Yes, if there was a function that automatically measured and corrected the DUT delay before sweeping, I'm sure there would be fewer level jumps.
However, this is not easy if the DUT includes equipment that is not a real-time system (such as a computer). Latency changes significantly each time.
APx500 has faster step sweep speed than AP2700. Version 8 was even faster. (I used it in the demo. I don't have it)
If that happens, it will become even more difficult.
In order to perform a high-speed step sweep under random latency without making mistakes, I think it is necessary to ensure the mutuality of the oscillation signal and the measurement signal.
For example, it would be interesting to be able to superimpose/capture a "step number signal" at the beginning of each step signal during sweep measurement.
Yep, these days one could pack way more intelligence into measurement to avoid such problems. The algorithm currently used dates back to very early beginnings of the AP systems (while still at Tektronix, probably).
As for USB and other playback latencies, those are variable but once the stream is running it never changes, obviously. So, the key is to keep the USB output stream alive at all times.
The attempt to speed up the sweep makes sense only for production testing. In the lab it makes no difference if it takes 10 seconds or 3 minutes.
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But the overall
good news is that the DAC linearity test is superfluous anyway for 99% of the DACs because they are Delta-Sigma type which is always 100% linear even way down into the noise floor. R2R DACs is probably the only type that really shows something in the linearity test.
EDIT: Some DACs have a "hidden" attenuation of, say, 10dB once the signal toggles only the last 4 bits or so (of 24) to bring the noise down when silent (and giving 'better' noise specs). The Apple Dongle is an example. With a fine-tuned linearity test one sometimes can see the transition into that attenuation which usually has time constants involved. It's visible in other tests as well, notably very low level (south of -100dB) stepped sine spectrum.