For anyone interested, here's the essence of a phase-locked loop:
Say you're climbing up a long staircase and the step height increases suddenly - then you'll bump into the next step. If the height were to go the other way i.e; decrease, then you'll put your foot down hard trying to place the next step. That change in step height is in fact a change in frequency, and you're forced to adjust your pace abruptly by adjusting the timing (phase) of your subsequent steps.
Is there a 'gentler' way to adjust the phase? Now say you're wearing some kind of spongy sandals that can take up the slack, so at every step you increasingly sense that the frequency has changed. This accumulation indicates that phase is mathematically the integral of instantaneous frequency with respect to time.
We now put this integral in a feedback loop. Then, if the staircase step height changes suddenly we use the slow accumulated phase to produce an error signal that gradually drives the frequency generator (in this case, our brain) to adjust the pace of our step till we get in lock-step.
The actual dynamics is more complicated, involving a non-linear frequency capture (which linearizes the system) and then the slower phase lock. You can see this in the waveforms in the original post.
Say you're climbing up a long staircase and the step height increases suddenly - then you'll bump into the next step. If the height were to go the other way i.e; decrease, then you'll put your foot down hard trying to place the next step. That change in step height is in fact a change in frequency, and you're forced to adjust your pace abruptly by adjusting the timing (phase) of your subsequent steps.
Is there a 'gentler' way to adjust the phase? Now say you're wearing some kind of spongy sandals that can take up the slack, so at every step you increasingly sense that the frequency has changed. This accumulation indicates that phase is mathematically the integral of instantaneous frequency with respect to time.
We now put this integral in a feedback loop. Then, if the staircase step height changes suddenly we use the slow accumulated phase to produce an error signal that gradually drives the frequency generator (in this case, our brain) to adjust the pace of our step till we get in lock-step.
The actual dynamics is more complicated, involving a non-linear frequency capture (which linearizes the system) and then the slower phase lock. You can see this in the waveforms in the original post.