I finally got done with analyzing all data I collected, so here are the results. For all data from banadic's 3458A my procedure was that I calculated the expected value from the calibration certificate by the formula the certificate gives: (lower limit + upper limit) / 2, and divide this by the reading to get the correction factor to convert the observed reading to what at the time of calibration would have matched the value of the cal lab. I did not have access to a calibration certificate for the Keithley 2182A, so I have not corrected these values. For all 3458A measurements the unit was set to defaults, NDIG 9, NPLC 100.
For the uncertainty, in the case of the 3458A, per GUM, I calculated it from these three terms:
1. The standard error of the mean from the observed measurements
2. The uncertainty from the calibration certificate (a 95% confidence interval) divided by 1.96 (the coverage factor of a 95% confidence interval as recommended per GUM)
3. The 90 day uncertainty (for absolute measurements) or 10 minute transfer stability (for voltage comparisons) as a rectangular interval converted to a standard uncertainty by \$\frac{a^2}{3}\$ where a is the specified uncertainty.
I calculated the sum of squares of these terms, and multiplied by the coverage factor k = 2.
For the Keithley 2182A I did not have a calibration uncertainty, and the uncertainty fo the 2182A was small compared to the observed standard error of the mean, so I took the most conservative 2 year specifications with analog filter on, converted this to standard uncertainty the same way, calculated the sum of squares of this and the observed, standard error of the mean, and multiplied this by the coverage factor.
DC voltage referencesFirst the results of comparing the various Fluke/Wavetek 7000 DC voltage standards. I did both absolute measurements with branandic's 3458A that had been calibrated about two weeks before the event, and also did relative measurements between my F7001, which was running on battery all the time and not running inside the mainframe, by connecting the negative terminals using a low-EMF spade lug lead, and then connecting the Keithley 2182A as measuring between the positive terminals.
With both methods I measured a roughly equal number of samples using both polarities of the meter, took the average of either sign, and then inverted the sign of the negative polarity readings, and report the average of the two groups with the standard error of the mean propagated all the way through. There was some confusing with the guard switch on the 3458A, which appears to become
a tradition at the Metrology Meet events: Both branadic and I had verified the guard switch was set to open in the morning. But somehow at the end of the day the switch had changed to connect guard to lo. And even without any other meters connected in parallel, connecting the guard to the same W7000 terminal as the lo lead resulted in a -2 ppm shift in reading compared to without guard connected (or with guard connected and the switch set to open). I don't understand this, and want to try to reproduce this on my own 3458As. So I ended up ignoring all data with guard connected and the guard set to lo.
I measured the ambient temperature using a Uni-T UT330C environmental logger and combined this with the other data based on time stamps.
Absolute measurements using 3458A| device under test | guard | count | ambient temperature (°C) | mean value (V) | expanded uncertainty (V, k=2) |
| Fluke 7001 on battery (alm) | with guard to open | 50 | 22.60 | 9.999935 | 0.000034 |
| Fluke 7000 on battery (#4) | with guard to open | 3 | 22.50 | 9.999986 | 0.000034 |
| Fluke 7000 on battery (#1) | no guard, to lo | 5 | 22.50 | 9.999959 | 0.000034 |
| Fluke 7000 on mains power (#2) | no guard, to lo | 10 | 22.45 | 9.999987 | 0.000034 |
| Fluke 7000 on mains power (#4) | no guard, to lo | 10 | 22.50 | 9.999987 | 0.000034 |
| Fluke 7001 on battery (alm) | no guard, to lo | 10 | 22.40 | 9.999937 | 0.000034 |
| Fluke 7001 on battery (alm) | with guard to open | 5 | 22.40 | 9.999936 | 0.000034 |
The first set of readings of my F7001 was done right after ACAL DC with a larger number of readings and proper guard connection, so is probably the best absolute DCV measurement of the bunch. The rest roughly an hour later, some on battery and some on mains power due to a low battery condition.
Relative comparisons using Keithley 2182AAs a secondary check we measured the difference between my F7001 and the other F7000 units using a Keithley 2182A nanovoltmeter. We used my F7001 as reference because it was fully independent, running from battery and not connected to the mainframe. This reduced the risk of ground loops, although in theory the F7000's isolated power supply should prevent those ground loops even when all are plugged into the same mainframe and running from mains power. I converted the mV values to ppm of the F7001 (alm) reference, and the expanded uncertainty to ppm of F7001 (alm).
| device under test | count | ambient temperature (°C) | mean difference to F7001 (alm) (ppm) | expanded uncertainty (ppm) |
| Fluke 7000 on battery (#1) | 27 | 22.500000 | 2.127129 | 0.008974 |
| Fluke 7000 on battery (#2) | 26 | 22.500000 | 4.986389 | 0.012099 |
| Fluke 7000 on battery (#4) | 25 | 22.540909 | 5.107528 | 0.011392 |
Comparing 3458A measurements and Keithley 2182A measurementsTo compare the 3458A values to this, we can also consider the 3458A readings taken within 14 minutes as a series of relative comparisons between the references. This reduces the uncertainty to the 10 minute transfer stability. For this, I converted the values to the difference to my F7001 (in ppm), since the 2182A measurements were also relative to my F7001. I also converted the expanded uncertainty to ppms of the F7001 (alm) value based on the transfer stability. For this I only considered readings with the guard disconnected (and set to lo).
| device under test | count | ambient temperature (°C) | mean difference to F7001 (alm) (ppm) | expanded uncertainty (ppm) |
| Fluke 7000 on battery (#1) | 5 | 22.50 | 2.263002 | 0.11695064 |
| Fluke 7000 on mains power (#2) | 10 | 22.45 | 5.096005 | 0.11834481 |
| Fluke 7000 on mains power (#4) | 10 | 22.50 | 5.098005 | 0.12231724 |
| Fluke 7001 on battery (alm) | 10 | 22.40 | 0.000000 | 0.11564350 |
These sets of measurements can be compared, with the K2182A clearly having the better resolution and noise under these conditions (error bars are expanded uncertainty at k=2):
The data as table:
| label | mean difference (ppm) | expanded uncertainty (ppm) |
| 1 - 3458A | 2.263002 | 0.11695064 |
| 1 - K2182A | 2.127129 | 0.008974 |
| 2 - 3458A | 5.096005 | 0.11834481 |
| 2 - K2182A | 4.986389 | 0.012099 |
| 4 - 3458A | 5.098005 | 0.12231724 |
| 4 - K2182A | 5.107528 | 0.011392 |
| alm - 3458A | 0.000000 | 0.11564350 |
To me the agreement confirms the validity of both setups, and that there were no ground loops or other things going on here.
AC voltage referenceI brought a Fluke 510A 2400 Hz AC voltage standard that I had no history on. I'll report the value here in case someone else measured this unit. I measured it using the 3458A and calculated expanded uncertainty the same was as DCV (obviously using different values for calibration data and specifications).
| device under test | count | ambient temperature (°C) | corrected mean (Vrms) | expanded uncertainty (V, k=2) |
| Fluke 510A | 16 | 22.5 | 10.000704 | 0.001895 |
ResistanceI brought an almost full decade set of standard resistors from 10 Ohm to 10 MOhm. I measured them using branadic's 3458A, relying on its absolute accuracy, with the following settings. For <= 1 kOhm range, I used 4-wire Ohms, NPLC 100, OCOMP ON, DELAY 0, NDIG 9 and otherwise defaults. For the 10 kOhm range, I used the same settings, but DELAY 1. For the 100 kOhm range, I used the same settings, but DELAY 5. For ranges >= 1 MOhm, I used 2-wire Ohms, OCOMP OFF, DELAY 0.
I had three temperature sources for this: The UT-330C measuring ambient temperature, an industrial PT100 sensor measured by a Fluke 189 that I put in the temperature well for the resistors that had one (including the SR104), and in the case of the SR104 the internal thermistor measured by branadic's HPAK 34401A.
| device under test | count | ambient temperature (°C) | temperature PT100 (°C) | SR104 thermistor (°C) | mean resistance (Ohm) | expanded uncertainty (Ohm, k=2) | difference from calibration value in ppm (year) |
| SR104-alm | 20 | 22.650000 | 24.679978 | 22.43565 | 9999.930300 | 0.099929 | -5.57 (1993) |
| SR104-S | 1 | 22.400000 | 25.000000 | 22.96400 | 10000.071999 | 0.099854 | +2.90 (2002) |
| SR104-alm | 5 | 22.500000 | 25.000000 | 22.68200 | 9999.981600 | 0.099856 | -0.44 (1993) |
| Guildline 9330-100k | 5 | 22.660000 | 24.993153 | | 100004.459999 | 1.034870 | |
| HP 11103A | 12 | 22.550000 | 24.605662 | | 1000.012408 | 0.010093 | |
| Fluke 742A-10 | 9 | 22.533333 | 25.944744 | | 10.000391 | 0.000237 | |
| Fluke 742A-1M | 10 | 22.600000 | 25.274134 | | 1.000020e+06 | 18.132762 | |
| Guildline 95206 | 51 | 22.492157 | 25.279643 | | 9.999867e+06 | 728.569857 | |
I'm slightly confused by the SR104 measurements: The initial series of measurements, shortly after ACAL DC+OHMS on the 3458A, had a lot of drift during the measurement, producing a standard deviation of 0.9 ppm over 20 measurements, while it was much more stable during the later series of 5 measurements, about 3 hours after ACAL. There is a 5 ppm difference between the two readings, which is more than I would expect either the SR104 or 3458A to change over the span of 3 hours. So I'm unsure which value to trust. The second value is closer to its 1993 calibration value, for whatever that's worth.
I attached all raw data as a zip file. Note that the UT330C clock was set to UTC+1. All other times are in UTC. I corrected for this in my results.
2023-11-20 Edit: I made a mistake calculating uncertainty for the 3458A DCV transfer measurements. I mistakenly included the calibration uncertainty, which is not relevant for ratio measurements like this, in the uncertainty calculation. I updated the two tables showing relative measurements based on 3458A data, and the figure comparing HPAK 3458A measurements to Keithley 2182A measurements.
Home
Help
Search
Login
Register
