From TCAS-2017: Design Methodology for Phase-Locked Loops Using Binary (Bang-Bang) Phase Detectors
\[\begin{align} H_{LP}(s) &= H_0 \dfrac{1}{1 + \dfrac{s}{\omega_0 Q} + \dfrac{s^2}{\omega_0^2}}\\ \mathrm{NBW}_{LP} &= \dfrac{\omega_0 Q}{4} (\mathrm{Hz}) \end{align}\] \[\begin{align} H_{BP}(s) &= H_{max} \dfrac{\dfrac{s}{\omega_0 Q}}{1 + \dfrac{s}{\omega_0 Q} + \dfrac{s^2}{\omega_0^2}}\\ \mathrm{NBW}_{BP} &= \dfrac{\omega_0}{4Q} (\mathrm{Hz}) \end{align}\]Proof
Using the result from book Theory of Servomechanisms
