For the record: Today I had the chance to test a Siglent SDG2000X+#$%@ generator and it shows exactly the same behaviour. At some point an AWG runs out of record length to produce a complex signal with the set frequency. However unlike Tektronix, Siglent does not specify the accuracy of the frequency setting.
It's not clear to me what it means to have an "accuracy" of the frequency setting. These are DDS AWGs that build their signals as a series of points in memory and then clock them out through a D/A converter. The actual frequency accuracy of a generated waveform would, I'd think, be determined primarily by the accuracy and jitter of the clock that is used to shift points out through the D/A converter. The
resolution of the frequency setting is clearly limited by that clock, a.k.a. the output sample rate. Of course, there are other factors that affect the ultimate shape of the waveform, but I'm having trouble seeing how they could affect the apparent frequency of the waveform, i.e. the rate at which the same point in the waveform repeats itself, unless perhaps the waveform frequency approaches Nyquist.
But here, the drift is in comparison to the other channel of the same AWG. Both channels have the same time source, or at least I would presume them to, so I'd expect them to be clocking out points in lockstep. The accuracy and resolution of the frequency setting should be irrelevant in that case -- this isn't a measurement relative to an external frequency standard, but rather relative to the same internal standard that is being used by the AWG. This, I believe, is why Shahriar believes it to be a bug in the firmware. Admittedly, this is FM, so the generator has to generate a continuously-varying-frequency signal, there will certainly be some error at any given frequency, and I suppose what we're seeing might be the result of the actual average frequency within the FM range deviating slightly from the designated carrier frequency. But as the sample rate of the AWG increases and the number of points available to construct one period of the waveform increases, I'd expect to see that average converge on the actual carrier frequency as the sample rate increases, in the absence of ways of constructing the samples of a frequency modulated waveform over time to ensure that the average winds up being the same as the carrier frequency.
Of course, if each channel gets its own separate clock (which would surprise me greatly), that would clearly make inter-channel frequency deviation a near-certainty.
That said, my SDG1025 shows the same behavior, too, and notably worse than what the video shows, at that. Its sample rate is 125MS/s. The sample rate of the SDG2000X series is 1GS/s. Just out of curiosity, if you use the same parameters as Shahriar used (1 MHz carrier, 10 kHz deviation), does the rate at which the modulated waveform moves relative to the pure base frequency signal seem to be about twice that shown in the video? The Tek has a sample rate of 2GS/s.
Also, do you have access to an AWG from Keysight or Instek? I'm curious if this behavior is present in those generators as well.