Gaussian Resistors

[BobInOhio]

Excellent blog and experiment Dave!  Enjoyed it very much ... wonder if you considered creating a statistical process control chart with your data?  Given that the resistors you measured were indeed manufactured in sequence, it would be quite interesting to create an x-bar and R control chart, averaging every four resistors and calculating the range of the four, to generate a 100 point control chart.  In fact, if you are willing to share the raw data I will be glad to offer to do this for you and also determine the process capability of the manufacturing process at Phillips given the +/- 1% specification.

Love the Vblogs ... keep up the great work!

Bob

[sub]

I too would be interested to see the raw data.  While it does look Gaussian, it might be interesting to run some formal tests-of-Gaussianness.  Since (according to Wikipedia) the resistors are made by etching a path in a film there are perhaps theoretical reasons for it to the case, however, since it is the sum of a a number of infinitesimal resistance elements.

[EEVblog]

Oops, forgot to share the raw data which I intended to do.
Attached, and also on the Youtube page.
Open Office and Excel formats.

I was happy enough when I got my apparent Gaussian response. But those who want to play around further and post the results, it would be most interesting.
I'm certainly no statistician or process control expert.

Dave.

[Rufus]

I am not that surprised at the observed spread with nothing over 0.6% out. If that is what the process does and you are getting all the samples from the process that is what you will see. They obviously target their process at the nominal value (where else would you target a process with a Gaussian distribution) but I wouldn't be surprised to see results with the same spread but biased away from the nominal value, depends how easy/quickly they can re-target their process at the nominal.

Also if they were 1% parts selected from something with a worse spread I wouldn't expect any to be 1% out, they would want to cover measurement uncertainty and ageing and probably one thermal cycle soldering shock and still be 1%. On top of that if their process has say 2% spread more than half their output will be 1% and if the demand for 5% and 1% resistors is 3:1 what do they do? Probably tighten up the tolerance for 1% selection to get less off them.

If someone wants numbers to play with I attach a .csv file with some production test measurements from assembled PCBs. The 1st and 3rd columns are 3 x 68k 1% resistors in series, the 2nd and 4th 6k19 0.1% resistors. The resistors probably came from two or three different batches and I doubt anything can be inferred from the order of the data. I have not analysed them at all so post if you find anything interesting.

Edit: Oops I lied, the 1st and 3rd are 3 x 68k and 1k in series for 205k nominal.

[BobInOhio]

I ran control charts on Dave's raw data, and in the attached also gave a bit of an introduction to SPC charting for those that may not be familiar ... please excuse the bloviation as this stuff is near and dear to my heart.

Results are interesting!  Though the resistors are well within specification, the process that produced them is not as stable as we might have imagined ...

[robrenz]

Having measured a bunch of 0.1% smd metal film resistors lately for a decade box project, I see results similar to Dave's. I had resistors from Vishay/Dale, RCD, Bourns, and Panasonic. I had 500 each of 3 different values from Bourns, 2 values fit the +/- 0.05% but one value had 17 out of 100 tested that were out of tolerance. (see my post http://www.eevblog.com/forum/index.php?topic=5174.msg67576#msg67576)  The Vishay/Dale and Panasonic also easily fit the +/- 0.05% range. I had 500 each of 3 different values from RCD.  They barely used +/-0.02% very impressive. 

As far as selective picking from production runs to achieve the tolerance ranges being a myth or not, my OPINION fwiw;
     Resistors that are manufactured by a process that allows trimming to spec after the initial manufacture process (laser trimmed metal film as an example) will show the Gaussian distribution. There is no reason for picking ones to reach a certain tolerance because the active trim process trims it to tolerance. (there may still be selective picking of these for the 0.01% tolerance. I don't know how precise the active laser trim systems go) In this case it is myth.
     Resistors that are manufactured by a process that does not allow adjustment after the initial manufacturing (carbon composition as an example) selective picking for tolerance may be the only viable method if the initial manufacturing process can not achieve the desired tolerance.  In this case it would not be myth.

[Zad]

I was going to make a similar point to that mentioned by Robrenz. Metal film resistors are automatically trimmed before encapsulation, so it is likely that any resistor with a value which is outside the allowed tolerance will be given a "zap" to push it closer to the nominal value. I imagine if the value is too high it will then be trimmed up to the next preferred value. Raw untrimmed values may well have a smoother bell-shaped curve.

[sub]

As far as selective picking from production runs to achieve the tolerance ranges being a myth or not, my OPINION fwiw;
     Resistors that are manufactured by a process that allows trimming to spec after the initial manufacture process (laser trimmed metal film as an example) will show the Gaussian distribution. There is no reason for picking ones to reach a certain tolerance because the active trim process trims it to tolerance.

Unless the measurement error were noise-limited, though, one would perhaps expect a uniform distribution for trimmed resistors rather than Gaussian due to the quantisation of the measurement equipment.  Then again, given the relative ease with which one can do high-resolution resistance measurements, perhaps noise is the limiting factor when churning out millions of the things and you want to keep measurement time down.

I suppose it all comes down to the relative levels of noise and quantisation error.  Does anyone have more experience here?

[pmichniewski]

There is a nice article about resistor tolerances here: http://www.edn.com/article/509250-7_solution.php

[alm]

I was surprised that Dave didn't use the four wire resistance measurement mode. Sure, in this case the two terminal measurement appeared quite stable, but if you have the ability anyway, why not? Was it lack of proper four wire leads and not wanting to clip two banana clips to each resistor lead?

[EEVblog]

I was surprised that Dave didn't use the four wire resistance measurement mode. Sure, in this case the two terminal measurement appeared quite stable, but if you have the ability anyway, why not? Was it lack of proper four wire leads and not wanting to clip two banana clips to each resistor lead?

Correct, I didn't have a suitable 4-wire lead and didn't bother making one up for the job.
The 2 wire mode was tested to be more than stable enough.
Even with 4 wire, you still have the issue of contact resistance on the alligator clips and oxidisation etc if you used a single alligator clip solution. And if you used a dual alligator clip solution as you suggested then you've just doubled your contact problems and time to connect/disconnect.

Dave.

[Zad]

Most 4-wire measurements only have 2 clips anyway, but in this instance it didn't really matter. The devices under test were all very similar in value, and the resistance of the 2 wires were constant anyway, and the setup was at a constant temperature.

[robrenz]

Most 4-wire measurements only have 2 clips anyway, but in this instance it didn't really matter. The devices under test were all very similar in value, and the resistance of the 2 wires were constant anyway, and the setup was at a constant temperature.

I was surprised that Dave didn't use the four wire resistance measurement mode. Sure, in this case the two terminal measurement appeared quite stable, but if you have the ability anyway, why not? Was it lack of proper four wire leads and not wanting to clip two banana clips to each resistor lead?

My understanding is the major error in a 2 wire measurement is the IxR drop in the leads because the voltage is sensed at the meter jacks in 2 wire mode.  So in this case assume 24" leads x 2 = 48" of 18 GA 65/36 wire at 0.000531833 ohm/inch = 0.025528 ohm.
probably 1mA drive current x 0.025528 ohm = 0.000025528 volt drop in the leads.  The voltage drop across the 1k resistor at 1mA drive current is 1 volt.   0.000025528/1=.000025528 in percent that is a .0025528% error  not relevant at this resistance as it is probably 5 times smaller than the 90 day accuracy of the meter.

[alm]

Real Kelvin leads have two isolated jaws per clip, one is used for current and one is used for sense. So as long as your contact resistance is within reasonable limits it shouldn't matter. The same can be achieved by just using two alligator clips per side, but I can understand that you don't want to clip on four clips times a few thousand resistors.

The main source of variability would be the contact resistance itself, eg. how well the oxidation is punctured. Like I said, it did seem quite constant here, but I would use Kelvin connections for anything involving sub-ohm resolution.

The voltage drop across the 1k resistor at 1mA drive current is 1 volt.   0.000025528/1=.000025528 in percent that is a .0025528% error  not relevant at this resistance as it is probably 5 times smaller than the 90 day accuracy of the meter.

This test was about resolution, not about accuracy, so whether it's below the 90 day accuracy is not really relevant. Dave didn't take the uncertainty into account anyway. You can just measure the lead resistance and subtract like Dave did, the issue is that contact resistance may not be constant, depending on the condition of the resistor leads.

[robrenz]

Real Kelvin leads have two isolated jaws per clip, one is used for current and one is used for sense. So as long as your contact resistance is within reasonable limits it shouldn't matter. The same can be achieved by just using two alligator clips per side, but I can understand that you don't want to clip on four clips times a few thousand resistors.

I made a set of kelvin leads with a current reversal switch that allows reversing the current direction without touching the leads.  The Kelvin clips are Mueller's from eBay.  The leads are Pomona silicone insulated lead wire. The switch unit was just a quick and dirty version.  I plan to do mini box with all 4 banana jacks in gold.  The current reversal allows virtual elimination of thermal Emfs by averaging the two readings( one from each current direction).  pretty important below 1 ohm.