Page 81 - Phase-Locked Loops Design, Simulation, and Applications

MIXED-SIGNAL PLL ANALYSIS Ronald E. Best 57

■ The damping factor ζ of the PLL corresponds to the damping factor ζ′ of the pendulum,
which results from viscous friction.
■ The weight G on the platform corresponds to a reference phase disturbance according to
the relation

(3.49)

Let’s now determine what the physical meaning of the term is in Eq.

(3.49). We first assume that the frequency of the reference signal has an arbitrary value:

where Δω(t) can be considered the frequency offset of the reference signal. The reference
signal u (t) can therefore be written in the form
1

Consequently, the phase θ (t) is given by
1

From this, it becomes immediately evident that the first derivative represents the
momentary frequency offset:

whereas the second derivative signifies the rate of change of the frequency offset:

The weight G placed on the platform is thus equivalent to a weighted sum of the frequency
offset Δω(t) and its rate of change

(3.50)