Apparently both frequency and phase are independent properties but what is the relation between frequency and phase in PLL?so that when one is locked ,other is also locked


no, frequency and phase are not independent quantities. phase is the integral of frequency. and in the VCO (or NCO) inside a PLL, there is an integrator. the frequency is proportional to the input of the VCO or NCO, but the phase (which is what goes into the phase discriminator) is the integral of that.

with feedback, a PLL is a servo-control mechanism. but because of the inherent integrator in the loop, the "controller" is either a PI or an I. not much of a D in that controller inside a PLL.

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  • $\begingroup$ Depends, if you add an secondary loop to lock the frequency (hybrid FLL-PLL), then techically it's almost like a PID. I guess it's mostly in power systems, not in communications, though $\endgroup$ – Ben Nov 5 '19 at 18:05
  • $\begingroup$ @Ben, you get the P and the I, but i still don't see where you get the D out of that. $\endgroup$ – robert bristow-johnson Nov 5 '19 at 18:07
  • $\begingroup$ you apply a gain to the frequency, and the frequency is the derivative of the phase. $\endgroup$ – Ben Nov 5 '19 at 18:10
  • $\begingroup$ but the processing block between the component proportional to frequency and phase is an integrator. there is no differentiator in that loop. there is a proportional path (if the VCO or NCO has a phase offset input besides the frequency input) and there is an integrated path (which is the frequency input to the NCO).. you would need a differentiator applied to the NCO phase input to get a D in there. $\endgroup$ – robert bristow-johnson Nov 5 '19 at 19:23
  • $\begingroup$ or the phase discriminator needs to be replaced by a hybrid frequency discriminator and phase discriminator. $\endgroup$ – robert bristow-johnson Nov 5 '19 at 19:28

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