For decreasing errors within an analog phase-locked loop, an all-digital phase-locked loop (ADPLL) with only digital components and digital operations is used. The ADPLL may also be used for direct frequency modulation (DFM). By modulating certain parameters within the ADPLL by following an all-pass frequency response, a loop gain of the ADPLL may be precisely modulated, and an available bandwidth of the ADPLL is also significantly broadened.