# PLL Loop Filter and its influence on speed

I was doing some research on Phase Locked Loops (PLLs). Now what I understand is, that the Loop Filter is first necessary to suppress unwanted signals on the VCO, so the tuning is controlled by the DC value of the Phase-Freqency-Detector (PFD). So the loop filter is a low pass filter and of course you want a low cutoff frequency $f_c$ for this reason.

Now to the second influence of the Loop Filter: If $f_c$ is low, the PLL will take longer to lock. But I don't understand this, how can the bandwidth determine the lock speed?

• Well, assume the loop filter was extremely slow. How long would it take the VCO output to change enough to match the input signal so that it can lock? – John D Aug 9 '17 at 21:32