# bandwidth and phase-locked loop

I've been told that phase-locked loop (PLL) increases the bandwidth and therefore makes the time constant smaller. ($\tau = 2Q/\omega_0$ and I understand $Q \propto 1/ \delta\omega_0$)

I heard this in the context of the detection of forces with tuning fork sensors here .

Could you given me an intuitive explanation as to why? The paper linked above explains it in terms of P and I constants but I wasn't able to understand it.

On page 22 (or page 30 of the pdf) here, it says the following "As explained in Refs. 54,56, a phase-locked loop (PLL) increases the bandwidth and makes scanning probe microscopy with tuning-forks possible at reasonable scan speeds."

I went to the references and from reference 54, I was able to understand that in general, without a PLL loop, high Q means a tiny bandwidth and that it takes a long time to complete a measurement round.

Reference 56 seems to explain why using a PLL loop does solve the extremely long measurement time issue but it was this explanation that I wasn't able to understand

• Per Gardner's book on PLLs, for loop stability the update rate needs to be AT LEAST 5X the loop bandwidth, and preferably 10X the loop bandwidth. Thus for GSM systems with 2.6MHz reference frequency (13MHz/5), the highest loop bandwidth would be (preferably) 0.26MHz. – analogsystemsrf Aug 17 '18 at 4:00
• My first response would be compared to what? – Sven B Aug 17 '18 at 14:30
• @SvenB I thought my question was generic but maybe it needed more context. I added the context and which part of the explanation I wasn't able to grasp – Blackwidow Aug 17 '18 at 15:07