Good evening!

I had a short discussion with Brooke and it seems like there are
a few more explanations required as to why I am doing what.

So I would like to give a quick run-down of the setup and settings
I'm using.

First of all. The setup is pretty simple and standard. An HP3458
with 4-wire, Kelvin connected measurement of a 10kΩ old resistance
standard made from manganin wire. As far as I am aware of, their
construction follows the one introduced by Thomas in 1930[1]
and later picked up by HP[2]. These resistors usually have a
temperature coefficient in the order of 10ppm/°C at 23°C that
goes to zero around 40-50°C. I do not have enough measurements
to get a number on the TC of this particular resistor, but
it seems to be in the ballpark.

My lead wires are Pomona 5295 type low-emf spade-banana test leads.
I suspended them in air, rather crudely, to ensure they are well
thermalized and that they don't couple anything via the metal
bits fo the table. Twisting the positive and negative leads
together didn't have any significant effect on measurement
performance, so I left them straight, with distance between
each other to minimize capacitive coupling and potential dielectric
absorption. The test leads are not the most optimal, as they
have a PVC insulation which has some dielectric absorption and
might be the cause of what I am seeing.

Now for the settings/script

As I wrote before, before the measurement runs, I frist
do an ACAL. 


On Fri, 28 Jan 2022 12:17:00 +0100
Attila Kinali <[email protected]> wrote:

> $dmm->write(command => "ARANGE ONCE");

I am planing to use the script with different
resistors, so I want the range to adjust to that.
The HP3458 does this by doing a short measurement first.
As I am not changing the resistor once the measurement
started, I only want the DMM to do that once and keep the
setting afterwards.

> $dmm->write(command => "AZERO ONCE");

AZERO does calibrate the zero point of the voltage measurements. 
There are people on the net who say that this is note required
for OHM/OHMF measurment as OCOMP takes care of that, the user
manual is quite clear that it's required:

---
Autozero should be on for 4-wire ohms measurements. If you must disable
autozero, be sure to make all measurement connections before disabling
autozero and ensure that the lead resistance will not change. If you disable
autozero before making the 4-wire connections, or if you have a varying lead
resistance with autozero disabled (such as when scanning), you will get
inaccurate 4-wire ohms measurements.
---

As AZERO doubles the time a measurement takes, I do it only once
and hope that the zero point doesn't move too much during the
measurement. This is a potential source of error.

> $dmm->write(command => "TARM HOLD");

Disable arming of the DMM for now. We will later arm
it manually.

> $dmm->write(command => "TRIG AUTO");

Set to trigger automatically.
This could be potentially set to TRIG LINE, which triggers at
the zero crossing of mains voltage.

> $dmm->write(command => "NRDGS 1,LINE");

Do only one measurement, initiate at zero crossing of mains voltage.
I guess that setting here LINE is enough and I don't need to do
the same for TRIG.

> $dmm->write(command => "NDIG 9");

Return all the digits the DMM calculates internally.

> $dmm->write(command => "OCOMP ON");

Set offset compensation for OHM/OHMF measurement on.
This does a zero-current measurement first, to measure
the offset voltage to later subtract.
From the manual:
---
With offset compensation enabled, the multimeter measures the external offset
voltage (with the ohms current source shut off) before each resistance reading
and subtracts the offset from the following reading. This prevents the offset
voltage from affecting the resistance reading, but it doubles the time required
per reading.
---


> $dmm->write(command => "NPLC $nplc") if $nplc != 0;
> $dmm->write(command => "APER $aper") if $aper != 0;
> $dmm->write(command => "DELAY $delay");

Set the number of line cycles to measure, the aperture period
and the delay before the measurement for the system to settle.
NPLC and APER are exclusive and one disables the other. IF NPLC
is used and it is set to higher than 10, then the measurement is
broken up into pieces of 10NPLC measurements that are then
internally averaged. But, keep in mind that OCOMP, AZERO and DELAY
are all applied to each measurement. I.e. setting NPLC to 50 means
that it's 5×( (10NPLC + DELAY) + (10NPLC for OCOMP + DELAY) )
If AZERO is set, then this doubles as an zero measurement is
inserted infront of each of them.

If APER is used then this becomes ( (APER + DELAY) + (APER for OCOMP
+ DELAY) ). Again, if AZERO is set, this doubles.

Keep in mind that the processor has to do some bookkeeping and
calculation after each measurement, which can take a lot of time.
E.g. for the APER case, it's an additional ~2.2s. For the NPLC
case, there seems to be a non-linear relationship between how long
the measurement takes and how long DELAY is. I have not figured
out what is exactly going on there. For a fixed DELAY setting, it
seems to be pretty linear, though.

> $dmm->write(command => "OHMF");

Last but not least, set to 4-wire resistance measurement.

> $dmm->write(command => "TARM SGL,1");

The measurement is then started by manually arming the HP3458.
The measurement data is later collected, after waiting the
approriate time and another TARM SGL,1 is sent.


To reiterate, what is puzzling me is that I see quite large
settling times, in the multiple seconds range. So much that
using NPLC becomes infeasible because of the long time it takes.
Using APER on the other hand, has the disadvantage of increased
noise and uncertainty.

So I am at the level, where I have to say that I have a measurement
uncertainty of somewhere in the order of 2-10ppm (depending on
how one judges the uncertainty), which is beyond what the HP3458
should be able to do, to reach the specified 2+0.2ppm accuracy
for the 10kΩ range. I am pretty sure that I am doing something
wrong or that there is something I didn't account for. But I
do not know what. And help or advice would be appreciated.

                        Attila Kinali


[1] "A New Design of Precision Resistance Standard",
by James L. Thomas, 1930

[2] "An Adjustable Standard Resistor with Improved Accuracy
and High Stability", by Hubbs and Hetzel, HP Journal April 1966
-- 
The driving force behind research is the question: "Why?"
There are things we don't understand and things we always 
wonder about. And that's why we do research.
                -- Kobayashi Makoto
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