I. Introduction
For better suppression of phase noise of voltage-controlled oscillator (VCO), the bandwidth (BW) of phase-locked loop (PLL) is desired as wide as possible. However, the BW of PLL is usually designed to be much smaller than its reference clock frequency to ensure stability and avoid unacceptably large reference spur [1]–[5]. In [1] and [2], a type-I PLL shows ~/2 BW while avoiding large reference spur by employing sampling loop filter (SLF). The type-I architecture, however, necessitates additional frequency acquisition circuit. In [3], a type-II PLL is allowed to have BW larger than /10 by employing SLF to isolate the instants when phase error is detected from the instants and the VCO frequency is updated. Because the frequency of phase error sampling and correction is still the same as that of the reference clock, there exists a limitation in increasing the BW of PLL.