This blog entry describes my experience with the histogram function on the Agilent 34461A 6 1/2 digit multimeter.
Note: the symbol table function in the e14 blog editor is not working for me tonight, so I've compromised by using the word "ohm", etc where a symbol would normally have been inserted.
My exploration of the histogram function begins with a plan to build up a histogram of single measurements on batches of same value through-hole carbon composition resistors all from the same production batch. All are 1/2 watt 5% tolerance. The table below lists the resistors I have available for this experiment and the calculated range of expected values based on the marked 5 % tolerance. Below the table are photgraphs illustrating what the resistors look like.
| Quantity | Marked value | Expected low limit | Expected high limit |
|---|---|---|---|
| 35 | 39 Ohm | 37.05 Ohm | 40.95 Ohm |
| 29 | 82 k Ohm | 77.900 k Ohm | 86.100 k Ohm |
| 35 | 27 k ohm | 25.650 k Ohm | 28.350 k Ohm |
My hypothesis is that I will get a histogram of values that fall within 5% tolerance of the marked value. Becuase I don't know much about how carbon composition resistors are made I'm at a loss to predict what the distribution will look like; will it be a normal distribution, will it be clustered tightly around one value, or will it be random within the +/- 5% tolernace range?
The Agilent was set up with a 10 PLC aperture (default) on 2 wire Ohm measurement mode. I used the mini-grabber accessory clips provided in the standard meter package and attached to the resistors as shown in the photograph below.
The data and screen captures shown below were uploaded to my laptop using Agilent's web server interface and Java control application.
So, let's see what the Agilent 34461A has to say about the 27 k Ohm resistors.
I'd like to mention that the mini-grabbers worked well - most of the time. There were four occassions out of 35 measuremtns where at least one mini-grabber popped off the resistor due, I think, to too much spring tension.
The data set and a screen capture of the histogram are shown below.
Statistics
Maximum +2.73474963E+04 
Average +2.70284436E+04
Minimum +2.68477032E+04
Max-Min +4.99793179E+02
Std Dev +1.21381349E+02
Samples +3.50000000E+01
Readings in Memory
1 +2.73474963E+004 OHM
2 +2.69631261E+004 OHM
3 +2.68739164E+004 OHM
4 +2.71572212E+004 OHM
5 +2.72346633E+004 OHM
6 +2.71610892E+004 OHM
7 +2.69721184E+004 OHM
8 +2.69428587E+004 OHM
9 +2.70358656E+004 OHM
10 +2.71179774E+004 OHM
11 +2.71977400E+004 OHM
12 +2.71104134E+004 OHM
13 +2.69775011E+004 OHM
14 +2.68982629E+004 OHM
15 +2.69891330E+004 OHM
16 +2.71619889E+004 OHM
17 +2.70255919E+004 OHM
18 +2.69424486E+004 OHM
19 +2.69425727E+004 OHM
20 +2.69995757E+004 OHM
21 +2.70591338E+004 OHM
22 +2.69333675E+004 OHM
23 +2.68949665E+004 OHM
24 +2.69386663E+004 OHM
25 +2.70410473E+004 OHM
26 +2.68530799E+004 OHM
27 +2.71647968E+004 OHM
28 +2.68477032E+004 OHM
29 +2.68888014E+004 OHM
30 +2.71103027E+004 OHM
31 +2.68996053E+004 OHM
32 +2.71378899E+004 OHM
33 +2.70726875E+004 OHM
34 +2.69801325E+004 OHM
35 +2.71217843E+004 OHM
My hypothesis seems to be holding up, at least on this first batch of resistors. The tolerance is in fact tighter than +/- 5 %, more like +1.23% and -0.56%. The distribution on the histogram only has 35 samples, but I'm imagining a normal-ish looking distribution around 27 k and another a little above 27.1 k. Can't really tell with so few samples, but the distribution does not look random to me.
For the next batch (27 ohm) I'm going to try controlling the meter remotely using the Java app.
Okay, that didn't work as expected. Everytime I issue a single measurement command, the meter erases the previous reading and displays the new reading on the histogram. I'm going to switch back to local control.
Here is the data upload and histogram screen shot from the tests on the thiryfive 39 Ohm resistors:
Statistics
Maximum +3.94152503E+01
Average +3.90134987E+01
Minimum +3.86178934E+01
Max-Min +7.97356924E-01
Std Dev +1.95523792E-01
Samples +3.50000000E+01
Readings in Memory 
1 +3.90358902E+001 OHM
2 +3.88118580E+001 OHM
3 +3.90688944E+001 OHM
4 +3.90347095E+001 OHM
5 +3.89345431E+001 OHM
6 +3.86178934E+001 OHM
7 +3.89141395E+001 OHM
8 +3.89478755E+001 OHM
9 +3.87854830E+001 OHM
10 +3.89800036E+001 OHM
11 +3.89409588E+001 OHM
12 +3.88595993E+001 OHM
13 +3.89785270E+001 OHM
14 +3.89142445E+001 OHM
15 +3.88326800E+001 OHM
16 +3.87932210E+001 OHM
17 +3.89549198E+001 OHM
18 +3.91400952E+001 OHM
19 +3.89353286E+001 OHM
20 +3.93903102E+001 OHM
21 +3.94152503E+001 OHM
22 +3.88626692E+001 OHM
23 +3.91126198E+001 OHM
24 +3.92140419E+001 OHM
25 +3.93256019E+001 OHM
26 +3.88831385E+001 OHM
27 +3.92743014E+001 OHM
28 +3.89708495E+001 OHM
29 +3.89907057E+001 OHM
30 +3.92882155E+001 OHM
31 +3.92911029E+001 OHM
32 +3.87861133E+001 OHM
33 +3.91051478E+001 OHM
34 +3.88135788E+001 OHM
35 +3.92679423E+001 OHM
Distribution looks like it might be heading toward normal if another dozen or samples were added. Tolerance on the batch is +1.06%, -0.98%.
On to the last batch of 82 k Ohm resistors.
Here is the uploaded sample data and a histogram screen capture for the 82 k set:
Statistics
Maximum +8.54020421E+04
Average +8.27459595E+04
Minimum +8.16834894E+04
Max-Min +3.71855267E+03
Std Dev +8.35697976E+02
Samples +2.90000000E+01
Readings in Memory
1 +8.32284702E+004 OHM
2 +8.17466775E+004 OHM
3 +8.54020421E+004 OHM
4 +8.25844720E+004 OHM
5 +8.22425058E+004 OHM
6 +8.32842572E+004 OHM
7 +8.28901213E+004 OHM
8 +8.31141028E+004 OHM
9 +8.24669051E+004 OHM
10 +8.28375632E+004 OHM
11 +8.24135370E+004 OHM
12 +8.27156239E+004 OHM
13 +8.16834894E+004 OHM
14 +8.17992854E+004 OHM
15 +8.29342385E+004 OHM
16 +8.52172421E+004 OHM
17 +8.25209963E+004 OHM
18 +8.22971059E+004 OHM
19 +8.21039877E+004 OHM
20 +8.24272434E+004 OHM
21 +8.21239864E+004 OHM
22 +8.22688290E+004 OHM
23 +8.25217364E+004 OHM
24 +8.27924554E+004 OHM
25 +8.24654742E+004 OHM
26 +8.30222581E+004 OHM
27 +8.26209760E+004 OHM
28 +8.24595790E+004 OHM
29 +8.34476653E+004 OHM
Tolerance on this batch is +4.15%, -0.39%. Histogram looks like it might be normal around 82 k.
For a comparison, I tested the 39 Ohm batch on a Tektronix DMM4050. The Agilent mini-grabbers fit perfectly over the Tektronix probes. Set up on the Tektronix was more involved than on the Agilent, but once set up, testing progressed identically to the Agilent. I haven't figured out the ethernet interface to the DMM4050 , so I took a picture.
Results compare fairly well with the Agilent. SD on the Tektronix is 0.19233 and 0.1955 on the Agilent. Average value on the Tektronix shows 38.4887 Ohms and 39.0135 on the Agilent. The differences can be explained by calibration tolerances on the two instruments and differences in contact resisitance between the two test runs.
I think I will give the thumbs up to the Agilent on the histogram feature. Except for the oddity with the Java app resetiting the histogram with every remote single measurement activation, it is easier to set up than the Tektronix and I prefer the colour graphic display.
Mark
November 24, 2013 update - Single Resistor Histogram
Following up on requests from DAB and Michael Kellett here are the results of taking 50 single shot measurements on a single 39 Ω resistor. The mini-grabbers were attached then left alone as I pushed the "Single" button 50 times, about once per second. Not bad, the range of values is only 15.999 mΩ.
Statistics
Maximum +3.93168063E+01
Average +3.93121523E+01
Minimum +3.93008066E+01
Max-Min +1.59997727E-02
Std Dev +4.87241628E-03
Samples +5.00000000E+01
Readings in Memory
1 +3.93008066E+001 OHM
2 +3.93022761E+001 OHM
3 +3.93025170E+001 OHM
4 +3.93033838E+001 OHM
5 +3.93039061E+001 OHM
6 +3.93049939E+001 OHM
7 +3.93050193E+001 OHM
8 +3.93059102E+001 OHM
9 +3.93058261E+001 OHM
10 +3.93063711E+001 OHM
11 +3.93069525E+001 OHM
12 +3.93075867E+001 OHM
13 +3.93079976E+001 OHM
14 +3.93091710E+001 OHM
15 +3.93095270E+001 OHM
16 +3.93100188E+001 OHM
17 +3.93105183E+001 OHM
18 +3.93110841E+001 OHM
19 +3.93115193E+001 OHM
20 +3.93125160E+001 OHM
21 +3.93129599E+001 OHM
22 +3.93134301E+001 OHM
23 +3.93139920E+001 OHM
24 +3.93141193E+001 OHM
25 +3.93145563E+001 OHM
26 +3.93150615E+001 OHM
27 +3.93152292E+001 OHM
28 +3.93153802E+001 OHM
29 +3.93157713E+001 OHM
30 +3.93158292E+001 OHM
31 +3.93158171E+001 OHM
32 +3.93160875E+001 OHM
33 +3.93160494E+001 OHM
34 +3.93159974E+001 OHM
35 +3.93163855E+001 OHM
36 +3.93165920E+001 OHM
37 +3.93168063E+001 OHM
38 +3.93165653E+001 OHM
39 +3.93162551E+001 OHM
40 +3.93166738E+001 OHM
41 +3.93163524E+001 OHM
42 +3.93163196E+001 OHM
43 +3.93160285E+001 OHM
44 +3.93162206E+001 OHM
45 +3.93161061E+001 OHM
46 +3.93159135E+001 OHM
47 +3.93157415E+001 OHM
48 +3.93156908E+001 OHM
49 +3.93158962E+001 OHM
50 +3.93158861E+001 OHM
One last test. Here I remove and attach the mini-grabbers before taking a single shot measurement.
I won't be doing that again; nearly went cross-eyed trying to see the mini-grabbers and the resistor lead. Like threading a needle.
Here are the results:
Variation is 43 mΩ. A little higher than repeated static measurements, which is to be expected.
Statistics
Maximum +3.93001830E+01
Average +3.92697205E+01
Minimum +3.92571718E+01
Max-Min +4.30111369E-02
Std Dev +9.65337414E-03
Samples +5.00000000E+01
Readings in Memory
1 +3.93001830E+001 OHM
2 +3.92927014E+001 OHM
3 +3.92938794E+001 OHM
4 +3.92780041E+001 OHM
5 +3.92720320E+001 OHM
6 +3.92824438E+001 OHM
7 +3.92862144E+001 OHM
8 +3.92713947E+001 OHM
9 +3.92659655E+001 OHM
10 +3.92638516E+001 OHM
11 +3.92655769E+001 OHM
12 +3.92670959E+001 OHM
13 +3.92626747E+001 OHM
14 +3.92613892E+001 OHM
15 +3.92836176E+001 OHM
16 +3.92744823E+001 OHM
17 +3.92645096E+001 OHM
18 +3.92653555E+001 OHM
19 +3.92627554E+001 OHM
20 +3.92696779E+001 OHM
21 +3.92602449E+001 OHM
22 +3.92646397E+001 OHM
23 +3.92689527E+001 OHM
24 +3.92633604E+001 OHM
25 +3.92615403E+001 OHM
26 +3.92584853E+001 OHM
27 +3.92571718E+001 OHM
28 +3.92591628E+001 OHM
29 +3.92619207E+001 OHM
30 +3.92623446E+001 OHM
31 +3.92621642E+001 OHM
32 +3.92604018E+001 OHM
33 +3.92754237E+001 OHM
34 +3.92707788E+001 OHM
35 +3.92894296E+001 OHM
36 +3.92694495E+001 OHM
37 +3.92773542E+001 OHM
38 +3.92741571E+001 OHM
39 +3.92710827E+001 OHM
40 +3.92685833E+001 OHM
41 +3.92682162E+001 OHM
42 +3.92696821E+001 OHM
43 +3.92666290E+001 OHM
44 +3.92668182E+001 OHM
45 +3.92680937E+001 OHM
46 +3.92663928E+001 OHM
47 +3.92667144E+001 OHM
48 +3.92656447E+001 OHM
49 +3.92638388E+001 OHM
50 +3.92635403E+001 OHM
Kind regards and thanks for reading.
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