Why does Costa's loop PLL bandwidth need to be narrow? Text books mention that and yet give no explanation
The main purpose of a phase synchronization system, whether Costas loop or a PLL, is to track the phase of an input signal. The bandwidth of a PLL determines whether the signal falls within the range it can track or suppress. If the signal can pass through and the bandwidth is narrow, less noise enters the system increasing the loop SNR, while a wider bandwidth allows more noise deteriorating the tracking performance. But do remember that the narrower the bandwidth, the longer the acquisition time due to the smaller variation injected by the PLL.