Low frequency modulation in high frequency DDS generated signal

[Quant01]

Hi all,
Recently, I posted the following message on another forum and was advised to ask around in a DSP forum :

"I've been using an arbitrary waveform generator for one of my projects, and specifically, I'm using a DDS option on that AWG (the waveform generator is an M4i6621x8 from Spectrum Instrumentation). Essentially, I'm sending asking the DDS to output a sum of RF sine waves, all of them being on the order of 10s of MHz, with a delta in frequency of at least 1Mhz. However, on the output signal, if I ask for a certain amount of sin waves (usually 5 or more), I start observing a modulation of the amplitude of frequency a few hundred mHz (orders of magnitude away from my input frequencies). The modulation is sinusoidal.
My questions are : why does this happen and how can I remove this feature ? I would expect some MHz beating because of how sum of sine functions work, but definitely not mHz.
Some additional information :
-the frequency resolution of the DDS is about 290 mHz, so this value seems to fit with the observed beating, but I fail to see how this could be related to the issue.
-I didn't notice such beating when using less than 5 frequencies as an input.
-I am using a ZHL-1-2W+ power amplifier at the output of the AWG, which is then connected to an acousto optic deflector (a device that diffracts a laser beam according to input frequencies). The amplitude modulation becomes visible on camera based on the intensity of the diffracted beams."

If anyone knows how to solve this issue or has any idea, it would be greatly appreciated.
Thanks in advance.

 

[D.A.(Tony)Stewart]

It could be just visual artefact of sine wave addition:
f1 = sin(2*pi*(0:1023)*.13);
f2 = sin(2*pi*(0:1023)*.27);
y = f1+f2;
plot ( y)

View attachment 195369

This can be what undersampled RF looks like

 

[kaz1]

This can be what undersampled RF looks like

What do you mean? there is no physical sampling rate.
f1 is normalised 0.13 of Fs of 1
f2 is normalised 0.27 of Fs of 1
both added as they are generated.

do FFT and you should see 0.13 and 0.27 with mirrored copies if frequency axis is set normalised between 0 and 1

 

[KlausST]

Hi,

I guess the root cause of the issue is already validated.

If it was a DAC nonlinearity ... why would this nonlinearity not happen when one changes the frequency by 0.29Hz?
(Relative) Nonlinearities may vary with amplitude ... but why with frequency?

And the magnitude of nonlinearity errors are rather small ... I guess below 1% .. so one would not even recognize them on a scope picture. (but on an FFT)
Mainly because nonlinearities cause overtones.

Klaus

 

[kaz1]

Hi,

I guess the root cause of the issue is already validated.

If it was a DAC nonlinearity ... why would this nonlinearity not happen when one changes the frequency by 0.29Hz?
(Relative) Nonlinearities may vary with amplitude ... but why with frequency?

And the magnitude of nonlinearity errors are rather small ... I guess below 1% .. so one would not even recognize them on a scope picture. (but on an FFT)
Mainly because nonlinearities cause overtones.

Klaus

ok so what is the cause called as technical term?

 

[KlausST]

It´s the effect of adding two signals with almost identical frequencies.
Some call it "beating", some call it "envelope" ...

It´s the same effect that is used to tune guitar (strings).

Klaus

 

[kaz1]

OK I can also see that in this basic simulation:
############################
f1 = sin(2*pi*(0:1023*10)*.1300);
f2 = sin(2*pi*(0:1023*10)*.1301);
f3 = sin(2*pi*(0:1023*10)*.1303);
f4 = sin(2*pi*(0:1023*10)*.1309);
f5 = sin(2*pi*(0:1023*10)*.140);

y = f1+f2+f3+f4+f5;
plot ( y)
############################

Clearly this is a time domain issue and is concern for applications like music or the issue of this thread.
It does not apply to frequency domain. The OP presented the issue as low frequency modulation.
Thanks for the clarification.

 

[KlausST]

The OP presented the issue as low frequency modulation.

OK.
I also had my issues with correct terminology in this thread.

--> I read it as: (the amplitude is) modulated with a low frequency. (or looks alike)

I´m with you: this is not "visible" in frequency domain.
The modualtion frequency you see is not a real frequency.

Klaus

 

[D.A.(Tony)Stewart]

Interference patterns are not AM

 

[KlausST]

Interference patterns are not AM

I agreed - twice - to it.

but it looks like one.

Or the other way round:

If you see such a pattern on your scope how can one distinguish if it´s frequency interference or AM?

(picture from: https://www.researchgate.net/figure...ies-f-1-and-f-2-blue-and-green_fig1_353337207)

Klaus

 

[Quant01]

Hi,

D.A. (Tony) Stewart : I did check FFT a while ago but it didn't reveal anything specific. However I do have IMD in my signal, IMD3 according to the frequencies generated, but these frequencies carry very low power compared to the desired ones.
I'm not sure what you mean by sensitive to interference pattern, could you please specify ?

Kaz1 : If the root of the problem is indeed IMD, do you know of/is there a systematic way of cancelling the low frequency components that occur in the system ? To be truthful, I don't think I understand the underlying reason behind the intensity modulation. Klaus kindly explained what seemed to be the problem in the case of the specific frequencies I provided, but is this a systematic issue ? Should the differences of the differences of input frequencies always be 0 to avoid the "beating of the beating" (leading to the observable intensity beating) ? If you happen to know any literature references on the subject I would gladly take a look.

 

[D.A.(Tony)Stewart]

Considering the range of f , do the patterns change with different sweep rates to ensure sampling rate is fast enough

 

[kaz1]

Hi,

D.A. (Tony) Stewart : I did check FFT a while ago but it didn't reveal anything specific. However I do have IMD in my signal, IMD3 according to the frequencies generated, but these frequencies carry very low power compared to the desired ones.
I'm not sure what you mean by sensitive to interference pattern, could you please specify ?

Kaz1 : If the root of the problem is indeed IMD, do you know of/is there a systematic way of cancelling the low frequency components that occur in the system ? To be truthful, I don't think I understand the underlying reason behind the intensity modulation. Klaus kindly explained what seemed to be the problem in the case of the specific frequencies I provided, but is this a systematic issue ? Should the differences of the differences of input frequencies always be 0 to avoid the "beating of the beating" (leading to the observable intensity beating) ? If you happen to know any literature references on the subject I would gladly take a look.

I see you are not sure about your problem.
Since laser applications is your area, we may not understand your problem. You need to word the problem "as is" rather than any lower level analysis or beatings or modulation.

The main question: is your application sensitive to time domain or not. I mean if you are just adding up clean tones you will get various patterns and peak-to average will change but frequency domain will be clean. The time domain issues are relevant is some cases such power amplifier's non-linear operation. So does your application fall into this category.
If it is IMD it will show on spectrum and will change in locations and power depending on generated tones though could be very weak in good design. There is plenty literature on IMD on the web.

 

[Quant01]

Hi,

D.A. (Tony) Stewart: for certain different frequencies (other than the ones I specified for Klaus earlier) the beating does occur but usually at 290mHz. From my resent testing of different scenarios based on Klaus' idea, it looks like the beating occurs at the frequency corresponding to the greatest common denominator of the input frequencies. Usually it is 290mHz because this corresponds to the resolution of the DDS, but I guess by pure chance it could happen at another frequency. And if you're referring to the patterns visible on the oscilloscope, apart from phase, they are always similar. I don't know if this answers your question ?

Kaz1: Then yes my application is sensitive to time domain. I'm using an amplifier and the manufacturer of the AWG informed me that such problems could occur if the amplifier was in non linear regime.
So to "state the problem as is" : I'm sending a RF signal comprising multiple sine waves of different, fixed, frequencies into an amplifier. This amplifier is connected to an optical device that diffracts a laser. The intensity of the laser oscillates at 290mHz because of this. By analyzing the output of the AWG on an oscilloscope, we see the 290mHz beating. By using a spectrum analyzer after the amplifier, something that looks like IMD3 is visible, but at significantly lower power than the main tones.
So maybe other types of IMD also appear (other than IMD3).
The laser itself is not a relevant component of the problem, it only serves, in this case, as a visual proof that there is a problem.
I think my next step is to find an amplifier that will operate in linear regime in my application.

 

[kaz1]

Also ADC clock frequency can modulate your tones.
The power amplifier may behave better if you randomise the phase to reduce peak/average, and dither each tone

 

[D.A.(Tony)Stewart]

Hi,

D.A. (Tony) Stewart: for certain different frequencies (other than the ones I specified for Klaus earlier) the beating does occur but usually at 290mHz. From my resent testing of different scenarios based on Klaus' idea, it looks like the beating occurs at the frequency corresponding to the greatest common denominator of the input frequencies. Usually it is 290mHz because this corresponds to the resolution of the DDS, but I guess by pure chance it could happen at another frequency. And if you're referring to the patterns visible on the oscilloscope, apart from phase, they are always similar. I don't know if this answers your question ?

Not quite. My hypothesis is interference patterns from sub-sampling with inadequate 100 MB buffer length to resolve 10's of MHz and 0.29 Hz at the same time.

I made discrete signals on Falstad's Analog simulator site, then it prompted me to increase the BW (or sampling rate as Falstad Sim only has a small buffer for browser simulation. But after, If I reduce the sampling rate 3 orders of magnitude from 3.125 ns to ms, I see the interference pattern as baseband. Only one signal had a 0.254 Hz offset . You can expect up to N multiples of the resolution with N signal sources.

This is the way old sub-sampling GHz scopes would work with fast capture but slow sampling rate.

Does that describe your capture?

sim https://tinyurl.com/2apq4qnq

 

[Firaconsortium]

Low-frequency modulation in DDS-generated signals often arises from DDS resolution limits, amplifier nonlinearity, or measurement artifacts like oscilloscope undersampling. Verifying with a spectrum analyzer and adjusting DDS settings can help. Using a linear amplifier or phase dithering may reduce intermodulation distortion (IMD), especially in precision applications like laser systems