A pretty good decade box

[CatalinaWOW]

There are a couple of threads on making decade boxes and at least one asking about performance of an inexpensive decade box.  The latter pushed me back into action on a project which had been set aside for a number of non-elx related activities.  I have been fascinated with substitution boxes/decade boxes since first introduced in a high school electronics course.  Going to university and learning how to calculate proper resistance values dropped the urgency, but the fascination remained.  And a luck find at a surplus store turned up a box containing literally dozens of decade thumbwheel switches.  I carefully salvaged them and had plans to build such a box, but then marriage, kids, career and other hobby interests took over and they sat in storage for decades. Somewhere along the line I acquired a GR five decade box and it satisfied my needs for quite a while.  Then I saw the threads on fabrication of multidecade boxes and my interest went up.  Comments in these threads pointed out the errors in such devices and I wondered just how good they can be.

The GR box I have is a wonder.  It can be set to any value between 0.0 ohms and 9999.9 ohms and is accurate to within a few tenths of an ohm over the range.  When opened up you can see what went into achieving this.  Huge switches with contact area approximating a square centimeter and carefully hand wound and trimmed resistors, presumably made with a wire having as close to zero temperature coefficient as possible. 

My approach was to be simpler and use those beautiful decade switches stored for so long.

The goals:  Seven decades with lowest range being ohms and error less than an ohm.

Each resistance element in the box would be a small network of standard one percent resistors, selected to get the network as close as possible to the ideal value.  I find it easier to work on computer and paper than with soldering iron and parts so the first step was some calculations.  The attached spreadsheet includes the key calculations and results.

The first approach was a network with two resistors in series chosen to provide a value just above the desired value, and then a third resistor in parallel with that series combination to trim the resulting network down to the desired value.  The tab named 3 Resistor Net 1 shows how that worked out.  The results for low values are very promising, with predicted errors a tiny fraction of an ohm for resistances up to 100k ohms.   But two problems crop up.  First the error is larger than an ohm for the megohm series.  And for the larger resistances the parallel resistor to trim down gets to large to be practical.  While it is somewhat possible to obtain resistors with values in the hundreds or thousands of megohms, it is exceeding difficult to control leakage resistances and get an actual operating value near the desired value.

The second approach placed the paralleling trim resistor in parallel with the smaller of the other two resistors.  This resulted in comparable errors and reduced the size of the largest trim resistor required to a couple of megohms, much more practical. 

After briefly toying with more complex networks to trim the highest value resistors I took a moment to evaluate stability over temperature.  Typical metal film resistors have a temperature coefficient of 250 ppm/Deg C.  It is relatively easy to buy resistors with lower temperature coefficient, but the price rises rapidly.  5-10 ppm/Deg C is about the best you can buy at "reasonable" prices, which for me was under $10 per resistor.  Your personal threshold may vary.  Columns to the right in the spreadsheet show this evaluation.  The results show that accuracy of one ohm or better is not practical at this price point.  The highest range will change by roughly five ohms per degree and even the next higher range will vary by a few tenths of an ohm per degree.  My lab varies by a couple of degrees over short intervals and by significantly larger amounts over the course of the year. 

Even though the numbers showed that a seven decade box couldn't be achieved at this level  of effort and expense, I decided to proceed.  It will still be fine for use as a substitution box and can achieved very good results on a percentage basis.  Two more theory points in this post.  A later post will show design and construction and initial trimming, which is still a work in progress.

Self heating was mentioned in another thread as an error problem.  The results from working out the math surprised me.  First I had to measure the thermal resistance to ambient of the through hole metal film resistors I planned to use.  I found that to be in the range of 30 to 100 depending on orientation, airflow and other factors.  The math then showed that the change in resistance depends only on the thermal resistance, the applied voltage and the tempco.  Not on the resistor value.  The values are quite acceptable for lower tempco resistors, although a bit large for standard 250 ppm units.  This calculation also shows what is a common fault mode in these boxes.  If set to a low resistance value while connected to a significant source of power they can easily burn themselves up. 

Next post should be along in a day or two.

[CatalinaWOW]

WARNING:  If you downloaded these files prior to January 26, 2022 please discard.  See post 9 for explanation. 

Just a brief post this time.  Design files for the electronics of the box.  Note to myself-do a better job of backing up and archiving.  A failed hard drive early last year resulted in some exciting moments.  I thought I had backed everything up, but am still looking for the box design files (.stl) for 3D printing.  These electronic files turned up on the last of several backup copies, and in an obscure location.

These are the corrected files.  When I get to the assembly and trimming post I will explain why that matters.  The first file is schematic and some views of the board.  The second file is the manufacturing package.

[trobbins]

Have you been able to modify your initial design to lower the thermal resistance of each resistor?  Eg. thicker tracks and pads, and radiator fins on leads and across rear-side pads, or additional fan-forced cooling.

At least you've bypassed the manganin mining option.

Does the resistor datasheet come with an impedance characteristic to indicate how far up in frequency you an use the box?

[Kleinstein]

One would normally not get a fixed accuracy in ohms, but more like a relative accuracy like 0.1% of the value for the larger resistors and than an additional fixed part of some 0.1 ohms (mainly from the switches).

The resistor comboination as should is not a good choice, as it include high value resistors. Quite often the resistors higher than some 1 M have not as good performence and >10 M is already a bit tricky to get with only a limited number of values.

So the more practical combination would be to replace the high values resistor with one in parallel to the lower resistor. So 1 M may be something like 990K in series with some 11 K and some 110 K in paralel. If needed the 110 K may even by a combination of a fixed value and than on idividually selcted one.
High grade resistors are only needed for the larger ones  to make up most of the resistance.

For the middle resistor values (e.g. 100 Ohms) the combination as shown my work, though more in a way to have 100 Ohms as 110 Ohms in parallel to 1 K and a slected resistor in series. So with a relatively small resistor as the direct path and the 2 in series for the fine trim.

The lower resistor values (e.g. 1 -100 Ohms) may want to use higher power resistors to reduce the chance of damage.

[CatalinaWOW]

One would normally not get a fixed accuracy in ohms, but more like a relative accuracy like 0.1% of the value for the larger resistors and than an additional fixed part of some 0.1 ohms (mainly from the switches).

The resistor comboination as should is not a good choice, as it include high value resistors. Quite often the resistors higher than some 1 M have not as good performence and >10 M is already a bit tricky to get with only a limited number of values.

So the more practical combination would be to replace the high values resistor with one in parallel to the lower resistor. So 1 M may be something like 990K in series with some 11 K and some 110 K in paralel. If needed the 110 K may even by a combination of a fixed value and than on idividually selcted one.
High grade resistors are only needed for the larger ones  to make up most of the resistance.

For the middle resistor values (e.g. 100 Ohms) the combination as shown my work, though more in a way to have 100 Ohms as 110 Ohms in parallel to 1 K and a slected resistor in series. So with a relatively small resistor as the direct path and the 2 in series for the fine trim.

The lower resistor values (e.g. 1 -100 Ohms) may want to use higher power resistors to reduce the chance of damage.

I should perhaps not let the spreadsheet do the talking.  I agree with all of your points.  The spreadsheet provides detail on why.  Including information on how high a power resistor is required to avoid damage (depending on your project usage, that is operating voltage). 

One of my purposes in doing this thread is to provide information for those becoming interested in these tools, what their limitations are, why those exist and so on.

Another small point in this direction:  I have seen people suggest fuses to prevent damage to these boxes.  When you search out the resistance of fuses of appropriate wattage you quickly determine that their resistance is totally unacceptable, becoming by two or three orders of magnitude the largest error source.  The only "workable" solution I have come up with is to have a monitoring function built into the box that monitors switch settings and applied voltage, calculates power dissipation and opens a relay if outside the safe operating zone.  Adds a lot of complexity and cost to a device which many may conclude does not justify such an investment. 

[CatalinaWOW]

Have you been able to modify your initial design to lower the thermal resistance of each resistor?  Eg. thicker tracks and pads, and radiator fins on leads and across rear-side pads, or additional fan-forced cooling.

At least you've bypassed the manganin mining option.

Does the resistor datasheet come with an impedance characteristic to indicate how far up in frequency you an use the box?

I have only briefly examined the details of the thermal resistance.  I concluded that I couldn't get it down enough to matter as far as self heating was concerned, and for my uses.  It might make sense to attempt better thermal management to improve the safe operating area of the box.  If your application involves high voltages and low resistances I would definitely look into it.

I don't do high frequency work so didn't check frequency response of the resistors.  In response to your question I checked data sheets for a couple of the vendors I used, and found only "very good high frequency response".  A very hard to quantify specification.  Typically metal film resistors are good to somewhere near 100 MHz, but if higher frequencies matter to you careful evaluation will be required, along with more attention to layout than I put into the provided PWB.

[Kleinstein]

How far the resistors are well behaving depends on the value. Usually resistors in the moderate range like 20-200 ohms are well behaved to high frequencies. Higher resistors get incresing effects from parasitic capacitance. Much lower resistor suffer from parasitic inductance.

For the protection things are indeed tricky temperature sensors and a realy to isolate may be an option, but quite some effort. The reaction may still be on the slow side and gross overload can damage a resistor before the temperature rise is noted.
The main resistors at risc are the 10 Ohms and 100 Ohms ones. A 1 K resistor gets 200 mV with some 14 V and can thus be OK for more nomal use.
The 1 Ohms resistors can usually survive way more current than the smaller ones.

[Conrad Hoffman]

FWIW, one advantage of wire wound resistors is crazy high pulse power capability. Inductance is often claimed as a problem, but it's not usually as much of a problem as made out to be unless the frequency is high and not much super precision work is done at high frequencies.

[trobbins]

Perhaps a good insight in to higher frequency impedance of a range of metal film resistors is the PRO1-3 https://www.vishay.com/docs/28729/pr010203.pdf.  Certainly better than vintage manganin, even when those are wound bifilar (I was able to practically balance the inductive phase shift of lower range steps in a vintage 4-decade box but not the capacitive phase shift in the highest 1-9k decade steps).

You may be able to supress the thermal resistance of key parts by improving thermal sinking at the part terminals (by soldering on say copper foil strips to enhance convection cooling) as the effective thermal resistance is dominated by what heat can be wicked away to ambient through the leads in small leaded parts like resistors.

[CatalinaWOW]

WARNING:  To those who downloaded the design files and schematic, I have since observed that they are incorrect and have removed them.  I am correcting both and will repost when completed.  This particular device has tripped me up multiple times and as I will explain in a later post I manufactured some to an earlier error.  This was supposed to be a corrected version, but it is far worse than the relatively minor mistakes I sent out.  I am terrible at proofing repetitive iterations on a pattern.

My apologies to Kleinstein who obviously looked at the schematic and whose comments should have triggered my discovery of the error.  The schematic does not implement the configuration analyzed in the spreadsheet.

[CatalinaWOW]

Continuing, I did get two copies fabricated in late 2020 before some other things took over my life.   My purpose in the thread is to show the problems in making a really good decade box and what can be fairly easily achieved.

The process here is to assemble the box with the base resistors and the series resistors and then measure those (to find where in the 1% tolerance the actual delivered resistors are) and then calculate the value for the trim resistor.

Taking a side path for a moment - there are other approaches to such a box.  One can buy large batches of resistors of the desired nominal value and select the ones closest to the desired value.  One of the biggest problems with this approach is that modern manufacturing is so consistent that it is not uncommon to find large numbers of resistors with nearly identical values, within the tolerance, but not on nominal.  Another approach would be to use the same three resistor module I chose, but use selected resistors of the nominal value with the much smaller resulting series resistor and trim resistor values.  This does count on finding values on the low side of nominal.  There are several other approaches.  All have advantages and disadvantages.  Thinking through the possible errors and your personal goals is well worth it in selecting an approach.

All of these general approaches share a common problem.  They depend on the ability to measure resistance to the desired accuracy.  In this case for measurement errors to be comparable to other error terms accuracy of about one part in a million.  My best meter operating in its best mode misses this by a factor of ten or more.  The best I can hope for is to make the overall box close to monotonic and with percentage errors in absolute accuracy with roughly the same order as the meter, or in the neighborhood of 0.01 percent of reading.

When assembled I found that there were errors in the PWB on two of the decades.  They were corrected with cuts and jumpers and measurements started.  A slow process since getting best accuracy out of the meter involved both long internal measuring times and averaging multiple reading.  More on these to follow in a later post. 

In the meantime I overconfidently ordered quite a few of the boards since the unit cost was low.  Anyone who doesn't mind dealing with cuts and jumpers is welcome to these boards for the cost of postage.   I also have a modest quantity of the Digitran 4500 series switches these are built around.  I don't know what to charge for them, but will be glad to hear your thoughts.
Message me if interested.

Attached is a proof of existence photo and a file documenting the needed cuts and jumpers on the bad boards.

[JohanH]

This is something that intrigues me and I've been thinking and planning now and then (for a couple of years) how to realize this myself without it becoming crazy expensive. I have these big switches that are of really good quality. The bad thing about them is that the box will become rack sized in width. So already box will become expensive.

Now for the resistors, I like your solution of tuning with smaller resistors in series/parallel. I built a voltage reference source and used the same principle for tuning the references. For the final, smallest resistor I used a trim pot, but voltage is still drifting a small amount during use. The main resistors in the divider are thin film metal 0.1% SMD resistors with 20 PPM/C or better. But trimmers are of course 100 PPM. I haven't done the calculation how much the trimmers are affecting the drift. Best would be to avoid them.

[SilverSolder]

If you design the circuit so the trimmers are in series with e.g. a 100x larger resistor, then the drift of the trimmer won't have much influence on the final result.   This way, it seems to me you just need to look for (or test and select from a big pile) resistors that have a good temperature coefficient, and not have to worry so much about their exact value.

[JohanH]

If you design the circuit so the trimmers are in series with e.g. a 100x larger resistor, then the drift of the trimmer won't have much influence on the final result. 

Yes, that's the idea. Attached is a schematic of one of the references. In this particular one, I was able to squeeze down the trimmer to 1k. It depends a lot on the tolerance of the chosen resistors how lucky you are to find yourself in the correct range of adjustment (otherwise you have to try to find other values for some of the resistors or use a large enough trimmer). It is battery powered and there is a constant current source feeding the reference. Please note, I'm quite a beginner in this area and this is one of my experiments. It's possible that the selected reference isn't ideal for a really precise application. But let's not hijack this thread. Idea with parallel and series resistors is the same, though.

[CatalinaWOW]

In the decade box circuit the primary resistor is about 30 times larger than the series resistor, and the trimming resistor is typically about that much larger than the series resistor.  The tempco of the series resistor thus has about 30 times less effect on the total resistance and the trimming resistor about 90 times less.  You can use very much lower grade resistors for those two locations, but in the larger decades they can still matter.  Garden variety thin film resistors can have tempcos of 250 ppm or more so a factor of 30 only gets you in the neighborhood of 5-10 ppm.  Not shabby but still as much impact as some pretty good quality resistors.

Measurements on an untrimmed box is provided below.  Also provided are measurements on my GR 1443-N box to show the difference between very good and my much lower performance  pretty good box.

First problem seen in the data is the resistance when all zeros.  This is the switch contact resistance and nothing can be done about it other than using better switches.  It consumes most of the goal tolerance of 1 ohm.  The spec on these switches assures less than 100 milliohms when new.  I don't know if they expected it to go down or up over time, but this is showing around 80 milliohms per switch, but with seven switches it adds up.  The contacts on these switches are gold plated and have multi-furcated fingers.  The only thing that can be faulted is the small contact area, and possibly small contact area.  Deoxit and other cleaners have made no meaningful difference in the resistanct.

Second problem is that I didn't make enough allowance for resister tolerances.  The sum series in some locations is too small to be trimmed down.  So for these locations the next step will be to increase the size of the small series resistor. 

Note that the G-R box shows about 100 milliohms or 20 milliohms per switch. It is meeting its 0.01% tolerance (assuming my meter is right, it is only informally calibrated) on all but the lowest range, and isn't that far off even there.  You can go buy one of these new from IET Labs who purchased manufacturing rights for this product for about $2500 and it will presumably meet spec.  Mine has had a long and hard life and I am actually quite pleased with the performance.  I also paid far less for it.

[JohanH]

Switch contact resistance is an issue. I have these NOS Russian military switches you can find on ebay from eastern Europe. I managed to find specifications from somewhere (can't find the source of it now). Specifications say 0.02 Ω, which I've also measured them to. One issue with them is they have double springs for the turn mechanism, so really hard to turn. Like REALLY hard. I almost broke a plastic knob. Now the spring doesn't have anything to do with the switch contacts, so I bent out the outer spring and now they are manageable also with normal size plastic knobs. The other issue is the size, so I'm still undecided which kind of box to use.

[SilverSolder]

[...] really hard to turn. Like REALLY hard. I almost broke a plastic knob. [...]

Plastic knob???  -  in keeping with the Russian spirit, the knobs need to be cast iron! 

[JohanH]

Plastic knob???  -  in keeping with the Russian spirit, the knobs need to be cast iron! 

Agree, if I'm able to find some suitable, which I'm a bit skeptical about. Would have to be in the size of a handle to get the leverage required. I'm convinced these switches have been designed for tanks or similar heavy equipment that don't lift easily when you grab the handle.  With the plastic knob I had to use a polygrip to actually get it to turn, I was really surprised.