TLC2932

HIGH-PERFORMANCE PHASE-LOCKED LOOP

SLAS097E – SEPTEMBER 1994 – REVISED MAY 1997

18

POST OFFICE BOX 655303

APPLICATION INFORMATION

Using the low-pass filter in Figure 25(b) and divider ratio N, the transfer function for phase and frequency are

shown in equations 1 and 2. Note that the transfer function for phase differs from the transfer function for

frequency by only the divider value N. The difference arises from the fact that the feedback for phase is unity

while the feedback for frequency is 1/N.

Hence, transfer function of Figure 24 (a) for phase is

F2(s)

F1(s) +

Kp

N

1

) s

s2

) s 1 )

Kp

N

)

Kp

V

N

(1)

and the transfer function for frequency is

F

OUT(s)

F

REF(s)

+

Kp

(T1

) T2)

1

) s

s2

) s

Kp

V

N

)

Kp

N

(2)

of equation 1 and 2 with the standard two-pole denominator gives the following results.

wn +

Kp

N

Solving for T1 + T2

T1

) T2 +

Kp

N

n

(3)

and by using this value for T1 + T2 in equation 3 the damping factor is

z +

wn

T2

)

N

Kp

V

solving for T2

T2

+

2

z

w –

N

Kp

V

then by substituting for T2 in equation 3

T1

+

K

V

N

n

–

2

z

w

n

)

N

Kp

V