Once the instrument was open, it became evident that the -15V rail of the power supply was missing or loaded down. They thoughtfully put a nice row of green LEDs on the I/O board at the top rear of the unit to indicate the presence or absence of the various power supply rails - it has eight of them - +/-5V, +/10V, +/-15V, +21V, +25V and finally, +38V.
By disconnecting all the ribbon cables feeding power to the modules then sequentially reconnecting them, I was eventually able to isolate the fault to the NSM OSC module (cable 44, roughly in the center of the photo below, connects to it). It took a few iterations of connecting and disconnecting things because at first I missed when the indicator LED went out, as it is on the end and not blatantly obvious when all the others are lit.
As I progressed in my plugging and unplugging things, the fault definitely made itself known when the suspect module belched a bit of smoke on power up. This was confirmed a moment later when all but two of the power supply LEDs went dark.
Opening the smokey module revealed a barbecued molded tantalum cap.
Definitely a bit past its prime...
A Digi Key order and a few weeks later I got back to it. The cap came out pretty easily, the soot was cleaned up with a q-tip and some denatured alcohol, and after comfirmation that the polarity was right, the new cap went in easily.
Cap extracted:
Partially cleaned board (I got the rest of the mess off when I cleaned the flux residue after reflowing the solder on the pads, but was on a roll at that point and put the new cap in without bothering to take another picture):
New cap in place:
Of course the fried cap appears to be the ONLY tantalum on the board that doesn't have a polarity mark next to it. An ohmmeter check confirmed that it was in correctly, positive to ground and negative to the -15V rail on the board.
With that module repaired and reinstalled, the next challenge was to figure out why there were now basically NO power supply rails - all that was lighting were the +21 and +25V indicators, and they're on whenever the unit is connected to power - the AC Mains switch does not affect that part of the supply, it is on at all times. I popped the power supply board out (great fun as it extends across the entire width of the unit, and has several daughter cards and short cables which must be disconnected/gently pried away from it, with limited access) and looked it over; nothing appeared to be cooked, and the fuses on it were good. I'd reassembled it hoping that whatever had tripped the supply was something that would reset (yeah, I know... But hope springs eternal...), but when it was turned on things were, unsurprisingly, still dead.
Troubleshooting was further complicated by the lack of documentation - this is new enough that a full service manual was not readily available for less than a small fortune, so I was working with a module level troubleshooting guide downloaded from Keysight. Digging through the manual revealed a combination block diagram/partial schematic of the supply, so I started taking measurements, and, concentrating on the -15V section, soon discovered an open fuse hidden away on one of the vertical daughter cards that's buried inside the rear of the generator. The easiest way to gain access to it was to disconnect the cables and remove the I/O board at the top; I wasn't pulling that damned power supply board out again if I could help it.
A trip to the hardware store later (I had no 3A fast blow fuses, and wasn't about to put a different value in for testing as it's such a PITA to get to) and a new fuse later, everything went back together and I had all power supply rails once more. They are apparently electronically interlocked, and if one goes away the rest shut down to prevent damage to the unit. I should have taken pics of the fuse board, but neglected to before reassembling things, but unfortunately didn't.
More below.
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