Why do some AWGs generate FM signals with an incorrect carrier frequency?

[kcbrown]

This is a continuation of the discussion that arose from my comment here: https://www.eevblog.com/forum/testgear/siglent-sds2000x-plus-coming/msg3401936/#msg3401936

In a video done by Shahriar (a.k.a. The Signal Path, a Youtuber who does truly awesome videos.  You should check it out if you haven't already), he shows what he calls out as a firmware bug in the Tektronix AFG31000 series AWGs.   Here's a link to the video at the relevant time: https://youtu.be/SOHjFtw0sgo?t=1248

The bug is that the carrier frequency of the modulated signal generated by the AWG seems to be slightly incorrect relative to an unmodulated signal of the same frequency as that carrier, as generated by the same AWG.

The question is: why is that happening in the first place?  If you follow the discussion, you'll see that the Tek isn't alone in that regard.  The Siglent series of AWGs does the same thing.

I can see it happening under some circumstances as a result of the amount of waveform memory that the AWG has.  If the waveform can't be constructed in full within the sample memory then the AWG would have to construct it on the fly.  As long as the AWG can manage to do so in such a way that the average carrier waveform within the modulation envelope has a frequency that matches the frequency of the unmodulated carrier, the end result should be an apparent carrier frequency that is a match (within, I'd guess, the jitter of the clock).

The example in Shahriar's video is a 1 MHz carrier modulated by a 10 KHz signal.  Now, the sample rate of the SDG2042X is 1.2GS/s, and it has 8 Mpts of memory.  The amount of time that a 10 kHz period represents is, of course, 100 us.  The entire period of the modulating signal, and thus the entire waveform that needs to be constructed, can thus be represented by exactly 120K points at 1.2GS/s.  Similarly, each period of the base carrier signal can be represented by exactly 1200 points (but since this is a FM signal, the number of points needed to represent a single period of the modulated signal will vary between 1188 points and 1212 points, roughly.  But for the purpose of this, given that an entire period of the modulating signal can be represented in memory, that doesn't matter).   Given that, why would the SDG2042X show any deviation between the modulated carrier signal and the unmodulated one, when the two signals are presented on the two outputs of the AWG?  Note, too, that the carrier frequency is an exact multiple of the modulating frequency, so there should be no problems with the values at the ends of the buffer failing to match up for the purpose of repeated play.  It's about as ideal of a scenario for an AWG as you can get.

For the AFG31000 series unit, it has 131072 points of waveform storage.  But it does 2GS/s.  That means there isn't enough waveform storage to represent an entire period of the modulating signal at the maximum sample rate.  But can't the AWG control the sample rate, or do sinc interpolation of a reduced sample set, and, thus, control the amount of memory needed to represent the waveform?  As long as the amount of memory is enough to properly represent the carrier at the highest end of the frequency range (1.01 MHz), i.e. satisfy Nyquist, why would it, too, see a difference between the average frequency of the modulated signal and the frequency of the unmodulated carrier?

My SDG1025 outputs at 125MS/s and has 16 Kpts of memory.  100 us of time requires 12.5 Kpts, so it, too, has enough memory -- but that's with only one channel active.  With 2 channels active it might have to either interpolate or reduce its sample rate.  But even with the sample rate cut in half, or with decimation and sinc interpolation, there's way more points per carrier cycle than needed to satisfy Nyquist.  So it, too, should be able to do this without issue.  And yet, it doesn't.  Why??

Finally, are there AWGs that don't demonstrate this behavior?  If so, which ones?  Anyone have a Keysight AWG to test this with?  An Instek?

[bdunham7]

I just noticed this myself the other day with my SDG2042X-H, and at first I thought it was another issue with the broken HP 5370B I was working on, but then it became apparent it wasn't.  I don't know how it does internal FM modulation--which  you might expect to work properly--but what really makes me wonder is how it does FM modulation with an external analog source.  In any case, I have noticed that when using the SDG2042X-H to broadcast to an FM radio, the signal is actually slightly distorted and noisy, sort of like multipath distortion.  I was working on old Zenith (tube) radio this way and I found myself wanting to adjust the antenna due to the background noise when I remembered I was using the sig-gen.  Switching to an old HP 8656A, even with its lower limit of deviation (99kHz) eliminated the noise. 

I put this second issue down to the limits of digitally outputting a 91.5MHz FM modulated signal without thinking about it too much, but I'd be interested in knowing exactly why these two things happen and if they can be improved.

[nctnico]

@bdunham7: is there some way to check the frequency spectrum for impurities from your signal generator? It could be a nice test to asses the quality of an AWG.
The carrier frequency offset is a few Hz at most so that should be a problem for testing radios.

[bdunham7]

@bdunham7: is there some way to check the frequency spectrum for impurities from your signal generator? It could be a nice test to asses the quality of an AWG.
The carrier frequency offset is a few Hz at most so that should be a problem for testing radios.

Yes, that was my next plan once I cleared off the bench a bit.  Unfortunately there isn't room for all of my monster-sized older test equipment, so I have to drag it out as needed.  I'll post photos shortly.

The carrier offset won't stop me from doing basic testing of old radios, but I had hoped to use the device for alignment and testing of newer FM receivers, which requires the ability to modulate an FM signal at 200kHz deviation and 38kHz modulation frequency with all distortion and noise components down at least -70dB.  It looks like the Siglent won't be doing that with an external modulation source and I'm not sure I can do it internally using the modulate via ARB method. 

I actually noticed the FM modulation issue simply trying to rebroadcast an FM radio station that I can't easily receive so that I could listen to it.  The carrier offset I noticed testing another instrument (HP 5370B) at a very low frequency.  I was actually testing the jitter testing function on the HP 5370B using an FM-modulated signal and noticed via another counter that is was consistently a bit low.

[nctnico]

This is something I can check albeit using a lower carrier frequency.

[bdunham7]

Here is the SDG2042XH compared to an old HP8656A.  I did 5 tests for each, the first two of a plain carrier at 91.5MHz, then three of that carrier FM modulated with 1kHz modulation frequency and 10kHz deviation, using the internal modulation feature of each.  Output was set at -30dB.  I did not observe any readily discernable change in the center frequency of either unit when I turned modulation on.

[TurboTom]

...

 In any case, I have noticed that when using the SDG2042X-H to broadcast to an FM radio, the signal is actually slightly distorted and noisy, sort of like multipath distortion.  I was working on old Zenith (tube) radio this way and I found myself wanting to adjust the antenna due to the background noise when I remembered I was using the sig-gen.  Switching to an old HP 8656A, even with its lower limit of deviation (99kHz) eliminated the noise. 

I put this second issue down to the limits of digitally outputting a 91.5MHz FM modulated signal without thinking about it too much, but I'd be interested in knowing exactly why these two things happen and if they can be improved.

The problem with external modulation of these modern(ish) digital AWGs is that in most of these units (actually, I'm not aware of any model that's working differently), the analog input is sampled by an eight-bit ADC, and obviously, that's simply not enough for decent audio quality. So unfortunately, nope, no remedy for this problem... 

[2N3055]

In addition what Tom said, these AWGs don't have analog control of frequency.
Nor they work on principle of old PLL direct synthesisers where they can set exact multipliers.
AFAIK, most of them use NCO principle, and they will have finite step resolution and that one won't be multiplier of 10...
So no infinite resolution, and no nice round numbers....

[AVGresponding]

My TTi TG2511 does not exhibit this behaviour. I haven't delved into its inner workings as yet so can't say how it goes about generating its output.

[David Hess]

I seem to recall that some (most?) DDS integrated circuits which support FM modulation limit the frequency resolution when FM modulation is used.

[bdunham7]

In addition what Tom said, these AWGs don't have analog control of frequency.
Nor they work on principle of old PLL direct synthesisers where they can set exact multipliers.
AFAIK, most of them use NCO principle, and they will have finite step resolution and that one won't be multiplier of 10...
So no infinite resolution, and no nice round numbers....

I seem to recall that some (most?) DDS integrated circuits which support FM modulation limit the frequency resolution when FM modulation is used.

I spoke too soon when I said the Siglent didn't have a noticeable offset, indeed it does have a very small drift compared to the same frequency unmodulated from CH2.  At 91.5MHz modulated at 1kHz with 1kHz deviation, it takes several minutes for one beat. 

In response to both comments above--these are touted as 'True-ARB' systems and should not have the same limitations as a plain DDS system like the FY6600 series.  Even a plain DDS system can accurately produce a sine wave of any frequency by simply solving the equation for that sine wave at the appropriate points and outputting those results at each point.  In theory, you could solve the slightly more complex function of an FM modulated signal for the appropriate number at each output point and that should be virtually flawless as well.  So there must be some slippage between that theory and actual practice here

[David Hess]

In theory, you could solve the slightly more complex function of an FM modulated signal for the appropriate number at each output point and that should be virtually flawless as well.  So there must be some slippage between that theory and actual practice here

I think the limitation had to do with how the hardware phase accumulator worked to support frequency modulation.  I just remember it being a limitation at least with older DDS chips.

[mawyatt]

As a possible work around using the available AWG, wonder if you could FM an external reference signal source (10MHz) by the required deviation in ratio?

Edit: Just tried this using the AWG in the SDS2102X Plus as the reference input to the SDG2042X which is set to 100MHz. I can deviate the SDG2042X AWG 10MHz reference input by up to +- 500KHz, or +-50,000ppm and the output behaves as expected (ref a@ 10.5MHz, output @ 105.0MHz, ref @ 9.5MHz output @ 95MHz, ref at 10.01MHz, output at 100.1MHz and so on)!!

Don't know how fast you can modulate the reference tho, as I don't have another source for 10MHz that can be frequency modulated.

Best,

[bdunham7]

As a possible work around using the available AWG, wonder if you could FM an external reference signal source (10MHz) by the required deviation in ratio?

Edit: Just tried this using the AWG in the SDS2102X Plus as the reference input to the SDG2042X which is set to 100MHz. I can deviate the SDG2042X AWG 10MHz reference input by up to +- 500KHz, or +-50,000ppm and the output behaves as expected (ref a@ 10.5MHz, output @ 105.0MHz, ref @ 9.5MHz output @ 95MHz, ref at 10.01MHz, output at 100.1MHz and so on)!!

Don't know how fast you can modulate the reference tho, as I don't have another source for 10MHz that can be frequency modulated.

Best,

I'll give that try the next time I have an FM radio on the bench.  Many devices with an external clock input won't work that way because they use a PLL or injection locking or something on that order to stabilize the internal clock rather than simply relying directly on the external clock.  I guess the SDG2042X isn't in that camp.  My known 'clean' source of FM signals is limited to 99kHz deviation (your plan fixes that issue) and rated for a 25kHz modulation bandwidth--but perhaps it will still work for the FM stereo signal, which I can hopefully generate with a good enough PC sound card. 

[mawyatt]

I'll give that try the next time I have an FM radio on the bench.  Many devices with an external clock input won't work that way because they use a PLL or injection locking or something on that order to stabilize the internal clock rather than simply relying directly on the external clock.  I guess the SDG2042X isn't in that camp.  My known 'clean' source of FM signals is limited to 99kHz deviation (your plan fixes that issue) and rated for a 25kHz modulation bandwidth--but perhaps it will still work for the FM stereo signal, which I can hopefully generate with a good enough PC sound card.

Think the SDG2042X uses the 10MHz reference for a frequency synthesizer to raise the clock for the DDS, probably 2.4GHz or higher. If this is true then the locking range of the synthesizer is the limiting factor, and the VCO loop filter determines the FM modulation bandwidth when used like this. We've used this technique decades ago for "thru-the-loop-modulation" before fractional N synthesis was available in integrated form, used a low frequency DDS to create the reference frequency for an integer synthesizer to upscale the frequency which the VCO was also modulated for around-the-loop. Both thru and around the loop were combined for total DC-maximum modulation bandwidth for use with a very early Gaussian-Minimum-Shift-Keying waveform.

Anyway, this should be perfectly linear static FM, but not sure how fast you can modulate the AWG internal synthesizer. The deviation is small for the indicated span (10KHz @ 91.5MHz or ~100ppm), so if one has a 10MHz VCXO, or another 10MHz source for the reference that would be worth a try.

Best,