as hold-in range, pull-in range, and pull-out range. Figure 5-4 illustrates these frequency ranges. Hold-in range Pull-in range Figure 5-4 Frequency Ranges of PLL Operations These frequency ranges are always quoted relative to the free-running frequency of the VCO (fo) and are specified in parts per million (ppm) or parts per billion (ppb). Because these are ranges, there needs to be both minimum and maximum values. If not explicitly specified, the range is inter- preted as including everything between the positive and negative values of the specified number. For example, if the range is specified as 4.6 ppm (or +4.6 X 10-6, the range is assumed to cover a range between -4.6 ppm and +4.6 ppm around fo. As per ITU-T G.810, the definitions of these frequency regions are as follows: Hold-in range: "The largest offset between a slave clock's input signal and the nominal (nat- ural) frequency of its VCO, within which the slave clock maintains lock as the frequency varies arbitrarily slowly over the frequency range." This is the range of difference between the nominal frequency and input frequency for which the PLL can steadily maintain phase tracking while in a steady (or locked) state. If the fre- quency of the input reference is slowly reduced or increased within the range, the PLL can still track it. The edge of the hold-in range is the point at which the PLL will lose the locked state. Pull-in range: "The largest offset between a slave clock's input signal and the nominal (natural) frequency of its VCO, within which the slave clock will achieve locked mode." This is the range of difference between the nominal frequency and the input frequency for which the PLL will always become locked throughout an acquisition (or tracking) process. Note that during this acquisition process there might be more than one cycle slip, but the PLL will always lock to the input signal. This is the range of frequencies within which a PLL can trans- ition from the transient state to steady (locked) state. Pull-out range: "The offset betw