TLC2942 Datasheet, PDF (23/28 Pages) Texas Instruments – HIGH-PERFORMANCE DUAL PHASE-LOCKED LOOP BUILDING BLOCK

TLC2942
HIGH-PERFORMANCE DUAL PHASE-LOCKED LOOP BUILDING BLOCK
SLAS146B – NOVEMBER 1996 – REVISED JUNE 1997
APPLICATION INFORMATION
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)
(6)
The standard two-pole denominator is D = s² + 2 ζ ω_n s + ω_n2 and comparing the coefficients of the denominator
of equation 5 and 6 with the standard two-pole denominator gives the following results:
+ ^Ǹ _@ ^@₎ w_n
Kp KV
N (T1 T2)
(7)
Solving for T1 + T2
@@ ^{) + T1}
T2
Kp KV
N w_n²
+ _@ ǒ ) _@ Ǔ ^{and by using this value for T1 + T2 in equation 7 the damping factor is:}
z
w_n
2
T2
N
Kp KV
(8)
solving for T2:
+ _@ T2
2z
w
–
Kp
N
KV
(9)
then by substituting for T2 in equation 7 and solving for T1 as given in equation 10:
@@ ^{@ + ) T1}
KV
N
Kp
w_n²
–
2z
w_n
N
Kp KV
(10)
From the circuit constants and the initial design parameters then:
ȧȱȲ ^@@ _@ ^{ȳȴȧ + * ) R1}
Kp Kv
w_n2 N
2z
w_n
N
1
Kp KV C1
ƪ _@ ƫ + * R2
2z
w_n
N
1
Kp KV C1
(11)
(12)
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