TLC2932_15 Datasheet, PDF (18/29 Pages) Texas Instruments – HIGH-PERFORMANCE PHASE-LOCKED LOOP

TLC2932
HIGH-PERFORMANCE PHASE-LOCKED LOOP
SLAS097E – SEPTEMBER 1994 – REVISED MAY 1997
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
@ ^{@ ȧȧȧȱȲ} _{ƪ @ @@ @} ^{ȳȧȧ + ) F2(s)}
Kp KV
@ ^ƫ @ _ȴȧ ^{F1(s) N (T1 T2)}
) s2 s
)1 s T2
) ₎ ) ₎ 1
Kp KV T2
N (T1 T2)
Kp KV
N (T1 T2)
(1)
and the transfer function for frequency is
@ ^ȧȧȱ _@ ^{ȳȧ FOUT(s) Kp KV}
ȧȲ _{@ƪ @@} @ _{Æ« @} @ _ȴȧȧ ^{+ )} ₎ ^FREF(s)
(T1
T2)
s2
s
)1 s T2
) ₎ ) ₎ 1
Kp KV T2
N (T1 T2)
Kp KV
N (T1 T2)
(2)
The standard two-pole denominator is D = s² + 2 ζ ω_n s + ω_n2 and comparing the coefficients of the denominator
of equation 1 and 2 with the standard two-pole denominator gives the following results.
w + ^{Ǹ @Kp KV}
@ ^{) n}
N (T1 T2)
Solving for T1 + T2
) + _@@w T1
T2
Kp KV
N
2
n
(3)
+ _@ ǒ ) _@ Ǔ ^{and by using this value for T1 + T2 in equation 3 the damping factor is}
z
w_n
2
T2
N
Kp KV
solving for T2
+ _@ T2 ²_wz – _Kp ^N _KV
then by substituting for T2 in equation 3
+ _@@ ) _@ T1
KV
N
Kp
w_n²
–
2_wnz
N
Kp KV
18
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