Hackaday Trims Its Own Resistors

There are times when you might want an odd-value resistor. Rather than run out to the store to buy a 3,140 Ω resistor, you can get there with a good ohmmeter and a willingness to solder things in series and parallel. But when you want a precise resistor value, and you want many of them, Frankensteining many resistors together over and over is a poor solution.

Something like an 8-bit R-2R resistor-ladder DAC, for instance, requires seventeen resistors of two values in better than 0.4% precision. That’s just not something I have on hand, and the series/parallel approach will get tiresome fast.

Ages ago, I had read about trimming resistors by hand, but had assumed that it was the domain of the madman. On the other hand, this is Hackaday; I had some time and a file. Could I trim and match resistors to within half a percent? Read on to find out.

Metal-Film, Through-Hole Resistors

All in the name of science

Your run-of-the-mill through-hole resistor is a metal-film resistor, made by depositing a thin layer of metal onto a non-conductive ceramic cylinder. The metal film is cut into a helix, and the length, width, and thickness of the resulting metal coil determine the resistance. Since the deposited metal is so thin, between 50 nm and 250 nm, you might think that trimming this down by hand is going to be a bit finicky.

Jumping straight to the punchline, when I was trying to change the resistance by small amounts, maybe less than 5% or so, it was trivially easy to land spot on the exact desired value. I had bags of 1 kΩ and 2 kΩ 1% resistors, and I figured I would make a whole bunch of mistakes while learning.

The reality is that I went over the target once out of seventeen attempts, and that only by one ohm. The rest of the resistors are trimmed as well as I can measure — down to the single ohm. (My meter and probes have a 0.3 Ω offset, but there’s nothing I can do about that.) I pitched the “bad” one, made one more, and had a perfect set in short order.

Here’s the whole procedure. I put the resistor into some insulated clamps, and clipped my ohmmeter to either end. I used a small round file, and just went at it. The first few strokes get you through the relatively thick coating, but once you see metal, or notice a blip on the ohmmeter, a very light touch with the file is the rule. Maybe blow some of the metal dust off between strokes when you’re getting close, but I didn’t notice that it made much difference. Seven or eight light strokes with the tiny little file brought the resistors to a ten-point landing.

Indeed, because it’s easy to go too far at first, I found that ideal candidate resistors to file were the 1,990 Ω ones. Many of my 1 kΩ resistors came in at 999 Ω, which makes it hard to get through the casing without overshooting the mark. I probably could have just left them. The good news is that most 1% resistors will be off by more than a few ohms in either direction, otherwise they’d be sold as 0.1% resistors. And of course, you need to pick source resistors with a lower resistance than the target — you’re not adding metal with the file.

So you only need to have one value of resistor in your kit, right? Absolutely not. Creating a 1.2 kΩ resistor from a 1 kΩ original is asking for trouble. I got it to work a few times, again down to the single ohm, by restarting the filing process in a different place rather than simply going deeper in one hole, but I don’t recommend it, and I can’t think of when you’d need to. Just add a 200 Ω resistor in series and trim that. Remember that you’re thinning down a metal spiral that’s only 100 nm thick to begin with. Easy does it.

Surface-Mount?

Filing down through-hole resistors to exact values was so much easier than I had anticipated that I decided to take on something harder. I tacked a 1206 2.1 kΩ resistor onto some stripboard. Wouldn’t you know it, it read out exactly 2,100 Ω, so 2,105 Ω became the target. That didn’t go well at all; I ended up with a 2,722 Ω resistor faster than I had expected.

Didn’t end well.

The second 1206 started out at 2,103 Ω, and I just went at it without a goal in mind. By going very carefully, I got it’s resistance down to 2,009 Ω before it jumped to 2,600 Ω and beyond. Lowering the resistance doesn’t make sense at all. Maybe I was dragging some solder into the gap and effectively thickening the metal layer? I went looking for information, but didn’t get any further into the construction than Vishay’s datasheet: “metal glaze on high-quality ceramic” which doesn’t enlighten much.

After two more attempts, I couldn’t get the SMT resistors in trim at all; the layer of deposited metal is just too thin. And anyway, I’m not sure how useful it would be — the thought of soldering and de-soldering seventeen of these isn’t very appealing.

Conclusion

Trimming through-hole resistors is awesome. I made a complete set of matched better-than-0.05% (!) resistors for an 8-bit DAC in half an hour with nothing more than a file and an ohmmeter. And on my first try. You could easily make a 10-bit DAC this way. The result was an order of magnitude better than I had hoped, and it wasn’t hard at all. Amazing. And nothing says cool like a hand-made, artisanal DAC. (For odd values of cool.)

My attempt at trimming surface-mount resistors, on the other hand, was a complete failure. Anyone out there care to guess why? Is it just the tweakiness of trimming a super-thin film? Anyone with a precise laser cutter want to have a go and write us about it?

94 thoughts on “Hackaday Trims Its Own Resistors

      1. Resistors sold as PTC or NTC usually have very big temperature coefficients, and often not linear. If you wanted to minimize temperature effects, it would be better to get regular (precision) resistors, and find two with opposite temperature coefficient.

        1. Temperature coefficient has little effect on a DAC, because what counts there is the ratio of resistances. As long as you have them mounted close together, with none of them next to a heat source, it woudn’t help at all.

          1. I know it doesn’t matter for a DAC, but those aren’t the only application for precision resistors. I use them mostly for Pt100 measurements, and for that purpose the exact value isn’t as important (I can calibrate them with a precision reference) as stability over time and temperature.

          2. Alan: that’s what I would say. There was an old trick that used to be common in building differential amplifiers, before IC op-amps: the transistor pairs would be wrapped with a strip of aluminum strip, to keep them at the same temperature, whatever temperature that was. So yeah, maybe somethng similar – epoxy the whole R-2R ladder to a strip of aluminum.

          3. @[BrightBlueJim]

            You could buy two transistors on the one die and in the same 6 pin package. It even had it’s own TO-xxx number. Not sure but I think it was a NPN PNP pair.

      2. You’ve just described a 5.6 Volt Zener diode. Zener / op-amp or comparitor always make better references anyway.

        This is why the internal ADC reference voltage on micro-controllers is not very accurate or stable. You can use an IO pin for a voltage doubler / charge pump so that you can have a 5.6 Volt Zener and use resistors to divide back below Vcc. If your using an active crystal then you can use the unused passive crystal pin instead of an IO but design is a little trickier because of the high frequency.

        For much the same reason, you can used normal diodes (forward biased) as temperature sensors. They have a very small voltage range but you can use two diodes as the ADC reference voltage in the same thermal environment and that gives a ratio that can be calibrated to temperature. Two diodes will give about 1.2 Volts – sound familiar?

        1. The 1,2V do perhaps “sound familiar”, but normally they come from a circuit called “bandgap reference”, which uses some physical parameters of the silicon which are not (at least not closely) related to the forward voltage of one (or two) silicon PN junctions.
          As a temperature sensor you still can amplify the diode drop voltage with a transistor. Yes the transistzor is also temperature dependent, but you want a temperature sensor anyway. If you do it right, you can omit the extra diode.

          1. Actually, I read a description of the bandgap reference circuit by Bob Widlar some time ago, so I can’t be 100% sure, but it seems to me he said that the circuit added the voltage drop across a forward-biased junction to the voltage drop across a resistor, with the value selected so that the temperature coefficients canceled out. The band gap is what gives a PN junction its 0.6V voltage drop.

        2. From https://en.wikipedia.org/wiki/Zener_diode

          “Zener reverse breakdown is due to electron quantum tunnelling caused by a high strength electric field. However, many diodes described as “Zener” diodes rely instead on avalanche breakdown. Both breakdown types are used in Zener diodes with the Zener effect predominating under 5.6 V and avalanche breakdown above.”

          “In silicon diodes up to about 5.6 volts, the Zener effect is the predominant effect and shows a marked negative temperature coefficient. Above 5.6 volts, the avalanche effect becomes predominant and exhibits a positive temperature coefficient. In a 5.6 V diode, the two effects occur together, and their temperature coefficients nearly cancel each other out, thus the 5.6 V diode is useful in temperature-critical applications.”

  1. Another method to consider as to removing the film could be using a laser. Once you get it focused, it should give you much preciser control as to how much material you remove. It’s also a method used in the industry.

    1. “…method used in the industry.” Not many of us have a powerful pulse laser at home. If you try any laser, let the resistor cool back to room temperature after each shot before measuring it. Micro sandblasting was (is?) also used to trim resistors.

      1. “let the resistor cool back to room temperature after each shot before measuring it”

        The lasers used to laser trim commercial parts are not that powerful. We were using 10 mW YaG lasers where I worked, but then that was resistors on chips, not big-ass 1/8 W film resistors. We had about 5 seconds to test and trim each part, so there was certainly no waiting for cooling, and yet the post-trim test never showed any problem with that. The heating is very localized.

      1. Oxidation would almost certainly cause the value to creep upwards. Resealing it with lacquer or varnish might help if you could prevent any moisture from being trapped under it.

  2. I used to use this technique to trim resistors for a 555 timer circuit back in the late ’80s. It helps to have a 4 wire ohm meter. I didn’t try then, but was wondering if applying a fresh coat of lacquer or enamel to reseal it would help.

        1. If you are just worried about ratios the resistance of the ohmmeter leads are consistent. A 4 wire ohmmeter really only comes into play when you have a lot of digits, like an HP3456 in ohms mode, or more commonly, when you are reading really low values and the resistance of the leads would be substantial part of the reading.

          In the past I have used low value trimmers in series with 1% R’s, but this probably does not have the best long term stability. I have cherry picked resistors for tightly matched values, and I have parallelled a very high value over a lower value to tune parts.

          Oddly enough one of the devices that I built that required the tightest component matching was a device to quickly help cherry pick resistors.

      1. Artenz: “Or measure the wire resistance, and subtract it.” We have a winner, or at least someone who read the article. :)

        I mention that my probes add 0.3 ohms to the setup. It’s below the least-significant digit when it’s in kilohm mode, though, so I can’t really subtract it out. Or we could all pretend that I did, because it won’t change anything at the reported precision. Four-wire people — there’s your answer.

        As a bunch of folks have stated, the absolute value of the resistance doesn’t matter too much, just the repeatability. I checked that out: a (single!) resistor that was 2000 ohms, pulled out of the setup, left on the bench while I ate lunch, and re-measured came in at 2000 ohms again. Good enough for me. (I’m being flippant, but I was actually concerned that my clips might add enough resistance to the setup to be measurable. They don’t.)

        There _is_ a problem even for the DAC application, though. I was actually trimming up 1 k and 2 k resistors. To get that 1:2 ratio exactly right on, I could use all 2 k resistors and parallel them up to make the 1 ks. But I was using actual trimmed 1 k resistors. So if my meter had an offset of 1% (10 ohms?) then they’d be 1.010 and 2.010 respectively. The ratio is no longer spot-on. At 8 bits, this is all overkill.

        But the point is that you’ll read on the Interwebs that an R-2R DAC is only good for five or six bits with commodity resistors. True, but trim them up yourself and you can very easily get much more precision than you’d need for eight bits. I’m stoked that it looks like I could pull off ten, but I can’t test that.

        1. Sure you can (measure it): any errors in an R-2R DAC result in nonlinearities, usually in the form of non-monotonicity, i.e., when you give it a regularly increasing code, the steps will not all be the same size, and in some cases actually cause a decrease in the output for an increase in the code. This can be verified on an oscilloscope, since it doesn’t require any precision measurement. You just generate a sawtooth with it, and magnify the heck out of the waveform so you can see each individual step.

    1. Consistency is surely the object here so if the 1k resistors all read 1k but are actually 1.0001k but consistently 1.0001k then thats fine.

      Assuming the meter is atleast consistent.

      1. Resistive touch is a sandwich with one layer having an array of tiny bumps to keep the layers separated when there is no touch. The finger or stylus does not make electrical contact.

  3. You’ll get systematic error if the meter you’re using is out of calibration. Though if all you need are matched resistors, that no longer becomes an issue.

    I’m curious what this technique does to the power rating of the resistor–I’d bet they can handle less current after the modification. Might be an interesting thing to test! Would also be a good way to see whether re-lacquering has benefit, since the exposed portions will likely oxidize rapidly with the heat.

        1. The point of a trim always creates a “hot spot” because it reduces the cross-sectional area of the conductor, which increases its current density at that point. In this application where probably 5 V is being put through roughly 4 kohms, that’s only about 6 milliwatts, but it can definitely be an issue in higher-power applications. When trimmed resistors fail due to over dissipation, it always happens at the point of the trim.

  4. If you look at trimmed smt resistors, or resistors on a substrate, the trimming is done in an “L” shape. if the connections are considered at the north and south ends of the resistor, the coarse trim is in the east-west direction across the element, the fine trim is in the north-south direction, where it effects less of a resistance change.

    1. This is true: the cut into the resistor is the coarse trim, and the one up its length is the fine trim. Makes for a very fast trim, but you still get a weakness (hot spot) at the trim.

  5. @ Elliot Williams: you should check how precision is influenced by time, humidity, light and vibration. So maybe just measure resistor values again in a month or so, and let us know the results.

    I had a case where 2 good resistors used to pull-up some 74hc00 input lines were touching. Even touch was enough to make the circuit inoperative from get-go. So even enamel is not always a very good insulator. Since then I keep my resistors well spaced from board and from each other.

    1. That thing with the 74HC00 is strange. I know CMOS is sensitive, but still. Could it maybe we wire-wound resistors (or even spiral-cut film like the ones in this article) forming a sort of transformer? Enough to couple very little current but perhaps enough voltage? Maybe they were faulty and there was something wrong with the insulating coating. What value resistors were they? Any ideas of your own about what was going on, apart from maybe the explanation you gave?

      1. Their bodies were touching, side to side. Terminals were not touching. This came about because I was trying to squeeze them to fit the 2.54 mm board pitch. They were usual 10 kOhm pull-ups.

        No, I don’t know why it happened. Voltage was only 5 V, resistors weren’t overheating at any point.

        As I spaced them out, the problems stopped.

  6. Now you have exposed the otherwise sealed resistor element to the Environment. The effect of this will eventually (likely sooner than you think, rather than later) render your efforts to trim the resistor worse than what you were trying to achieve in the first place. Regardless, if you need this level of tolerance in your design then either (1) your design is bad, or (2) choose a higher tolerance part from a highly reputable manufacturer and (important) a highly reputable distributor of said manufacturer’s components (e.g., China = Danger).

  7. I wonder what effect trimming has on power rating. since you’re trimming only one section, I would assume the power rating goes down much more rapidly than the increase in resistance

  8. I’d wonder about stability, is air going to get into this, and is it going to attack it over time? A good test would be to put your newly calibrated resistors in a drawer somewhere, then forget where they are, simulating real-world usage.

    Then in a year, accidentally come across them while looking for capacitors, and measure them up. See how they’ve done. It’d be interesting, it’d be some scientific data, and you’d get paid twice for the same article.

    Also, surely there’s money in hand-trimmed DACs for the audiophool market? If they’ll buy solid silver mains cable, they’ll surely want handmade, completely analogue DACs. Even a DAC in a box is a component manufacturers will sell separately, get a chip to do the S/P-DIF interface. Output can be some precision op-amp, or a valve.

    1. “completely analogue DACs.” That almost slipped by me.

      See the Wikipedia article: https://en.wikipedia.org/wiki/Resistor_ladder#Accuracy_of_R.E2.80.932R_resistor_ladders
      In the paragraph on unequal rungs, they touch on the subject of trimming to circuit accuracy, one bit at a time, rather than trimming to exact resistance values. They don’t go into the details, but this would also compensate for other circuit variables like switching resistance and op-amp offset.

      If you’re going for the audiophile market, though, you have to be careful to use oxygen-free epoxy to seal the resistors after trimming.

      I walked into a high-end audio store once. I asked the salesperson what was making that buzzing sound. She didn’t know what I was talking about until I zeroed in on the culprit – the power transformer in a $10,000 amplifier. I think sometime around the early 1990s audio got as good as is possible. Ever since then it’s all been about how to make it more expensive.

      1. I think audiophile gear now is about seeing how expensive your test equipment has to be to find a flaw :D On the engineering side it’s still fun, one the consumer side it’s a waste of money.

        1. No. It does not have a connection with test equipment. It is all a question of finding the right marketing buzzwords to get people to pay 100 to 1000 times more than it’s real value for stuff. It relies on a close relative of the placebo effect. Basically people have to believe that it sounds better than cheaper gear to justify their astronomically exaggerated spend on the piece. Otherwise they would commit to themselves that they had made an expensive mistake.

          1. It’s basically electronic homeopathy. Dozens of similarities in the psychology of it, the methods, the cherry-picking, the subjectiveness, designing the experiment around getting the results you want, etc. Same weaknesses in the human brain, and there’s all sorts of ways for enterprising scumbags to take advantage.

            Advertising is the same thing, only done properly, not slapdash and amateurish.

  9. This was common in ancient times when resistors were carbon composition. They were like a carbon rod (The inanimate carbon rod?) and you could notch them with a triangular file. With so much material, it was a lot easier to adjust and without doing much to the resistor wattage or current carrying ability. Seal with a little shellac.

  10. As a former laser trim engineer “for a major manufacturer”, I think you may be thinking about this the wrong way, Elliot. It’s not the thickness of the material you’re trying to remove; it’s some of the width. The total resistance is proportional to the length/cross-sectional-area. On that spiral, you can get very fine control of resistance by filing in parallel with the edges of the metal, whether this is in the middle of the track or at the edges. Think very narrow grooves. You want to be careful not to file across the conductor because this can leave a spot with little power dissipating capability. (I once had recurring problem with step attenuators on some RF equipment – they were rated at 1 W, but were failing at much less than that. Turns out they were laser-cutting straight into the resistors, and this is where they were all failing.) The problems you had with SMD parts probably come from two different things: 1) the area of the resistor is very small, so you don’t have to remove much material to raise the resistance, and the over-coating on SMD resistors can be pretty hard. My approach to SMD resistors would be to file or grind away at the edges of the resistive area. Maybe notch them in from the edge on the widest part using a Dremel with a cutoff wheel. But I’ve never actually tried this.

    In any case, the coating over both surface-mount and leaded components isn’t just to make them pretty; it’s to reduce moisture absorption that can affect the value over time. I would at least put a drop of superglue over the spot where the coating has been removed, as soon as it’s trimmed. I wouldn’t trust lacquer to be adequate protection if you want your 12-bit DAC to keep its precision.

    As for all of the talk about 4-wire measurement and specs of meters, in a R-2R ladder DAC, the actual absolute resistance is only very roughly significant; what really matters is having them all match, so as long as you’re measuring them all the same way – same meter, same leads, same temperature, sufficient stabilization time – that should be good. A 3-1/2 digit meter spec’d at 1% is still repeatable to +/- 1 digit, which at 2 kohm is .05%, and you can fudge it even closer than that (even if you can’t prove it) if you can trim it to where it’s reading 2.000 half the time and 2.001 the other half, because then you can be confident it’s pretty close to 2.0005 k.

    I also worked at a mil-spec avionics contractor whose name cannot be uttered, whose practices made me shudder. They provided locations on PCBs for critical adjustments for two resistors in series, which were then selected in test. But were the resistors that were actually selected in said test shipped with the units? No, of course not, because the test technicians weren’t allowed to solder finished parts, and the soldering technicians weren’t allowed to measure. So once the test technicians had tacked the proper resistors to the boards, the soldering technicians would remove these, get new resistors of the same nominal values from stock (because it wasn’t permitted to solder any part twice), and solder them in. *facepalm*

    1. Actually, once you get a “reference” resistor that is of the desired value, one way to get the next one to the same value precisely would be to feed each resistor with a constant current supply and feed the voltage across each resistor through a precision op-amp; one into the negative input, the other into the positive.

      The output of the op-amp should tend to zero when the two resistors are the same value.

      1. Yes – you’ve basically described an amplified Wheatstone bridge. You would have to compensate test the offset of the op-amp, though, by swapping the inputs and comparing the results.

      2. And, once you have a collection of trimmed resistors of one value, you can compare the resistance of two in series to a resistor you’re trimming to be 2R. This leads to almost perfectly matched R and 2R values without the need for a known accurate ohmmeter.

    1. I took apart a UHF tuner once, for parts. What I found were conductive ink marks (carbon) between various traces, apparently part of their factory alignment process.

      In a different era, I worked on a height finding radar system that used very large precision potentiometers (about 8″ diameter) to send angle information to the analog computing system. These wore out often, since they rotated as the antenna nodded, 24/7. I took one apart, and it was a marvel of silver ink calibration. X-acto blade cuts where the resistance was too low, silver ink where it was too high.

  11. Now this is the sort of Hack I’ve come to expect from HAD. My chest got hairier just reading it, and those close up pics, pfoorrr!

    For the surface mounted resistors in particular you can try trimming them with acid just wire them up to your tester then pull and neutralise as they hit the sweet spot. The next step would be having a full electrochemical rig where you can alternate between deposition, erosion and testing using a MCU to control everything. Grow your own resistor films.

  12. I have heard of this technique before but only with a little detail but This write up has cleared any questions I had about it. I have no need for high precision resistors anytime soon but I think I am going to play with this idea, This is what you call a proper Hack. I as others have said was wondering about “resealing” them from moisture etc, It would be interesting to try a few different seals like nail varnish, enamel etc and checking for precision drift over time.

  13. Just a thought — would it be easier to get an accurate result if you connected, say a 1k Ohm resistor and a 20 Ohm resistor in series and filed the 20 Ohm one? Would you get finer control? You’d end up with maybe all your resistor pairs at 1025 Ohms, but if they’re all the same that should be OK.

    1. Very probably right. I was so freaked out by how well the 1 k / 2 k experiment went that I didn’t bother with lower resistor values. But it stands to reason that they’ve got a thicker metal layer and should be easier to trim even more precisely. If you’ve got the precision ohmmeter to back it up, give it a try and report back?

  14. ” you’re not adding metal with the file.

    So you only need to have one value of resistor in your kit, right? Absolutely not. Creating a 1.2 kΩ resistor from a 1 kΩ original is asking for trouble ”

    You want to think that section through again? Sure sounds like you’re contradicting yourself a mere sentence later :P

  15. wow, a lot of comment on here so this one might get lost..
    IF you see this Elliot, I’m surprised I couldn’t find any reference to Thick-film and in particular thick-film resistors and trimming.

    At my university I took a class on thick film design, a practice where you silkscreen traces and resistors into a ceramic substrate. the interesting thing is that you have different pastes, for example 1k, 10k or 100k paste that you screen on and then bake. the traces are made using 0R paste.
    after baking you can solder on the traces – unless of course you put on a dielectric layer of glass.
    a lot of the design involved the question of having wires crossing or not. if you have you need another layer of dielectric and trace paste before you carry on.

    The resistors are all designed too low and after baking you trim up the value with a small precision sand-blaster. it was a very interesting procedure and a look into a process that only a very few people use today. the ceramic have great thermal properties and thus you can cool the backside of the substrate and still get great cooling.

    On a 1 by 2 inch substrate we made a 40W class AB amplifier.

    If you want I could do a writeup of the process and see if I can dig up some more information about the project :) mail me!

  16. UV cure “blue light” nail varnish :-)
    Works for me. It also works for those times you broke a very expensive glass lens (don’t ask!) and need to glue it back together while the replacement turns up.
    Provided its held securely when glued and you scrape off the excess once set, it works fine.
    Also handy for “trimpot” tweaking, fixing optics, and other interesting though esoteric projects like homemade EL sheet using defunct LCD panels and salvaged-then-dried-out EL phosphor from Greedbay or a peeled panel from something else.

  17. Wasn’t my idea, Jeri was the one who came up with it.
    I did notice that the recent E-ink mod uses uncured Epoxy, with EL you really need a solid dielectric.
    For that matter why not use a 3D printer to lay down lines of UV ink mixed with the RYB phosphors
    and DIY your own colour display?

    I think the main reason this is not done is that TFEL is much lower power and cheaper to make.
    Some of the displays have an MTBF of 20 years, they are still being used in the B-2 from what I can find out.

  18. Also relevant: locate a really old LCD panel (or for that matter an OLED TV which some eejit broke) and harvest the RGB filters from it.
    IIRC these are way better than what you find normally and are 1080P.
    You could feasibly make a really good reliable E-ink colour display from an old monochrome panel, the problem is finding one.
    Little hint: ten seconds with an X-acto knife works for “rapid” harvesting from dead OLED TV, the actual filter is in that front plastic sheet and it has a rear striped ITO conductor as well.

  19. RE: Trimming SMT resistors. I once worked in a factory that made a device that was tuned to a specific frequency by trimming the values of SMT resistors. We did this under a high magnification lens using a sandblasting rig with a tiny (sub millimeter) sized nozzle. We were tuning for a target frequency and bandwidth for the completed device rather than a target resistance for any one resistor. We trimmed one resistor for frequency, a different one for the bandwidth. A further complication was that the sandblasting stressed the resistors, and to ensure long-term stability, the device had to be stress-relieved by baking in a 200 degree oven and then rechecked and the tuning re-trimmed by more sandblasting, then another bake and then a final check. The resistor trimming only took the tuning in one direction, so if you overshot, you had to replace the resistor and start over.

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