5.4.1 Transfer Function in Analog PLLs

The first-order loop has some drawbacks. If the PLL lowpass characteristic should suppress noise in the input signal, it is necessary to reduce the loop gain and to lower the cutoff frequency. However, the loop gain must be high to improve the response speed and the frequency synchronization range. These two requirements conflict and it is difficult to satisfy both at the same time in the first-order loop. Moreover, the first-order loop also generates a significant steady-state phase error if the input differs from the free-running frequency of the controlled oscillator. A filter circuit between the phase comparator and the controlled oscillator improves the situation. Three filter types are used (see Figure 5.14): the lag filter, the lag-lead filter, and the complete integral filter. The lag filter can be considered as a variant of the lag-lead filter. The lag-lead filter is a passive filter, while the complete integral filter is an active filter. Transfer functions for the passive and active filters are given by (5.33) and (5.34), respectively.

Figure 5.14: Analog filters used in PLLs: (a) passive filter and (b) active filter.

where ? ₁ = R ₁ C, ? ₂ = R ₂ C.

where ? ₁ = R ₁ C, ? ₂ = R ₂ C, and the amplifier gain is assumed to be infinite.

Magnitude plots of these transfer functions are shown in Figure...