Absurdly high Frequency resolution of function generators?

[I_am_learning]

I checked some common commercial high-quality lab function generators and they seem to provide frequency output upto 50 Mhz (not a big deal), but with resolution of 1 uHz ! That means, they can generate signal with 50000000 Hz and also with 50000000.000001 Hz ?? That would equate to time-period difference of 4.00355*10^-22 seconds between those two signals! How can they possibly generate pulses with that high of time-resolution?

Any idea?

 

[meBigGuy]

I've seen jitter on the pulses but the long term average is as they say. They use DDS techniques which cannot be more edge accurate than the source frequency. For sine waves they filter the output so the jitter is not apparent, but it's there on square waves.

I was pretty disappointed.

Check out http://en.wikipedia.org/wiki/Direct_digital_synthesizer

 

[I_am_learning]

Ok, does that mean, the I am getting the 1uHz resolution only on-average, but pulse-to-pulse frequency can vary by several Khz (with the average frequency = desired 1uHz resolution frequency) ?
I am new to this DDS technique; this is the first time I am hearing about it.

 

[Baluncore]

Most DDS synthesisers have an internal local oscillator at above 300MHz that can be locked to an external local reference. That external reference is locked to GPS or some local master such as a hydrogen maser.

Clocking a DDS at 300MHz gives an output edge resolution of 3.33nsec. That will be the maximum possible jitter in a raw DDS square wave output.

But the DDS does not necessarily generate square waves directly, the accumulated DDS phase angle is used to look up a sine function table, so the output DAC generates a stepped approximation to a sine wave. The noisy sine wave is filtered to remove DDS clock noise, then low pass filtered to remove noise above the output frequency. The resulting sine wave then has a much lower phase noise. If the purified sine wave is then fed to a digital comparator the jitter in the resultant square wave is greatly reduced below the raw DDS most significant bit output.

There are applications where phase errors accumulate and cause problems. For example VLBI data acquisition requires a known timebase as errors in time will make correlation difficult to track and so blur the image. It may take 11.6 days to accumulate a full cycle of 1uHz error, but that is critical over a period of 12 hours if more than a 15° phase error would become a problem.

The 1uHz frequency resolution is not “absurdly high” when it is actually needed. Maybe you just don't need it yet.

 

[I_am_learning]

meBigGuy and Baluncore,
Thanks for your replies and explanation,

Clocking a DDS at 300MHz gives an output edge resolution of 3.33nsec. That will be the maximum possible jitter in a raw DDS square wave output.
But the DDS does not necessarily generate square waves directly, the accumulated DDS phase angle is used to look up a sine function table, so the output DAC generates a stepped approximation to a sine wave. The noisy sine wave is filtered to remove DDS clock noise, then low pass filtered to remove noise above the output frequency. The resulting sine wave then has a much lower phase noise. If the purified sine wave is then fed to a digital comparator the jitter in the resultant square wave is greatly reduced below the raw DDS most significant bit output.

The Function Generator I am using (Rigol DG4162) has sampling frequency of 500Mhz and can generate upto 50Mhz square wave.

So, for example if I am generating an 50MHz square wave, you are saying that, the Generator first creates stepped 50 MHz sine wave (it must use 10-points to create the sine-wave, right? since the DDS clock frequency is 500Mhz). Oh, so, by using different values for the sine-wave, you can place the +ve and -ve half at different places. Aaha!

In the above figure, while creating the sine wave, each point is still created 1/500Mhz apart (since that's the max clock cycle of DDS), but by varying the Magnitude, we can create sinusoids (and hence square waves) of fine-tuned frequency.
So, does that mean, the frequency resolution is affected by the vertical resolution (i.e. how fine is you voltage levels)?
Also, its interesting that they allow upto 160 Mhz for sinusoids, but only upto 50Mhz for square waves? What might be the reason? If you can create sinusoid with 160 MHz, then just past it through a comparator and you have square wave with same res, no? Maybe because of the limitation of the comparator

The 1uHz frequency resolution is not “absurdly high” when it is actually needed. Maybe you just don't need it yet.

I knew they have it there for a reason :) ; I was just fascinated that you could achieve that high of a resolution.
I am digressing, but I think Time is the only physical quantity that can be measured with super-high resolution; from years to pico-seconds. What instrument can, let's say, measure Length , or mass with that much resolution? Isn't that interesting? :)

 

[Baluncore]

A DDS has an accumulator for phase angle, that indexes the sine wave table.
The frequency resolution is determined by the number of bits in that accumulator.

A 500MHz clock with 1uHz resolution requires a Log2(500e12) = 49 bits.
Probably only the 16 most significant bits will be used to index the sine table. The lesser significant bits keep track of the long term phase.

Frequency is only as good as the reference. That will be 8 digits for a compensated crystal oscillator, many more digits for GPS locked atomic standards.

 

[meBigGuy]

Assume as baluncore said, that a 49 bit accumulator is used to generate the signal. Say we want a square wave at 15.625 Mhz and for simplicity the MSB is the squarewave output.

At 500Mhz we need to toggle the MSB every 16 clocks. So we do that by adding 16 == 2^4 so we need to add 1x2^45 to the accumulator. So what frequency do we get if we add 1x2**45 plus 1. Most of the time the MSB will toggle every 16 clocks, but once in a while it will toggle after 17 clocks. The long term average is slightly below 15.625MHz (I'm too lazy to do the math).

You can now connect a memory to to top X bits and use that to drive a DAC for the desired waveform. Adding 2**45 was just a simplified example.