Replacing specialized resistor values with modern components... Series or Parallell?

[NoPegs]

So I'm dicking around with excel and calculating how to replace some precision¹ resistors in a few pieces of vintage test equip I have and the thought has occurred to me:

I can build up series strings to hit my target value, or I can build up parallel strings to do the same. I could even go further and do both² in the same string if I really wanted to.

My current parameter is no more than 4 resistors total to achieve target value, strongly preferring combinations of 2 from the E96 set, but if they're E24 or E12 values I'll go up to 3 units (cost is less, usually.) and if they're some happy combination of E12 values I'll give 4 a try.

Actual example: I need a 7.00 MOhms resistor, the current one is a 1% spec unit and it is measuring 7.189 MOhms, so it is currently 1.7% out of tolerance(2.7% total deviation from spec.) and needs replaced. I can't get a 7 Meg resistor in 1% or better for any sane price, but I could get a 5 and a 2 and series them for all of $1.85, both are 1% resistors. I could also get a 33 and an 8.87 for $1.22 and parallel them for 6.991 MOhms which is 0.1% from target.

So my question is, if I series them, the tolerance error of the string is the same as the units themselves. (So 1% if I use all 1% units.) If I'm paralleling 1% units, is the additional 0.1% margin from not hitting the target value precisely more or less helpful than the series option? Its one order of magnitude less than my target tolerance.


Now if I did something really silly³ and sourced 0.5% or even 0.25% units, even with the additive 0.1% error I'm going to net to something less than 1%, right? 0.6% and 0.35% respectively.


Returning things to the less side of the line, in the parallel example I *know* I'm going to be 9.076 KOhms short of ideal, so lets fix that. Now I'm going with a 33 and 8.87 in parallell, and then put a 9.09 KOhms in series, I get 7,000,090 Ohms, which is 0.0013% over target value.† Total cost on this is: $1.37, a savings of $0.48 over the straight 1% tolerance series combination.


I'm basically asking someone to confirm my math here, it is entirely possible I haven't paid enough attention to how tolerances work when making strings. I'm operating under the supposition that if I string together two 1% tolerance units I'm actually statistically more likely to get a value that's off by less than 1%. (Say the first unit is over by 0.39%, and the second one is under by 0.24%, if they were both the same marked value then in series they'd be 0.15% over marked x 2.) I'm not entirely sure how that kind of thing works with parallel. I am sure it would be a very serious spreadsheet indeed, because the % deviation of the higher value affects the equation differently than an equivalent % deviation of the smaller value would.


Additionally, I'm actually restoring three electrically identical units of one device, and two of another. So in both cases, I could measure the resistors I receive and possibly pair them up to hit even closer to target when the same resistor is out of spec in more than just one unit.


I'm interested to hear what you have to say on the subject. I do value‡ your input.












¹ For the purposes of our discussion this will be the original stated design tolerance of 1%. I'm aware of the fact that what I'm doing here is seen by some as stupid. Sure, I do own very nice modern test equipment that is also quite accurate. I can see no reason why I can't improve the accuracy of things I work on beyond their original design spec by replacing out of spec things with original spec value but to the tighter tolerances that are easily affordable in modern times... Yes, I am taking the temp-co of the components purchased into consideration, as that affects the actual accuracy more so than stated tolerance and value at 19C.


² I will agree that this is slightly over the "obsessive" line, for certain. However, sometimes you can get three more common value resistors for much less than two not-so-common but not-quite-unavailable values.


³ Purely a what-if scenario. The cost to do this is .


† Because, you guessed it! 9.00 KOhms isn't a sane value. Sure, I could get one, for a whopping $2.11, but . Plus its quite large, physically...


‡ What unit do we use to express that? dB? Possibly dB/fg? (Decibels referenced to a single "fuck given?" )

[jr_tech]

This might be useful:
https://answers.yahoo.com/question/i...7092025AAywmQS
jr

[powerking]

I can only imagine what type of "gear" you are trying to restore here and hopes of some kind of out of this world precision performance you're trying to attain. I would also hope your resistance ranges on your meters for this precision measurement are also calibrated to like 10 to the minus 12 parts per million or something like that (LOL). Why not just buy like qty=10 of DigiKey/Mouser PN PPCHF6.98MCT-ND @ 45 cents each and hand select a near spot on 7.0Meg 6.98Meg(nominal) one? I did this with 10 qty of 1% resistors when restoring the Solar condenser tester and got about 3 of each value nailed on the money (using 2 different DVM's for confirmation); the 7 others in the 10 qty lots were like .5% higher and lower/ in between.

Tom (PK)

[NoPegs]

Originally Posted by powerking

I can only imagine what type of "gear" you are trying to restore here and hopes of some kind of out of this world precision performance you're trying to attain. I would also hope your resistance ranges on your meters for this precision measurement are also calibrated to like 10 to the minus 12 parts per million or something like that (LOL). Why not just buy like qty=10 of DigiKey/Mouser PN PPCHF6.98MCT-ND @ 45 cents each and hand select a near spot on 7.0Meg 6.98Meg(nominal) one? I did this with 10 qty of 1% resistors when restoring the Solar condenser tester and got about 3 of each value nailed on the money (using 2 different DVM's for confirmation); the 7 others in the 10 qty lots were like .5% higher and lower/ in between.

Tom (PK)

Ok, so that's a vote for the selective breeding style, I had considered but dismissed it earlier, and will probably spend an hour doing some data gathering and analysis with my huge collection of unused resistors tomorrow. I'll model all 3 of my examples, plus I'll grab datasets from any values that I have at least 10 of to model yours. I had earlier presumed that my path would be cheaper than 10x of closest E96 value, but maybe not if I can on average get within 0.2% of target with just running a tournament ladder on 10 cheapies. Also some of the values I may need are truly one-of-a-kind, so those I wouldn't be able to cull by exploiting process variations as easy.


As to my gear and the gear being restored: I try to get 0.5% or better accuracy when choosing contemporary gear for my bench. The things I'm restoring are 5% @ 3/4 deflection nominal accuracy, using 1% parts in places, but mostly 10% or 20%. I'd like to think that with some attention to detail and planning I can achieve 1.25% @ 3/4 deflection.

Think of accuracy as a competitive sport. A batting average of 335 is pretty good, but 350 is still much better.

[jr_tech]

Originally Posted by NoPegs

The things I'm restoring are 5% @ 3/4 deflection nominal accuracy, using 1% parts in places, but mostly 10% or 20%. I'd like to think that with some attention to detail and planning I can achieve 1.25% @ 3/4 deflection.

Have you checked the accuracy/linearity of the basic meter movement in the device? I suspect that may be a source of errors greater than 1.25% no matter what you can achieve by selection of other components.

jr

[Findm-Keepm]

Originally Posted by jr_tech

Have you checked the accuracy/linearity of the basic meter movement in the device? I suspect that may be a source of errors greater than 1.25% no matter what you can achieve by selection of other components.

jr

+1 - Basic Metrology will always tell you that without center null, the best accuracy achievable with a D'arsonval meter movement full scale versus cardinals is ~2%. It's easier to achieve max accuracy with an analog movement at one point on the scale. Differential voltmeters using an analog meter are always null (center null) for this reason. Linearity with an analog D'arsonval movement like that shown is +/- .25% at best in panel mount (near another magnetic source) applications.

Good luck in achieving 1.25% - if you do, you'll have beat ol' man Fluke and his millions....

As to selecting resistors, make sure you match the TC, else you'll have resistors fighting each other when the temperature varies. In a VTVM, cold resistance is not operating resistance, as you'll have about a 10-15 degree rise (celcius) when that tube heats up. Enclosed? More temp coefficient variations...

[Findm-Keepm]

If you are looking for precision resistance measurements, get a bridge and use kelvin clips - otherwise, you add way too many variables in your measurements.

Take a look at your meter - you have a power transformer with no magnetic shielding right behind the meter. No way you will ever get repeatable accuracy with 60 cycles of induced power being delivered to the meter movement just centimeters away...

Looks like a hobby grade Conar or Heathkit meter - a HP 410C is pro grade, and can be had for a few dollars in unrestored condition, giving you a magnetically isolated power supply, megohms of input impedance, and the important expanded resistance ranges, better than today's dmms.

Cheers,

[Findm-Keepm]

Are you measuring the resistors in circuit? If so, you'll get other circuit components in the mix.

If you are measuring resistance with the Fluke, manually select the resistance range, as the "hunt" current source can induce small (.5% or less) errors. From the 70 series on up, Fluke has always stated that you should use manual stepping/selection of the resistance ranges if measuring a known resistance. It's how Fluke measures resistance in the combined diode junction/resistance mode - they flow a small current through the leads, and through the unknown component. The current flow induces a voltage drop which is either directly or indirectly measured - directly for diodes, and indirectly for resistances. The meter will step through the ranges, hunting for a value of 1.00 plus (thus you don't get odd measurements like .900 kohms, but a value of 900 ohms.) This hunting will cause undesired current fluctuations as the meter hunts. Manually selecting the range stops the stepping and the undesired fluctuations. Probably not a big deal in your application, but could be in others...