PREDICTABILITY OF SOLID STATE ZENER REFERENCES

Transcription

1 PREDICTABILITY OF SOLID STATE ZENER REFERENCES David Deaver Flke Corporation PO Box 99 Everett, WA Abstract - With the advent of ISO/IEC 175 and the growth in laboratory accreditation, more complete, detailed ncertainty analyses are reqired. This often points ot the need for improved accracy starting from the top of the traceability chain of a calibration laboratory. This paper describes a program that has been in place for several years to provide better ncertainties for solid state 1V zener references. This program is an on-site calibration service that can model a reference s drift performance reslting in a very predictable projected vale. An evalation of the accracy of the predictions is presented as well as a description of the tools sed to make the predictions. INTRODUCTION Prior to the development of the solid-state zener reference standard (DCVS), standard cells were sed by most laboratories to maintain the volt. Pampered, they are qiet and have very predictable drift characteristics. However, they are poor travelers making it very difficlt to send them for calibration or to se them to deliver accrate voltages to a prodction line or remote site. Zener references were conceived as a means to easily transfer dc voltage anywhere that it was needed. For manfactrers of precision calibrators, the need was to deliver 1V accrate to abot parts in 1 6. Soon, many laboratories wanted to be able to maintain their own zener references so calibration ncertainties were improved to abot a part in 1 7. With mltiple standards, some history and the se of regression models,.3 parts in 1 6 can be maintained with annal calibrations [1]. With frther characterization and care, zener references can be sed for intercomparisons between Josephson Arrays with transfer ncertainties of abot a part in 1 8 []. Thogh zeners travel mch better than standard cells, the demand for increasingly better ncertainties also increased the relctance of some owners to allow them to do so. Many of them se an on-site calibration service that ses a wellcharacterized zener reference with demonstrated ability to travel well. A proficiency test is performed, then the calibration sing a procedre from the calibration service provider. This process was accredited in 1995 by NVLAP and in 1998 by DKD, the German accreditation body. After calibration, sers employ a nmber of methods to re-assign the vale throghot the calibration interval. Some se the calibrated vale throghot the interval and increase the ncertainty by the drift specification. This works well if the more accrate workload can be schedled early in the calibration period. If the ncertainty demands aren t as great, a simpler approach is to increase the ncertainty for the maximm drift immediately and se the same ncertainty as well as assigned vale throghot the interval. A more sophisticated approach is to se a drift model for the reference and change the assigned vale and ncertainty dring the calibration interval. To execte this strategy, one mst have some previos calibration history for the nit, knowledge of the behavior of similar devices, a mathematical model to apply, the ability to perform the drift and ncertainty calclations and create a table of assigned vales and ncertainties to be sed throghot the calibration interval. As the manfactrer, we were in the best position to look at large poplations of the references to develop the models and evalate the reslts. In 1996, we started spplying projections based on linear and non-linear drift models pon the third calibration event. In 1998, a stdy was performed [3] to evalate the reliability of those projections. This paper repeats the stdy for a mch larger poplation, separates the reslts for 73A and 73B references and provides drift data for the poplations.

2 LINEAR AND NON-LINEAR DRIFT MODELS A linear regression model for the zener standard is calclated sing historical calibration data. The otpt voltage of the standard is estimated by the following eqation: V = ax + b ± K s reg 1 + n ) ( x x nsx + cal + TC + p + s ax+b represents the assigned vale for the voltage, V, for any time, x, sing a and b, the slope and offset terms for the regression. The remaining terms describe the ncertainty in the assigned vale. Under the radical, the ncertainty of the regression based on its calibration history is combined with ncertainties de to calibration, temperatre, pressre and seasonal effects based on poplations of similar references. The combined ncertainty is expanded by the coverage factor, K. Non-linear drift is modeled by making a transformation of the time axis: x =log (x d) and then sing x instead of x in the eqation above. A detailed description of the model and ncertainties was presented at NCSL in 1996 [1]. Figres 1 and show the linear and non-linear models applied to the same calibration data. The linear model reslts in an ncertainty at the end of a one-year calibration interval of abot 1 part in 1 6. By transforming the time axis prior to applying the linear regression tools, the ncertainty can be halved. For this example, the offset sed in the transformation was 11/13/93. Or experience has shown that the transformed time axis works best for abot 6 of the projections for either the 73A or the 73B. EVALUATION OF THE PROJECTIONS The qality of the projections is evalated by comparing the measred vale at the end of the calibration interval to the vale that was projected at the beginning of the interval. Since the ncertainty of the prediction varies somewhat, these prediction errors are normalized by dividing them by the prediction ncertainty. Projections are made for a year following the calibration. Often, the next calibration occrs somewhat beyond the 1-year projection. In this case, the projection and ncertainty cold be calclated frther. However, we chose to calclate the projection error as the difference between the 1-year projection and the calibrated vale. This may have cased the ot-of-confidence (OOC) rates to be slightly overstated. The 1998 Stdy In 1998, 53 calibrations were stdied with respect to their previos projections [3]. Two of the calibrations were fond to fall otside of the confidence interval for an OOC rate of 3.8%. The data are plotted as a fnction of the calibration interval in Fig. 3 and by nmber of calibrations in Fig. 4. The stdy conclded that the goal of maintaining a confidence level of 95% for the one-year projections was met. It conclded that the ncertainty for the projections based on few calibrations may be slightly nderstated bt somewhat overstated as the nmber of prior calibrations becomes greater. 73A Projection reliability For the crrent stdy, Fig. 5 shows that 1 of the 68 predictions made for the 73A were fond to be otside the prediction interval for an OOC rate of 4.5%. Of the 39 cstomer-owned nits, 96% were calibrated at the cstomer s location. As in the 1998 stdy, the ncertainty for the projections were fond to be a bit nderstated for small nmbers of calibrations bt decrease with more calibrations. Fig. 6 shows the standard deviation of the normalized prediction errors. It can also be seen that the prediction errors are fairly Gassian with little (9%) bias so the 95% confidence level is abot two sigma.

3 73B Projection reliability For the crrent stdy, Fig. 7 shows that for of the 15 predictions made for the 73B were fond to be otside the prediction interval for an OOC rate of 3.8%. Of the 73 cstomer-owned nits, 96% were calibrated at the cstomer s location. The ncertainty for the projections for the 73B show better than 95% of the measred vales at the end of the calibration period were fond to be within the confidence interval for all the projections. This stdy again fond that the confidence is lower for a small nmber of calibrations (Fig. 8). However, for the 73B, the standard deviations began to increase again for a high nmber of calibrations. This brings p the isse as to when early data shold be exclded for the projections. Again, the prediction errors are fairly Gassian with almost no bias (1%). 73A Drift Rates DRIFT RATES While analyzing the prediction reliability, we took the opportnity to examine the data for drift rate. Annalized drift rates were calclated from the shifts seen between adjacent calibrations. To keep short intervals from prodcing misleading drift rates, only calibration intervals of at least 7 days were considered. Data were also exclded when an adjstment was made to the otpt. 7 calibration pairs remained for analysis. Seasonal effects may make the slopes reported for the shorter intervals slightly higher than wold be seen over a year period. Fig. 9 shows the 73A drift rates are normally distribted with a mean of / yr and a standard deviation of / yr. 73B Drift Rates The drift rates for the 73B are shown in Fig. 1 for 335 calibration pairs. Here a bimodal distribtion is evident with some nits having a positive drift rate and a distinct separate grop having mostly negative drift rates. The data were plotted in a nmber of ways to attempt to explain this distribtion. Fig. 11 shows the 73B drift rates in serial nmber order. Here it is evident the higher serial nmbers are associated with the negative drifts. Some of the lower serial nmbers bear prototype or hardmodel serial nmbers so may not fit prodction seqence and exhibit the negative drift rates as well. Some research showed that the positive drifts were associated with the Motorola references sed in the 73A and early 73B nits. The negative drifts were associated with Linear Technology references. Fig. 1 shows a plot of the errors for the 31 predictions made for the higher serial nmber nits having Linear Technology references. One nit was fond to deviate from the predicted vale more than the prediction interval for an OOC rate of 3.%. The figre again shows the predictions getting better with more calibrations. CONCLUSION This stdy repeated the 1998 stdy with 7 times as many nits. The reslts again validated the ability to project the zener reference vales to a greater than 95% confidence for calibrations performed at the cstomer site and remaining at the cstomer site dring the calibration interval. Thogh many factors are otside the control of the calibrating laboratory, this stdy shows there is adeqate srveillance to maintain at least a 95% confidence in the projections. In addition, the drift data for over a thosand calibration pairs was presented. The drift characteristics of the Motorola and Linear Technology references are shown.

4 REFERENCES [1] Kletke, Raymond, Maintaining 1 Vdc at.3 ppm or Better in yor Laboratory, NCSL Conference and Symposim, 1995 [] Deaver, David, Hamilton, Clark, Jaeger, Klas, Miller, William, Pardo, Leonard, Plowman, Dennis, The 1999 North American 1V Jospephson Array Interlaboratory Comparison, NCSL Conference and Symposim, [3] Kletke, Raymond, Predicting 1 Vdc Reference Standard Otpt Voltage, NCSL Conference and Symposim, 1995 The athor wold like to express appreciation to Jeff Gard who did the blk of the extraction of the raw data from the files for over a thosand calibrations.

5 Linear Regression with 95% Prediction LImits Non Linear Regression with 95%a Prediction Limits 1/8/95-1 3/11/97 7/4/98 1/6/99 4/19/ /8/ /11/97 7/4/98 1/6/99 4/19/ Fig. 1 Linear Drift Model Fig. Non-linear Drift Model for Same Device as in Fig 1 % of Claimed Uncertainty Months Percentage of Claimed Uncertainty Nmber of Calibrations (N) Fig. 3 Prediction Error vs. Calibration Interval, 1998 Stdy Fig. 4 Prediction Error vs. Nmber of Calibrations, 1998 Stdy

6 4 73A Percentage of Claimed Uncertainty Days - Std Dev of Dev/U (% of Claimed Uncertainty) Nmber of Calibrations Fig. 5 73A Prediction Errors Fig. 6 Std Dev of 73A Prediction Deviations vs. Prediction Uncertainty 73B 73B Percentage of Claimed Uncertainty Days Std Dev of Dev/U (% of Claimed Uncertainty) Nmber of Calibrations for Projection Fig. 7 73B Prediction Errors vs. Calibration Interval Fig. 8 Std Dev of 73B Prediction Error vs. Prediction Uncertainty

7 4 3 1 Ag-87-1 May-9 Jan-93 Oct-95 Jl-98 Apr-1 Jan Sep Jan-93 Jn-94 Oct-95 Mar-97 Jl-98 Dec-99 Apr Drift Rate (ppm /yr) -4. Drift Rate (ppm/yr) Fig. 9 73A Drift Rate (parts in 1 6 / year) Fig. 1 73B Drift Rate (parts in 1 6 / year) Deviation from Prediction (% of Claimed Uncertainty) Nmber of Calibrations for Projection Fig B Drift Rate (parts in 1 6 / year) in Serial Nmber Order Fig. 1 73B Prediction Error for Linear Technology (high s/n) i