SUCCESS !!! 
Can't believe it, just when I was starting to be real pessimistic about this repair, suddenly fixed it !
Was all due to corrosion, surprise surprise....
There are a couple small (2.2uF) SMD electrolytics near the ribbon cable connector. During my first attempt back then, I remember their terminals looked crusty, so I removed them and replaced them with what I had at hand at the time : my big collection of leaded/through hole electrolytics. Found a couple 2.2uF, in a tiny package.... as tiny as this kind of package can get anyway, but of course was still huge compared to the original SMD parts... but still, I though better non-corroded parts, than no part at all. Was hoping maybe there was some kind of decoupling issue because of these bad caps, but that didn't fix the problem so I gave up at the time.
So I removed this ugly hack and soldered a couple nice Tantalums of the same value that I had salvaged recently while I was trying to get the hang of my new little hot air station. On one of the caps, one of the pads came off as I removed the leaded cap. Oh well. Scrapped the adjacent trace to reveal some fresh copper I could solder to, as that did it. The cap package was a little small to bridge the gap so had to install it sideways and had not much pad an trace to solder its terminals too, but that did it OK.
Then next to one of the caps, I noticed a crusty looking resistor. Probed it... hmm... an open trace on the pad nearest the capacitor ? Am I dreaming ? Have I just found a practical/real world example of this electrolyte corrosion that plagued my TDS 544A ?? My first encounter with corrosion damage ?? Couldn't see anything with naked eyes, and the solder mask doesn't help..So I scraped the trace by the solder joint. removed the resistor, some flux and solder wick, cleaned the pads... then a high resolution macro pic of the pads, then zoom on the pic afterward.. OH ! Taht becomes quite obvious now ! Yes indeed a cut trace ! Right by the pad, and the pad itself is eaten all around, slowly but surely. The PCB itself looks brand new, the cut show to the naked eye ! Not mine anyway.
Tried to repair it with just a blob of solder but it would not bridge, so had to put a wire, but even my AWG 30 "mod" wire looked quite big and would not stick to the thin trace. So had to run a much longer wire to the nearest big pad so I could more easily solder to. That turned out to be the tantalum cap I had just put in place.
Then looked this resistor up in the schematic... was the pull-down for the MCU's Reset line. Hmm I thought, sure enough the MCU does run, so clearly this floating reset line never stopped it from initializing, however maybe some internal peripheral might require a "cleaner"/more predictable Reset... something like maybe the ADC ?! So I thought why not, maybe this will fix my problem with the analog knobs... no joy, no improvement what soever
Oh well, at least it was worth a try, and this pull-down definitely had to be fixed anyway, couldn't possibly let it flap in the breeze eh ?!......
Original was 10K, closest I found was 3.3K, good enough, it's just a pull-down...
So I had quite mixed feelings at this point : "happy" I had now gained experience of how to find and recognize and fix a cut trace... but quite frustrated that it did not actually fix anything and I was back to square one !
But, at leas tit showed that there WAS some corrosion damage on the board, so why not some more ? Maybe if I could find & fix some more corrosion it might improve things.
So I started probing around the switches area. I tired all push buttons and figured only two of them were not working : one in the bottom right of the front panel : " Force Trigger ", and one in the top right corner : the "Acquire" menu. According to the schematics they shared a line.
Was probing a long line that went from right behind the "Force Trigger" button, straight to the MCU area, near one of the two leaky caps.... there was a via. Bingo, that trace was cut, right by the via next to the capacitor. Soldered a long jump wire: easy, just stick the ends of the wire straight into the holes of the via !
Hey what do you know, my two buttons are now working ! Yes ! Making progress, 100% of the (push) buttons work now ! And that was due to corrosion.
So... probed some more, hoping to find another cut somewhere, that would fix the remaining, big issue with the analog rotary knobs, but no joy. Was depressing again, grrr.... So tried again to make some sense of the behavior of these buttons, actually managed to find a very distinct pattern but I just had no idea what cold cause this behavior.. because this circuit is quite straight-forward and I had already probed/tested 10 times every signal involved in this circuit and never found anything wrong ! So was out of idea on this front sadly !
So I thought well, I have run out of ideas here, so I might as well probe agaiiiin for cut traces... I maybe have missed one or two, you never know.
So at this point I was not trying to figure out with naked eyes which solder joints looked dull/susceptible of hiding corrosion damage. No, I turned my brain off at this point, and just used brute force : I probed each and every pad and via one by one, no questions asked, methodically, without holding much hope but well what else could I do. And what do you know : the very last thing I checked, was defective ! A via that was hard to see and a pain to look at/work on, buried half-way below a corner of the MCU package. Was looking like a pain to deal with, so avoided looking at it, hoping I would find a cut somewhere else that would be more easy to work on... but no, the cut was there ! So fixed that. I thought oh no, if this doesn't fix it, I will probably have to remove the MCU chip so I can inspect underneath it, might be more vias under there. So in order to assess my chances of this via fixing my problem, I looked it up in the schematics to see what it did. Via is connected to pin #7 of the MCU.... where is it... pin seeeeeeven..... ah, there it is. So, what does it do exactly....... eh ? OHHHHH !!!! Its only purpose in life is to connect to ground, the lower voltage reference of the ADC !!! Yes, that's highly likely to fix my problem !!!!
Couldn't wait to power up the scope see how it would react ! BINGO ! Problem fixed, all analog rotary knobs now work perfectly !
Scope is now 100% fixed ! No weird problem with the front end in the end, was 100% due to the defective front panel driving the scope nuts !
I did a quick sanity check and seems OK : fed a sign wave, tried all the basic controls, on both channels, all fine. Also ran an SPC calibration routine, came clear !
so I call this a fix !
Then I hooked GPIB and tried to clear the error log using the same little software that I used the other day on my TDS 544A. It's advertised as being able to handle pretty much all the old TDS scopes, a bunch of them any way. Worked like a charm ! The 130+ errors are now gone, clean bill of health !
I noticed that this also cleared the "PowerUp" counter.... was 2500+, now zero. I think this must be a bug/unintentional... Clearing the log is one thing, it's perfectly normal/acceptable to do it if you know that you have fixed the problem. However clearing the Power Up counter is just plain lying ! Might send an e-mail to the author of this software, maybe nobody ever told him about this unfortunate side effect.
Anyway, I am so happy that I was finally able to fix what looked at first like a really, really sick little scope that I was having a hard time to figure out !
Also real happy that I now have practical experience dealing with electrolyte corrosion, will no doubt come to good use in future repairs !
Lessons I learned while doing this :
1) even if the PCB looks brand new, there can still be corrosion. Don't rely on the cleanliness of it.. Maybe in some severe cases, with very big caps leaking, you can see deposits/gunk on the solder mask, but in my case with just 2 tiny 2.2uF low voltage caps, there were nothing to see.
2) don't waste time looking all around the board... if corrosion there is, it will be only in the vicinity of an electrolytic cap. In my case it looked like a radius of an inch around a given cap, was a generously sized area. No need to look 3 or 6 inches away from the nearest cap.
3) don't waste time/bother inspecting closely each and every trace on their full length : the electrolyte doesn't seem to be able to eat though the solder mask. It will "run" and end up getting trapped around vias and pads, which it will eat because it's the only thing not protected the solder mask.
4) the trace is being usually much narrower than the pad or via it connect to, the cut will will be right thre, between the end of the solder mask layer and the edge of the pad/via.. hence here to see by eye.
5) Look/probe first for the pads/via that are closer to the caps, and those that look the more dull... but if nothing stands out and/or your problem is not fixed, then check all vias/pads because even not so dull looking ones can still have a cut trace. So check all of them one by one, methodically, making sure not to miss any.
6) once you have found a possible candidate, scrape the trace with a sharp blade to reveal fresh copper you can solder to, and this also makes inspection easier. Remove the component (and replace it if looking to crusty/not trust worthy anymore) to reveal the pads, clean them with some flux and fine solder wick. Then use a microscope to confirm, or if like me you don't have one : you can make do by taking a high-resolution pic (8M pixel or so) or so of the pad, then using the "macro" mode of your still camera. Move the board around so as to get the best possible lighting on the suspect. Then zoom on the pic big time. See below for the pics I took, I think it's decent enough to be able to clearly see where there is a cut and where there is not.
I was able to get away with this method because the area to check was small and the components are quite big and comfortably spaced, compared to modern SMD "standards"... but next time I have to search for corrosion (ie, next time I work on any thing that uses electrolytics ...) here are the things I wold like to improve, based on this first experience :
1) a "proper" good quality scalpel/sharp blade.
2) better probes more suited to small SMD components and corrosion : gold plated tips, thin, very pointy, sharp and durable, so that with minimal pressure, you can pierce though surface oxidation of solder joints and component terminals. This way you the search is made quicker and more reliable.
3) a different wire : this wire wrapping/ 30AWG mod wire is not only too big, it's also very fragile and breaks very easily : I would solder it, then brush the area LIGHTLY with a soft ESD safe brush, and even though I would of course take care not to stress the wire joint too much... sometimes i would break anyway.
Looking at Louis' Rossman Youtube Channel, where does it these things for a living all day long repairing densely packed modern Apple Mac Book mother board, it seems that enameled wire salvaged from a some small SMD coil (from whatever DC-DC converter for example), works just fine.
4) Kits of SMD passive parts of all kinds and package sizes.... so you can easily/quickly replace any crusty little component. I was lucky to happen to have these tantalum SMD caps of the appropriate value and package size, but for the pull-down resistor of the Reset line, a simple 10K thing, well I didn't have that. glad it was just a pull down so the value didn't matter much, but most of the time the value WILL matter of course... so one needs a decent collection of values to chose from, eventually combining several resistors to achieve the required value.
5) A bloody microscope !!! This very low-scale/modest first experience on this little front panel was eye opening, pun intended.... it was a pain ! I just can't imagine using a similar process on a large scale, never mind do it multiple times on several instruments. And since I do plan on repairing more old instruments in the future, because I like it and because I don't enough money to buy more recent stuff anyway.... then yes I will definitely buy a microscope. Looking at Louis' channel, his scope is good enough to my taste, and not too much money IIRC. Still some money though, of course ! So if my next repair happens before I have the money to get a microscope, then AT LEAST I will buy some cheap(er) way to magnify the image... ANYthing will be better and more comfortable than naked eyes.
So... what's left to fix this scope ?
A couple little things still need my attention before I can put back together for good :
1) the membrane keypad for the soft buttons : the POWER/Standyby button is completely worn out, impossible to start the scope from the front panel. Yeah I could just wire a push button on the back panel and call it done... I guess, but I would rather try to fix the keypad. I think there exists kits to restore the carbon conductive surface on the contacts... but what I see on Ebay costs 50 bucks, which is what I paid for the scope ! Still, I would be prepared to pay this amount if and only if 1) It's quality stuff that actually makes a good and durable job. 2) there is enough of the stuff to repair many keys, so I can reuse it for future repairs and 3) the stuff once opened, doesn't dry out to fast and has a shelf life of several years so I can reasonably expect it to still be usable in my future test gear repairs. Might post on the forum for buying advice from people who have actually been there done that...
2) Unit is missing its cooling fan !!!! I tossed it back then, can remember why exactly. Would have done such a thing lightly obviously, so either its was plain not working, or very, very, very loud/worn out. Looking at the shroud on on the case, looks like a standard 120mm unit, and from memory it runs from 12V DC from the third-party power supply board. I have a dozen computer power supplies, these typically have either an 80mm or 120mm fan I think, so no doubt I have one of those at home. Not sure if these are usually power from the mains AC or from the local 12V rail though, will have to check. Worse case, might shell out a few Euros for a brand new one... can't be that expensive, and I intend to keep this scope anyway, so might as well do things well.
Then might try hacking it. The TDS 310 is the bottom of the line. 50Mhz 200MS/s. It's biggest brother the TDS 360 can do 200MHz and 1GS/s, much better !!!! Now if I could figure that out, I would be a happy camper ! Will post on here, you never know your luck, someone might have done it already...
Obviously the schematics aren't available for this 310/320/350, but the schematics I have been using here, for the 340/360/380, which are so incredible close to my 310, are nice enough to clearly show you what the differences are ! At least on the hardware... I guess the NVRAM and/or FW would need updating and of course that can be show stopper, how to figure this out. So I am not holding my breath on this !
Anyway, 3 scopes fixed in the lab in just 2 months, most of which was spent on the 2232 repair ! Not bad for a first dive into instrument repair, I am starting to enjoy this stuff as much I imagined I would !
Can't wait to have some money and buy a new old instrument for repair and add functionality to my lab !
Yeah, no point in buying yet another scope, even if I would love to ! Hard to resist , when I find something I like on Ebay ! LOL But it's more reasonable to concentrate my modest income on getting new types of instruments, to make the lab more useful, and more pleasurable.
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