The Mysterious "7th Digit" (HP 3457a DMM)

[CaptnYellowShirt]

The HP 3457a was marketed as a "6.5/7.5 Digit DMM", but what happened to that 7th digit?

The internet is full of forums that say its next-to-impossible to access or only accessible by taking the GPIB toll road.

First, its actually a lot easier to access than most people think. Here's the button sequence: 1) "Blue Shift Button" 2) "8" 3)  2x "Down Arrow"   It takes just about as long to access as changing the PLC integration time. This gives you the HI-RES command which after you hit 'enter' gives the remainder of the sample value that wasn't displayed on the front LCD. Granted, this is only good for 'single shot' measurements, but its still there.

Now comes my question:  How accurate is it?

Well my knowledge of statistics is a bit rusty, but I was hoping to ask the group here to take a look at the problem.

To help out, I've included a few excepts from the February  1986 edition of the HP Journal in which the design engineers of the 3457a talk about its guts. Here's what they say about the HIRES mode:

While the front-panel can display BVz digits (± 3,000,000 counts), a seventh digit is available. This extra digit is continuously written into a math register when using the longer integration times (10 or 100 PLC). To access the seventh digit over the HP-IB, the user can recall the high-resolution math register (HIRES). Since this register is already scaled, it can be added directly to the current reading to get a 7 1/2-digit measurement. Fig. 4 shows typical 3V-range noise for 7 1/2-digit readings.

Figure 4 is shown as an attachment. It shows one standard deviation of 0v noise(?) being 110nV when operating over its maximum integration time (100 PLC). On the 3 volt range, that's around 0.04 ppm. And even though my 3457a needs a calibration, the short-circuit reading is on that level (+/- 100 nV).

So hopefully that gives you all an idea of how accurate the ADC is. Obviously, giving any real meaning to the measured values (beyond ratios of the same unit) requires a low drift reference. Here's what the HP guys say about that:

Long-term accuracy of a DMM is fundamentally limited by three sources of error: the ratio stability of critical resistors, the stability of calibration adjustments, and the long-term drift of the instrument's voltage reference. In a real environment, significant errors may be produced through exposure to vibration, temperature cycling, or humidity changes, conditions prevalent in many system environments. The HP 3457A uses an HP fine-line resistor process which exhibits extremely low long-term drift. Resistors from this process are used in all critical applications. The resistors of the ADC and input signal conditioning sections that can contribute to long-term drift are examples. Another dominant factor contributing to the long-term stability of an instrument is the ability to hold a calibration adjustment. Environmental factors are of major importance here. The HP 345 7 A has entirely electronic calibration. Electronic correction cannot account for future changes to mechanical settings, so electronic calibration means that there are no mechanical adjustments in the circuits that can affect calibration integrity. The third factor in DMM long-term stability is the instrument voltage reference. In an instrument with electronic calibration like the HP 3457A's, the voltage reference is by far the dominant term. However, if this were not the case, the calibration adjustment stability could be of similar or greater significance. The HP 345 7A uses a pretested voltage reference assembly to guarantee the long-term stability characteristics of the instrument. Each reference assembly is monitored for a two-month period in a temperature stabilized environment. Individual reference drift rates are determined and compared against acceptable limits. Reference boards that drift beyond these limits are rejected. Much effort was placed on fine-tuning our ability to test and characterize reference assemblies in a production environment so that a reliably low-drift voltage reference could be achieved. Fig. 9 shows the results obtained. The mean long-term drift of the references for one year is characterized to be approximately 3.5 ppm. Also shown is the sample mean plus three standard deviations. This data shows an expected maximum drift of approximately 12 ppm in one year, a significant improvement.

Also attached is Figure 9, which shows a mean drift value of 1ppm/sqrt(mo). The adherence to this standard deviation approach between different boxes seems to imply that the manufacturing process is going to smile on some and fart on others. You may buy a killer unit, or you may get a (comparative) dud -- but with some certainty, it will be within 12 ppm/year.

Does anyone have any experience with these types of drift measurements? Do they slow down with age, etc? Are they slow enough to give any certainty to that 7th digit?

So please weigh in! Is the 7th digit a zero or hero?

[CaptnYellowShirt]

Attached is the full article for those of you who are interested....

[CaptnYellowShirt]

pt 3

[cellularmitosis]

subscribed.

thanks for digging up those articles.

[TonyGreene]

The 7th digit is also available by using STATS when running at max res.   NPLV down arrow to 100.  Digits DISP 6 ENT.  Blue then STAT.  Let it run a while, then BLUE and R.Mean, BLUE and R.SDEV, BLUE and R.NSAMP, BLUE OFF when your done.

I have ran some long term test on the meter and in general the meter is in the 1.5 to 2 PPM class.

[casinada]

I don't think you can see 7.5 digits on the screen but for sure using GPIB commands

[AlfBaz]

I don't think you can see 7.5 digits on the screen but for sure using GPIB commands

That wont do it either. You need to do the same with the SCPI commands that you would do on the front panel. Take a reading, read the hires register, carry out the math, and ensure you round to the 7th digit

[Dr. Frank]

Hello,
the complete HP Journal Feb. 1986 can be found here: http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1986-02.pdf.

Then, I was asked by the TO to comment the 7th digit performance, although I do not own that instrument.

Well, most of the newer HP DMM deliver one additional digit directly over the GPIB, beginning with the 3458A, the 34401A, and so forth.
By proper averaging, and especially in higher ranges, that could be stable enough for short term stability measurements.
This way, I have measured successfully the < 1ppm linearity (worth 7 digits) of the 34401A's A/D on the 10V range. 

It's a little bit complicated to get the 7th digit from the 3457A, though.

The statistical distribution for the 3V range shows, that you get +/- 3 digits of fluctuation from reading to reading, which can be averaged over 100 samples to a standard deviation of 110nV, that means, the 7th digit of the 3V range will be stable enough for short term measurements. (*)

But it also shows, that manual reading of the 7th digit math register over the front panel will NOT be stable enough,  as there is no averaging and the +/- 3 digits fluctuation will apply. To use the 7th digit from the front panel, it is necessary to use the averaging math function of the instrument, instead. (*)
 
As the source of the +/- 3digit noise is not further described in the article, i.e. whether it originates mainly from the A/D, or from the DCV input conditioner, the 30, 300mV may not produce a stable enough 7th digit, or may require much more averaging, i.e. over 10,000 samples.

Under the mentioned preconditions, the 7th digit is for sure usable in the 3, 30, and 300V ranges.

If you look into the specifications of the 3457A, neither the performance of the 7th digit is specified, not even mentioned, nor the so called Transfer Stability, or 10min stability.
For that parameter, the internal reference (LM299H) would be stable enough.

That's a pity, as latter parameter can be easily derived from the statistical distribution in the HP Journal. I think, it would be identical to the 1 sigma value of that average.
 
Frank

(*) Rem.: If  I understand the HP Journal article right, for usage of the 7th digit with 110nV sigma stability, it is necessary to use 100 NPLC and additionally to average over 100 of those readings.
That would require 166 sec measuring time for 7 stable digits.
An analogous statistical test should be done with NPLC 10, if that already yields that level of stability.

[PA4TIM]

I allmost bought a HP3457 because I wanted an other 7,5 digit meter but did not because IU was in doubt about reading about that "hidden" digit. I then bought a Prema 5017. I also have a Keithley 2000, I hooked it up to a Linux machine and read the data dumped through the RS232 and cutecom. I was supprised to see it had 8.5 digits.

I was wondering if some meters in a family are for a great deal the same but limmited to some number of digits out of commercial reason.  (not talking about this HP, but just in General, I hope you excuse me this little sidestep in this topic)

[CaptnYellowShirt]

(not talking about this HP, but just in General, I hope you excuse me this little sidestep in this topic)

Oh no, it's great. I'd love to hear more about anyone's experiences with extended DMM resolution.

Did you get the 8th digit on the keithley or the prema?

[PA4TIM]

On the Keithley 2000. That has RS232. I do not have a GPIB interface. I do not even know which  meters have a GPIB. I think my  Keithley 196 has one and the solartron 7061 too

[robrenz]

8846A in stat mode or trend plot goes down to 100pV resolution if the range is low enough.
This is the output of a PD supply at 100mV for 22 mins.  Total span if 187.9nV  If nothing else the PD supply is impressive

Some other 8846A stuff in this thread

[KedasProbe]

Just as extra info for comparison: 6.5 DM3068
Note: It's possible that the environment changed the measured value.

[CaptnYellowShirt]

The 7th digit is also available by using STATS when running at max res.   NPLV down arrow to 100.  Digits DISP 6 ENT.  Blue then STAT.  Let it run a while, then BLUE and R.Mean, BLUE and R.SDEV, BLUE and R.NSAMP, BLUE OFF when your done.

I have ran some long term test on the meter and in general the meter is in the 1.5 to 2 PPM class.

I am always amazed at how much I learn when I post questions here!

Thanks for the tip, Tony. I had never played around with the STAT function on my 3457a's before today. I'm glad I did!

Also thanks Frank for your read on the HP article. I hadn't read the 110nV noise as being over 100 samples -- each being 100 integrations (NPLC). Now that you point that out, its really clear that's what the article was intending.

I've tried my own impromptu test with the information I've gathered here in the past 24hrs. I hooked up two HP 3457a's to a Fluke 5100b calibrator (4 1/2 digit source -- not the best, but the most stable thing I have access to).

Here are the results using Tony's STAT suggestions.

3 Volt Range / HP DCV: +2.999887 V
R.stdev = 5.4352680E-6

N.samp	V.mean
2	2.9998886
22	2.9998852
75	2.9998817
108	2.9998796

0 Volt Range / HP DCV: +00.00025 mV
R.stdev = 50.204883E-9
(input shorted)

N.samp	V.mean
6	263.33335E-9
27	320.71428E-9
48	327.11111E-9
80	322.12500E-9
100	326.69999E-9

Included here is a picture, just to show everyone that I'm not reading these off a GPIB link.  The HP 3457a can actually display not only 7, but actually 8 digits.* The top unit is reading voltage and the bottom is reading number of samples.

*That being said, it does look like the last few digits in the 0 Volt range are an artifact of binary to decimal conversion and not a "real" indication of the device's ultimate performance.

[CaptnYellowShirt]

Someone's going to need to remind me of the name of this statistics principle that deals with the noise floor of measurements like this. The idea is you need X number of samples to get out of the 1/f noise range, but after Y samples (where Y>X) your noise floor starts to increase again. Point being there's a sweet spot for the number of averages you take -- and there's a name for this...

[AlfBaz]

Here's another little tip.
You can turn the half a digit into a full one (ie instead if 05.xxxxx you get 5.xxxxxx) by pressing blue button, MATH 13 (scale mode)

The display = (reading - offset) / scale. On power up the default values are offset = 0, scale = 1

[bingo600]

I did some 7.5 digit logning here in Python
https://www.eevblog.com/forum/reviews/linux-gpib-and-python-keithley2015-hp3457a-10v-logging/msg368668/#msg368668

Well just logging , and usling the High res register

/Bingo

[Dr. Frank]

I did some 7.5 digit logning here in Python
https://www.eevblog.com/forum/reviews/linux-gpib-and-python-keithley2015-hp3457a-10v-logging/msg368668/#msg368668

Well just logging , and usling the High res register

/Bingo

Would you mind to explain those graphs/measurements?

You read out the 7th digit of the 3457A, and then average over 1 min, or so, i.e. over 6 36 samples NPLC100.
Correct?

The output still shows some jitter.

What do you think is necessary in practise for averaging, to get a smooth +/1 digit fluctuation on the 7th digit?

Is it really 100 samples of NPLC100 (166sec), or is it less?

Frank

[bingo600]

@frank
This's is 100nplc wo. Any averaging at all.
Just a test of Reading the High res reg.
Logging is once a minute, mening every 12' Reading is logged.

No rounding done , so it's just proof of concept.

/Bingo

[CaptnYellowShirt]

Someone's going to need to remind me of the name of this statistics principle that deals with the noise floor of measurements like this. The idea is you need X number of samples to get out of the 1/f noise range, but after Y samples (where Y>X) your noise floor starts to increase again. Point being there's a sweet spot for the number of averages you take -- and there's a name for this...

It took me a while, but I found it.... Allan Deviation. Check it out...



http://tf.nist.gov/general/glossary.htm

[KedasProbe]

I found this PDF link related to Allan Deviation
http://www.leapsecond.com/hsn2006/pendulum-tides-ch2.pdf
http://www.leapsecond.com/hsn2006/pendulum-tides-ch3.pdf

and just averaging: http://en.wikipedia.org/wiki/Signal_averaging

[Mickle T.]

Allan Deviation in MS-Excel:

[CaptnYellowShirt]

Allan Deviation in MS-Excel:

Very nice. What kind of voltage standard did you have hooked up to it?

[Mickle T.]

Simple LTZ-based reference with statistical step-up