A frequency synthesizer includes a phase-locked loop (PLL) and a loop bandwidth controller. The PLL generates an output clock according to a reference clock. The loop bandwidth controller checks at least one indicator indicative of injection pulling/pushing of the PLL to configure a loop bandwidth of the PLL. In one exemplary design, the loop bandwidth controller sets the loop bandwidth of the PLL by controlling a configuration of a loop filter included in the PLL. For example, the PLL is an all-digital phase-locked loop (ADPLL), and the loop filter is a digital loop filter of the ADPLL.