Hello everyone.
The "Jitter" issue is normally over for modern DACs, and
I'm sure some will be annoyed that we're talking about "jitter" again.
I wanted to know the exact impact, so I created a few
scripts with "octave" to simulate the jitter.
I'll leave my conclusions here.
I have a topping D10S and a D50III that will serve as a basis for comparison.
It's mainly the D10S, which has relatively high jitter, that will be highlighted.
I'll be working mainly at 1 kHz; jitter doesn't only have an impact at 12 kHz.
Here's an example of what can be approximated by simulation:
Simulation Implementation ::
I used as a reference the excellent paper by "Julian Dunn"
mentioned by @Amir in his video on jitter.
"Julian Dunn paper"
What interests us are the equations on page (5) of the paper
by "Julian Dunn".
I use the first equation and replace (sin wjt) with noise.
Since I have no knowledge of the phase noise of the jitter, I successively approximated
the shape of the jitter by creating white noise that I filtered
with a first or second-degree low-pass Butterworth filter with a
fairly low cutoff frequency. I normalize the resulting noise to align with (sin wjt),
whose maximum amplitude is "1."
I add noise to this signal to align it with the noise before the measurement
frequency. (The noise can be created with Octave or Audacity.)
The shape of the jitter depends on the amplitude of the frequency at which it is being
observed, on "J," which has a particular impact on the amplitude of the jitter, and on the
noise bandwidth, which has an impact on the jitter width.
Here are 2 simulations on topping D10S and D50III
In the first simulation, we see that the noise of the D10S decreases after the
measurement frequency, let's see what happens when I don't add
floor noise to the jitter simulation.
The general shape of the spectrum is similar to that of the D10S.
We have a noise plateau before the measurement frequency and a
noise decline after the measurement frequency.
Without adding any noise to the simulation, the jitter adds noise to
the entire spectrum.
This last observation is not obvious; we would have to calculate the spectrum
of a phase modulation with noise as the modulating signal and with a carrier
also having its own noise. I'll leave you with
the Bessel equations if you're brave enough; we can't simulate all of this
with the "Julian Dunn" simulation equations.
I simulated a jitter with 4 frequencies as phase noise;
this is the general shape of the spectrum (without added noise).
Now let's look at the jitter when analyzing multiple frequencies.
Here are the shape and amplitude of the jitter across three frequencies
of the same amplitude on the D10S and the D50III.
We see that the shape, amplitude, and bandwidth are identical regardless of the frequency.
To simulate this, "J" must decrease as a function of frequency.
Attached is the simulation with 3 frequencies, without added noise:
In the simulation equation, we see that the jitter amplitude is
proportional to "Jwi", and it is "Jwi" that remains constant in the DAC.
This observation is not easy to explain.
Let's take each frequency and look at the noise in the simulation.
We see that the noise before the analysis frequency decreases,
let's see what happens with the D10S.
The noise also decreases with the measurement frequencies; the limit will certainly be thermal noise.
The simulation is quite close to reality on the D10S.
Conclusion:
When the jitter is significant enough, we see that it adds noise across
the entire spectrum. The lower the frequency, the higher the added noise.
The impact on THD+N will increase slightly as the frequency decreases.
The general pattern for high jitter is always a plateau noise before the
analysis frequency and a descending noise afterward,
of course, if the thermal noise is not high and does not mask the jitter noise.
Hoping for low noise with high jitter is an illusion; jitter will prevent you from doing so.
A perfect simulation of the jitter effect is not complete with the equations
proposed by Julian Dunn in his paper. If anyone has an idea to improve it,
I'll take it.
Example on ASR ::
PS : octave script attached
FFT measure : E1DA cosmos ADC + scaler
FFT view : DIY tools
The "Jitter" issue is normally over for modern DACs, and
I'm sure some will be annoyed that we're talking about "jitter" again.
I wanted to know the exact impact, so I created a few
scripts with "octave" to simulate the jitter.
I'll leave my conclusions here.
I have a topping D10S and a D50III that will serve as a basis for comparison.
It's mainly the D10S, which has relatively high jitter, that will be highlighted.
I'll be working mainly at 1 kHz; jitter doesn't only have an impact at 12 kHz.
Here's an example of what can be approximated by simulation:
Simulation Implementation ::
I used as a reference the excellent paper by "Julian Dunn"
mentioned by @Amir in his video on jitter.
"Julian Dunn paper"
What interests us are the equations on page (5) of the paper
by "Julian Dunn".
I use the first equation and replace (sin wjt) with noise.
Since I have no knowledge of the phase noise of the jitter, I successively approximated
the shape of the jitter by creating white noise that I filtered
with a first or second-degree low-pass Butterworth filter with a
fairly low cutoff frequency. I normalize the resulting noise to align with (sin wjt),
whose maximum amplitude is "1."
I add noise to this signal to align it with the noise before the measurement
frequency. (The noise can be created with Octave or Audacity.)
The shape of the jitter depends on the amplitude of the frequency at which it is being
observed, on "J," which has a particular impact on the amplitude of the jitter, and on the
noise bandwidth, which has an impact on the jitter width.
Here are 2 simulations on topping D10S and D50III
In the first simulation, we see that the noise of the D10S decreases after the
measurement frequency, let's see what happens when I don't add
floor noise to the jitter simulation.
The general shape of the spectrum is similar to that of the D10S.
We have a noise plateau before the measurement frequency and a
noise decline after the measurement frequency.
Without adding any noise to the simulation, the jitter adds noise to
the entire spectrum.
This last observation is not obvious; we would have to calculate the spectrum
of a phase modulation with noise as the modulating signal and with a carrier
also having its own noise. I'll leave you with
the Bessel equations if you're brave enough; we can't simulate all of this
with the "Julian Dunn" simulation equations.
I simulated a jitter with 4 frequencies as phase noise;
this is the general shape of the spectrum (without added noise).
Now let's look at the jitter when analyzing multiple frequencies.
Here are the shape and amplitude of the jitter across three frequencies
of the same amplitude on the D10S and the D50III.
We see that the shape, amplitude, and bandwidth are identical regardless of the frequency.
To simulate this, "J" must decrease as a function of frequency.
Attached is the simulation with 3 frequencies, without added noise:
In the simulation equation, we see that the jitter amplitude is
proportional to "Jwi", and it is "Jwi" that remains constant in the DAC.
This observation is not easy to explain.
Let's take each frequency and look at the noise in the simulation.
We see that the noise before the analysis frequency decreases,
let's see what happens with the D10S.
The noise also decreases with the measurement frequencies; the limit will certainly be thermal noise.
The simulation is quite close to reality on the D10S.
Conclusion:
When the jitter is significant enough, we see that it adds noise across
the entire spectrum. The lower the frequency, the higher the added noise.
The impact on THD+N will increase slightly as the frequency decreases.
The general pattern for high jitter is always a plateau noise before the
analysis frequency and a descending noise afterward,
of course, if the thermal noise is not high and does not mask the jitter noise.
Hoping for low noise with high jitter is an illusion; jitter will prevent you from doing so.
A perfect simulation of the jitter effect is not complete with the equations
proposed by Julian Dunn in his paper. If anyone has an idea to improve it,
I'll take it.
Example on ASR ::
PS : octave script attached
FFT measure : E1DA cosmos ADC + scaler
FFT view : DIY tools
