I have had two 3455As through my hands and on both, the last digit bounced around when in Hi-Res (i.e. 6.5 digit mode) with Auto-Cal on. See the blue line in the graph.
If you listen carefully, you can hear the auto-cal relays clicking. The last digit jitter is in time with the relays... hmmm. Now the way auto-cal works is that the meter reads an auto-cal constant for every real reading it takes. There are 13 auto-cal constants. I set up a Labview program to read a value from the meter every second and the graph is the result. The spikes in the graph are every 13 readings, pretty much confirming that the bouncing is related to auto-cal; but how?
I consulted with cncjerry who has seen/fixed several 3455As and we went through various testing, up to his very generous loan of one of his working AtoD cards. Thanks again Jerry! His AtoD card was more stable, so I was pretty sure it was something on the AtoD card.
I found that the zero-crossing output was unstable. I made it more stable by increasing the positive feedback (2Mohm to 1Mohm resistor), but no change.
I found the resistor in the integrator capacitor reset circuit was 39Kohm but 24Kohm on the schematic. I reduced it to 11Kohm eventually with no change. I measured the residual voltage on the integrator capacitor as the meter stepped through the auto-cal constants, finding something like 0.2mV max difference - once count is about 0.8mV on the integrator capacitor, so that was a dead end.
I found lots of noise looking at the input to the zero-crossing detector, so replaced the opamps that drove it - again, no change (and I'm not sure that the noise wasn't common mode noise, it being difficult to get a decent ground on the AtoD board).
I then monitored the counts being returned from the inguard module using a Digilent Analog Discovery - the counts can be read using the Discovery's SPI decoding and it is happy to accept the 5V levels. I found the pattern in the counts I read. I could see the auto-cal constant counts interleaved with the counts for the meter input. I could see the pattern in the counts for the meter input and in all cases, where there was a spike, the previous auto-cal count + or - 10V. +10V and the next input reading spiked up; -10V and the next input reading spiked down. The AtoD was either showing a memory effect, or there must have been leakage of the previous input onto the integration capacitor.
Leakage was eliminated by monitoring the signal that held the integrator in reset and the signal that gated the input to the AtoD board. They change simultaneously. That pretty much left the integration capacitor as the only thing that could have memory.
So I considered dielectric absorption in the integration capacitor. I noted that during the integration of a full scale input, the voltage on the integration capacitor averages +/- 9V depending on the sign of the input. See the scope screenshot (yes, the ramp on the peaks of the triangular waveform is normal and appears on one of the screenshots in the service manual). It is interesting to note that the 345
6A service manual, in section 8-60 comments: "The average charge before rundown is kept low to minimize integrator capacitor dielectric absorption". Presumably they had noticed the effect on the 3455A when they designed the 3456A.
The integration capacitor is a polypropylene capacitor which should have very low dielectric absorption. It's 0.082 uF 200V. I found some on ebay and tried one. No change. I read Bob Pease's article on Dielectric Absorption as well as the mentions in "The Art of Electronics". Time to try for a Teflon capacitor. Nothing to be found other than surplus Russian capacitors on ebay. So, I ordered one. The thing is huge compared to the original (see picture). I installed it and... problem fixed. The last digit is much stabler, bouncing one digit occasionally, similar to what my other meters do at 10PLC integration period (the 3455A actually uses 8PLC). I let the Labview program run overnight with the result in the final attachment. I think that is as good as I can expect from a 3455A.
So, if the last digit on your 3455A bounces around in time to the relay clicking with auto-cal on, consider replacing the AtoD integrator capacitor... there are no more Russian 0.082uF teflon capacitors on ebay, but 2x0.039 200V 5% in parallel would do the trick given the tolerance on the original 0.082 capacitor was 10% (and they might even fit in the original space with one on each side of the board). I used a carefully sited dab of hot glue to hold my monster capacitor in place.
[Edit - additional information]
The hot glue failed. I need to find a better way of securing the capacitor.
It's two counts out in low-resolution mode with a 10V input. I don't know why yet. It's one count out with the old capacitor, but flashing down to 0 counts out once per auto-cal cycle.
US Patent #US4357600 A which was for the 3456A (
http://www.google.com/patents/US4357600) describes the 3455A's failings well in its "Background of the Invention" section which is basically a description of how the 3455A works. They specifically mention dielectric absorption as a problem.