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I assume the reader is aware of how a DPLL works.

  • The DPLL oscillates with a frequency of \$F_{out}\$.
  • The DCO free running frequency is \$F_{free}\$.
  • In the model of our DPLL we've only considered the TDC quantization noise.
  • The instantaneous frequency deviation is given, which is the change from \$F_{free}\$ to any frequency we want it to lock onto, say \$F_{out}\$. The following plot shows a 1MHz change until it locks:

enter image description here

where CKR with the average frequency \$F_R\$ is the retimed clock used to synchronize the internal DPLL operations. The index k represents the kth occurrence of the CKR's rising edge. Let's say that this curve is stored in a vector called ifd, which has a length of k, obviously.

Now given the frequency deviation I'm not sure as to how I could find the power spectral density of the output phase noise, which is mainly due to the TDC quantization with a limited resolution.

I understand that the phase is the time integral of the frequency multiplied by 2\$\pi\$, or \$\phi=2\pi\int{ifd \ dt}\$. We know ifd so we know \$\phi\$ by integration. Now in the context of MATLAB language the PSD is obtained

phi=2*pi*cumsum(ifd)/FR;
pn=f(phi);
% PSD
fs=10*FR;
[pxx,f]=pwelch(pn,[],[],[],fs,'onesided');
XdB=10*log10(pxx);

I'm actually stuck at the second line, where I don't know what f should be. Does anyone know what I should replace f with? Is that simply a sin function or something more complex than that?

Thanks for your attention,

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  • \$\begingroup\$ I recall the phase in an FM system is deltaF/Fmodulation. Here you have a discretized FM system. \$\endgroup\$ – analogsystemsrf Jul 21 at 1:58

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