### Author Topic: DMM linearity comparison  (Read 32703 times)

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#### e61_phil

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##### DMM linearity comparison
« on: November 16, 2017, 09:24:55 pm »
Hi,

after the nice thread about DMM noise, I would like to compare DMM linearity. I think this is the most important thing for metrology use. I want to derive all decades from a single voltage source (7V LTZ1000 for example). This is not only useful for DCV, even resistance transfers can be done like that.

The meter should give at least 7.5 digits for this comparision.

There are severeal ways to measure the linearity. The easiest way is the way Dr. Frank showed some time ago. One will use a stable controllable voltage source and measure different voltages with the DUT in parallel to a 3458A. After that you will calculate a linear regression against the 3458A values and plot the error from the linear function.

Another approach is to use a chain of equal resistors. At first you measure the voltage on every single resistor and after that you measure the summing voltages.

I did both for my two 34401As (see attachments)

Another thing I tried with my Agilent 34401A is to use the good linearity to calibrate itself and using a calibrated LTZ1000 (7.156V) as a starting point. For this experiment I wrote a little script (Python) which measured some voltages (see selfcal.png) from the Fluke 5440B in parallel with a 3458A. At first I short the measurement cables and the script will measure the offsets in all ranges. After that I connected the cables to the Fluke 5440B and the script takes all the listed measurements.

For the calculations I used the 7.156V measured by the 3458A as the "true value" and calculated everything else from the measurements. As you can see my 34401A can bring itself easily below the 24h specifications.

I'm very interested in how linear are other DMMs below the 3458A price class which also gives 7.5 digits or more (over GPIB).

Best
Philipp
« Last Edit: November 16, 2017, 09:28:38 pm by e61_phil »

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#### lukier

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##### Re: DMM linearity comparison
« Reply #1 on: November 16, 2017, 09:59:21 pm »
Good idea.

I always wondered what's the real life linearity of my DMMs (3457A, K2015, K2001, 34401A we know from Dr Frank's research).

Unfortunately, being a low rent volt-nut, I don't have 3458A. I do have Fluke 5440B, but I don't trust it that much as it was subject to serious repairs (I got it for parts or repair), also even brand new it is specified to 0.5ppm + 1.5uV on the 0-11V range, therefore very close to linearities in DMM specs (usually something like 1ppm + 1pmm).

I've read about the resistor divider chain method here on the forum so I might try that, I have some 10 pcs sets of Vishay's S102K 10k and 100k and some Soviet S5-61 hermetic resistors. I would need to think a bit and do some math to figure out what are the limitations of this method.

#### tggzzz

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##### Re: DMM linearity comparison
« Reply #2 on: November 17, 2017, 12:12:12 am »
There are severeal ways to measure the linearity. The easiest way is the way Dr. Frank showed some time ago.

I'm feeling lazy; do you have a URL for that?
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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #3 on: November 17, 2017, 06:46:24 am »
There are severeal ways to measure the linearity. The easiest way is the way Dr. Frank showed some time ago.

I'm feeling lazy; do you have a URL for that?

https://www.eevblog.com/forum/testgear/hp34401-measurement-of-linearity/

34401A we know from Dr Frank's research

Yes and no. There are some differences between the individiual 34401As. I tested three and they differ (see first post). Moreover, the Fluke 5440B at work isn't as linear as the 5442A from Dr. Frank. The tested 34401As are around the 5440B. One is worse, one is better and one is more or less equal.

If you really want to know how linear your instrument is, you have to measure exactly yours. But nevertheless, one get a good overview which instruments are good for a transfer and which ones not.

Edit: The two curves shows the results from two different 3458As. Both were measuring at the same time. Therefore, even the 3458As aren't perfect, of course .
« Last Edit: November 17, 2017, 06:53:08 am by e61_phil »

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#### Mickle T.

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##### Re: DMM linearity comparison
« Reply #4 on: November 17, 2017, 06:47:07 am »
INL: Solartron 7081, Datron 1271, Advantest R6581T, HP 34401A, Keithley 2100.
Voltage source is Datron 4000A, calibrated to better than 0.1 ppm INL.

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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #5 on: November 17, 2017, 08:25:39 am »
And here are severeal runs with a Keysight 34470A and a Keysight 34461A

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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #6 on: November 17, 2017, 08:44:05 am »
and separate graphs for the measured 34401As...

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#### HighVoltage

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##### Re: DMM linearity comparison
« Reply #7 on: November 17, 2017, 10:25:57 am »
Very interesting, I have plenty of DMMs to compare.
Now I need to get up to speed on Python.
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#### TiN

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##### Re: DMM linearity comparison
« Reply #8 on: November 17, 2017, 11:10:29 am »
Is there an app that makes this plots?
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#### tszaboo

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##### Re: DMM linearity comparison
« Reply #9 on: November 17, 2017, 11:12:51 am »
Is there an app that makes this plots?
It is an app called Microsoft excel.

#### e61_phil

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##### Re: DMM linearity comparison
« Reply #10 on: November 17, 2017, 11:49:20 am »
Is there an app that makes this plots?
It is an app called Microsoft excel.

The Fluke 5440B and the resistor measurements are plotted with Excel. All other plots are done by Python with matplotlib.

#### try

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##### Re: DMM linearity comparison
« Reply #11 on: November 17, 2017, 12:37:12 pm »
Hi e61_Phil,

INL: Solartron 7081, Datron 1271, Advantest R6581T, HP 34401A, Keithley 2100.
Voltage source is Datron 4000A, calibrated to better than 0.1 ppm INL.

good stuff.

Now give me all the information you have!
I want to see the difference between both 3458As in a graph and a calculated standard deviation over that series.

Gruß
try

#### e61_phil

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##### Re: DMM linearity comparison
« Reply #12 on: November 17, 2017, 12:45:34 pm »
You can see the difference between the two 3458A in the Fluke 5440B plot. Both plots are measured  simultaneously.

#### TiN

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##### Re: DMM linearity comparison
« Reply #13 on: November 17, 2017, 04:27:11 pm »
Now we talking, and

Quote
All other plots are done by Python with matplotlib.

« Last Edit: November 17, 2017, 05:17:36 pm by TiN »
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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #14 on: November 17, 2017, 04:50:26 pm »

#### TiN

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##### Re: DMM linearity comparison
« Reply #15 on: November 17, 2017, 06:21:33 pm »
I just wanted to see if there is a ready to use Py app, which collects data and plots near graphs.

10V linearity is part of my calibration software, but it does not plot any graphs. Attached are results of four 3458A's tested vs 5700A (within 2 days calibration).
It's more test of linearity of calibrator, than a meters though.
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#### Andreas

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##### Re: DMM linearity comparison
« Reply #16 on: November 17, 2017, 08:25:50 pm »
Hello,

more interesting would be the parameters used to make the measurements.
For the 34401A I guess it is 100NPLC in 10V range as the noise is around 2uVpp.

But the 34461A looks weird to me.
below 2V the noise seems to be around 0.2uVpp and above it seems to increase up to 2uVpp.
Do you switch ranges during the measurement?

With best regards

Andreas

#### e61_phil

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##### Re: DMM linearity comparison
« Reply #17 on: November 17, 2017, 08:59:27 pm »
I just wanted to see if there is a ready to use Py app, which collects data and plots near graphs.

10V linearity is part of my calibration software, but it does not plot any graphs. Attached are results of four 3458A's tested vs 5700A (within 2 days calibration).
It's more test of linearity of calibrator, than a meters though.

I put some lines of Python together to control the Fluke 5440B and read the DMMs. The data was written into an Excel File. Another Python script reads the Excel data, calculate the linear regression and plot the data. The scripts are on my measurement computer. I search them tomorrow. Nothing fancy and only hacked together..

Hello,

more interesting would be the parameters used to make the measurements.
For the 34401A I guess it is 100NPLC in 10V range as the noise is around 2uVpp.

But the 34461A looks weird to me.
below 2V the noise seems to be around 0.2uVpp and above it seems to increase up to 2uVpp.
Do you switch ranges during the measurement?

Some of the measurements are already quite old. But, I'm sure I used fixed 10V range and 100NPLC for the 34470A and 34461A. On the 34401A I normaly use 10 times 10NPLC. For the selfcal I used 1000NPLC on the 3458A and 100 time 10NPLC on the 34401A.

Did anyone measure a Keithley 2000?

#### e61_phil

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##### Re: DMM linearity comparison
« Reply #18 on: November 17, 2017, 10:31:43 pm »
10V linearity is part of my calibration software, but it does not plot any graphs. Attached are results of four 3458A's tested vs 5700A (within 2 days calibration).
It's more test of linearity of calibrator, than a meters though.

Can you explain a bit more over the first three rows? And do you have the data in a text format which is easily python readable to create a similiar plot as mine?

#### Andreas

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##### Re: DMM linearity comparison
« Reply #19 on: November 17, 2017, 10:32:50 pm »
Hello,

I did a check (would not say measurement) on my K2000 + 34401A.
Method:
- resistor string of 20 not calibrated resistors (metal film 1K 0.1% with 15ppm/K)
- source from battery supplied LM399#2 6860 mV
- resistor string is tapped at 7/10 to get a buffered ~10V output voltage. (battery 2)
- the difference of the resistor string is buffered (battery 3) and output to the DMMs.
offset measured at beginning and end of the measurement.

As noise is relatively high I average the measurement values over 1 minute to get below 0.5uVpp noise for a single measurement.
As 3 measurements (or 4 with the offset) are used for 1 INL value the total noise is sqrt(3) * single value.
HP34401A ~15 samples 100 NPLC averaged in 10V range
K2000 ~94 samples 10 NPLC averaged in 10V range

I measure U10 and then a pair of voltages (U3  and U7)
The error E = U10 - U3 - U7 is distributed across the 3 voltages according to the distance from 0V or 10V (approximation of a parabola = green dots on pictures).
A error E = 10uV (maximum measured value) gives around 5uV for U3 and 5uV for U7. (red dots on the pictures)
So typically a error from 3V is also mirrored to 7V (perhaps a better pin pointing would be possible with additional difference measurement to U5).

There also seems to be a instability at the 7V tap which is probably no INL error but due to the 7->10V buffer.
I will have to do additional measurements.

All in all I am below the 1-2ppm specced INL.

with best regards

Andreas

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#### saturation

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##### Re: DMM linearity comparison
« Reply #20 on: November 18, 2017, 12:43:24 pm »
Best Wishes,

Saturation

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#### Dr. Frank

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##### Re: DMM linearity comparison
« Reply #21 on: November 18, 2017, 12:59:18 pm »
You can see the difference between the two 3458A in the Fluke 5440B plot. Both plots are measured  simultaneously.

Hello,
I propose, that you run both 3458A against each other for several more passes, as you did with the other instruments. (see also hp journal 4/89)
These linearity tests are very sensitive to fluctuations / noise, especially, when you approach the 3458As region of resolution and linearity, on the order of 0.01ppm.

Finally, it would be great, if you would draw the difference between both 3458A, but not vs. the 5440B.
That would better display the non-linearity of the A/D of the 3458As, so that you get a real quantitative measure of the INL (is it really about 0.02ppm??).

Frank
« Last Edit: November 18, 2017, 01:47:12 pm by Dr. Frank »

#### e61_phil

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##### Re: DMM linearity comparison
« Reply #22 on: November 18, 2017, 01:10:10 pm »
I stored for every measurement the value of the Fluke 5440B, both 3458A and the DUT. Therefore, I have plenty of data in which I can compare both 3458A.
I will have a look into the data in the evening.

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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #23 on: November 18, 2017, 08:40:51 pm »
I've attached first data for HP3458A vs HP3458A. The picture contains 68 measurements (data set from Keysight 34461A). If I have time I will create a graph with the average INL and error bars (and more datapoints).

I also attached the scripts I used. Both very simple and not written for anybody else than myself...

lin_meas.py is the script which runs the measurement. It simply steps the Fluke 5440B from 0V to 11V and repeats the measurement until both 3458A stays within 1µV. The data is written in an Excel sheet.

read_lin.py reads this Excel sheet and uses Scipy linregress to calculate the linear regression.

Both scripts contain some silly stuff which I wouldn't do this way in python today (especially the for loop can be done much more elegant with a numpy vector). Nevertheless, one can see how the measurements were done.

PS: Hmm, I can't upload Python files (*.py).. I renamed it to .txt

Edit: Added a picture with 149 measurements

Edit2: You have to keep in mind, that one run will take about 55min. Therefore, there is also a lot of drift included in the measurements.
« Last Edit: November 18, 2017, 09:08:11 pm by e61_phil »

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#### e61_phil

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##### Re: DMM linearity comparison
« Reply #24 on: November 19, 2017, 08:06:27 am »
To get a feeling of the drift of both 3458A against each other I took again the data from the 34461A measurement. I took the 10V measurement values and calculated the difference between the 3458As. After that I calculate the derivative of the drift curve. This should reflect the drift within a measurement. (X axis is the still the measurement time)

Edit: Added the averaged INL of the 3458As. Error bars represent one sigma.
« Last Edit: November 19, 2017, 09:37:26 am by e61_phil »

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