Page 103 - Phase-Locked Loops Design, Simulation, and Applications

MIXED-SIGNAL PLL ANALYSIS Ronald E. Best 69

Figure 3.11 Waveforms of the average phase detector output signal (upper trace) and
the scaled-down radian frequency ω ′ (lower trace) for the case where the radian
2
frequency offset Δω is identical with the lock range Δω .
L

It is easily seen now that the PLL acquires lock within one beat note when equals the
radian frequency offset Δω

(3.64)

Under this condition, Δω is identical with the lock range Δω . Combining Eqs. (3.63) and
L
(3.64), we obtain the nonlinear equation.

Using the same substitutions as for the type 1 phase detector, we get the simplified
expression

(3.65)