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Research paper : National electrical standards supporting international competition of Japanese manufacturing industries (Y. Nakamura et al.)−218−Synthesiology - English edition Vol.3 No.3 (2010) of the quadrature bridge. From this diagram, the equilibrium condition of the quadrature bridge is as follows: 2C1C2 R1R2=1 (3)Here, is angular frequency, C1 and C2 are capacitances, and R1 and R2 are resistances. In determining the capacitance based on the resistance of the quadrature bridge, the bridge balance frequency is determined uniquely. (As it is apparent from equation (3), when the resistances R1 and R2 and the capacitances C1 and C2 are set as fixed values, there will be only one bridge balance frequency .) Therefore, the capacitance derived from the quantized Hall resistance is limited to the value at a certain frequency. (Normally, to attain C1 = C2 = 1000 pF and R1 = R2 = 100 k, the equilibrium frequency is = 104 rad/s, or about 1.592 kHz.) This is a disadvantage against the capacitance standard using the cross capacitor (since, in principle, the cross capacitor is not dependent on frequency).As shown in Fig. 1, the direct supply destination of the developed capacitance standard is the upper-tier calibration labs that disseminate high-precision calibration service. We conducted a survey for the needed calibration frequency of the capacitance standard of the measuring instrument manufacturers and private calibration labs that were candidates of upper-tier calibration labs, and found that “the request is calibration at 1 kHz”. However, using the circuit shown in Fig. 4, the capacitance derived from the quantized Hall resistance is limited to the value of 1.592 kHz. There was a general thinking that the difference between 1 kHz and 1.592 kHz, or 592 kHz, could be ignored, but we decided to satisfy the industrial demands before we started to disseminate the standard. It was necessary to measure and evaluate the frequency characteristics around 1 kHz for the fused silica standard capacitor that will be the subject of calibration. Revisions were made to the circuit in Fig. 4, and we devised a quadrature bridge with new circuit configuration where the bridge balance frequency can be varied. Figure 5 shows the circuit for the multi-frequency quadrature bridge. When two inductive voltage dividers are added to the conventional circuit (Fig. 4), the bridge balance condition of the bridge can be expressed by equation (4). 2C1C2R1R2= 1 2 (4)Here, 12 is the voltage ratio of the newly added inductive voltage dividers. By taking the partial pressure ratio 12 arbitrary, in principle, the quadrature bridge will reach bridge balance at all frequencies. In practice, the bridge was built by using = n/8 (n = 1, 2, 3, …), and we created a multi-frequency quadrature bridge where the bridge balance frequency was 1.25n/2 kHz[10]. Using this bridge to measure the frequency characteristic of the fused silica capacitor, as shown in Fig. 6, it was found that capacitance change occurred according to the frequency variation around 1 kHz in a certain type of capacitor (GR1408). We obtained new findings that refuted the general thinking of, “there was no frequency dependency between the range 1.592 kHz and 1 kHz in fused silica capacitor”[11]. At the same time, for the AH11A standard capacitor that was assumed to be the major secondary standard, it was confirmed Fig. 7 Capacitance standard based on quantized Hall resistance (national standard)Fig. 8 Result of the international comparison of capacitance standardFig. 6 Frequency characteristic of the fused silica standard capacitorAH11AGR140880010001200140016001800Frequency (Hz)Change in capacitance (ppm)0.2000.000-0.600-0.400-0.200-0.800-1.000Participating NMIsCMS (Taiwan)KIM-LIPI (Indonesia)KRISS (Korea)NIM (China)NIMT (Thailand)NMIA (Australia)NMIJ/AIST (Japan)NMISA (South Africa)NPLI (India)SCL (Hong Kong)SIRIM (Malaysia)SPRING (Singapore)VNIM (Russia)100 pF(APMP.EN-S7)Deviation from reference value (ppm)43210-4-3-2-1

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