Page 160 - Phase-Locked Loops Design, Simulation, and Applications

PLL PERFORMANCE IN THE PRESENCE OF NOISE Ronald E. Best 99
where is the area under the curve in Fig. 4.4d. Making use of Eqs. (4.5) and
(4.6), we get

(4.7)

The integral is called noise bandwidth B ,
L

(4.8)

The solution of this integral reads 1

(4.9)

Thus, B is proportional to the natural frequency ω of the PLL; furthermore, it depends on
L n
the damping factor ζ. Fig. 4.5 is a plot of B versus ζ, and B has a minimum at ζ = 0.5. In this
L
L
case, we have

(4.10)