, the uncertainties at other NMIs are over 0.1 ppm. Also, the Electrotechnical Laboratory (currently AIST) had fabricated and realized the cross capacitor before, but has not achieved uncertainty 0.1 ppm or below[8].Another method for realizing the capacitance standard is the method using the resistance standard based on the quantized Hall resistance, as shown in Fig. 3. Since 1990, it has been agreed worldwide that the standard for DC resistance will be determined by the quantized Hall resistance. The Electrotechnical Laboratory (current AIST) has disseminated the resistance standard based on the quantized Hall resistance, by organizing and developing the quantized Hall resistance standard according to the agreement (Recommendation of the 77th Comité International des Poids et Mesures [CIPM], 1988)[9]. If the origin of the standard is set in the quantum effect, same results should be obtained any time, anywhere, and by anyone. Particularly, the equation for expressing the quantum Hall effect is shown by equation (2). As it can be seen from the equation, absolutely no other standards are necessary to determine the quantized Hall resistance RH (h is the Planck’s constant, e is the elementary charge of electron, and i is the integer that represents the degree of quantization).RH(i)= h / ie2 (2)This is an advantage that differs greatly from the cross capacitor method where the length standard will always be required to determine the capacitance no matter how precisely the electrode rods are fabricated. Also, as mentioned above, the quantized Hall resistance is the origin of the DC resistance standard. If it is possible to derive the capacitance from the quantized Hall resistance, then sharing and efficient use of the devices can be achieved, and the maintenance and management will be easier after developing the standard. Therefore, we decided to employ the method of deriving the capacitance standard from the quantized Hall resistance.3.2 Development of the new method to respond to the demandsTo derive the capacitance from the quantized Hall resistance, various bridge circuit and special resistors are necessary, as shown in Fig. 3. Specifically, these include the AC resistance bridge, quadrature bridge, capacitance bridge, and a specially shaped resistor that can calculate the AC/DC difference. The capacitance can be derived from the quantized Hall resistance by developing these devices at high precision, and then using them to sequentially measure from resistance to capacitance. In this series of measurements, the quadrature bridge that converts the resistance to capacitance is particularly important in determining the final uncertainty of the capacitance standard. Figure 4 shows the circuit configuration Fig. 5 Multi-frequency quadrature bridgeFig. 3 Capacitance standard based on quantized Hall resistanceDCCalculable AC/DC resistor(10 kΩ)AC resistor(100 kΩ)ACCapacitance bridgeQuadrature bridgeAC resistance bridgeCapacitor(1000 pF)Capacitor(100 pF)Capacitor(10 pF)Quantized Hall resistance( = 2)iV-VR1R2D1D21C2CjVV-VR1R2D1D21C2CjVρ1ρ2

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