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This presentation describes investigations carried out in the BIPM electricity section of the variation of the 1.018 V and 10 V outputs of 17 Fluke 732B Zener standards. Overall, the relative voltage changes due to pressure are very small (less than five parts in 107 for the greatest pressure changes normally encountered) but the effect can be important to national metrology institutes and users of Josephson voltage standards.
The pressure coefficient of a Zener is determined by placing the instrument in a temperature-controlled, pressure-tight enclosure and varying the pressure. The voltage reference standards are a standard cell (in a temperature-regulated enclosure) for 1.018 V and a Zener for 10 V. Only the Zener under test, no other equipment, is subjected to pressure changes. Output voltages are measured while varying the pressure in the enclosure. The upper plot of Figure 1 shows the pattern of pressure variations imposed on a Zener in a typical measurement. Pressure ranged from 850 hPa to 1050 hPa (one standard atmosphere = 1013.25 hPa). The period of a complete pressure cycle is about 7 h, and each plateau of pressure is held for about 45 min. The Zener output voltage, U, can be expressed as a function of pressure, p, by
U(t, R) = U0 [1 +  (p –
p0)],
where is a coefficient relating the relative change in output voltage to the pressure; U0 and p0 are constants. In this example, = 1.81 x 10–9 hPa–1 with a Type-A standard uncertainty of 3 x 10–11 hPa–1.
| Figure 1. |
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Figure 2 summarizes the results for 732Bs fitted with the newer L-type reference/amplifiers. It shows the relative pressure coefficients and the 1  uncertainties of fifteen instruments for both the 1.018 V and 10 V outputs. In the 732B, the 1.018 V output is derived from the 10 V output using a resistive divider. If the pressure coefficients of the two outputs were due to a common source, one would expect the points in Figure 2 to be clustered about the diagonal line g1.018 = g10, and for nine of the fifteen instruments this is the case. For the fifteen L-type instruments the mean values of the pressure coefficients are: g1.018 = 1.93 x 10–9 hPa–1 and g10 = 1.83 x 10–9 hPa–1. Some earlier versions of the 732B were fitted with M-type reference/amplifiers and for these we found negative pressure coefficients with absolute values approximately ten times smaller than those of the L-type.
| Figure 2. |
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Although meteorological pressure changes of 30 hPa or more may occur in a laboratory, the greatest pressure changes are likely to occur when Zeners are used as travelling standards. For altitudes y < 3000 m, p = ps exp (–y/a), where the constant a = 8004 m and ps is the pressure at sea level. Thus a laboratory at 2000 m altitude would measure a voltage change of about 4 parts in 107, which is 70 times the Zener noise level. This error can be effectively eliminated by measuring the pressure coefficient and applying a correction.
Details of the pressure coefficients measurements are given in the following reference:
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Summary
