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ML13176 View Datasheet(PDF) - LANSDALE Semiconductor Inc.

Part Name
Description
Manufacturer
ML13176
LANSDALE
LANSDALE Semiconductor Inc. LANSDALE
ML13176 Datasheet PDF : 16 Pages
1 2 3 4 5 6 7 8 9 10 Next Last
LANSDALE Semiconductor, Inc.
Legacy Applications Information
Figure 11. Block Diagram of ML1317x PLL
ML13175/ML13176
θi(s)
fi = f ref
Pins 9,8
Phase
Detector
Kp = 30 µA/rad
θe(s)
Low Pass
Filter
Pin 7
Kf
fn = fo/N
θn(s) = θo(s)/N
Pin 6
Divider
Kn = 1/N
N = 8 : ML13175
N = 32 : ML13176
Amplifier and
θo(s) Current Controlled
Oscillator
Ko = 0.91Mrad/sec/µA
Pins 13,14
fo = nfi
Where: Kp = Phase detector gain constant in
= µA/rad; Kp = 30 µA/rad
Kf = Filter transfer function
Kn = 1/N; N = 8 for the MC13175 and
Ko = 1/N; N = 32 for the MC13176
= CCO gain constant in rad/sec/µA
Ko = 9.1 x 105 rad/sec/µA
LOOP FILTERING
The fundamental loop characteristics, such as capture range,
loop bandwidth, lock–up time and transient response are con-
trolled externally by loop filtering.
The natural frequency (ωn) and damping factor (L ) are
important in the transient response to a step input of phase or
frequency. For a givenL and lock time wn can be determined
from the plot shown in Figure 12.
Figure 12. Type 2 Second Order Response
1.9
1.8
ζ = 0.1
1.7
1.6
0.2
1.5
1.4
0.3
1.3
0.4
1.2
0.5
1.1
0.6
1.0
0.7
0.8
0.9
1.0
0.8
0.7
1.5
2.0
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10 11 12 13
ωnt
For L = 0.707 and lock time = 1.0 ms;
then ω = 5.0/t = 5.0 krad/sec.
The loop filter may take the form of a simple low pass filter
or a lag–lead filter which creates an additional pole at origin
in the loop transfer function. This additional pole along with
that of the CCO provides two pure integrators (1/s2). In the
lag–lead low pass network shown in Figure 13, the values of
the low pass filtering parameters R1, R2 and C determine the
loop constants ωn and L. The equations t1=R1 C and t2=R2C
are related in the loop filter transfer functions F(s) = 1 +
t2s/1 + (t1 +t2)s.
Figure 13. Lag–Lead Low Pass Filter
Vin
R1
R2
VO
C
The closed loop transfer function takes the form of a 2nd
order low pass filter given by,
H(s )= KvF(s)/s + KvF(s)
From control theory, if the loop filter characteristic has F(0) =
1, the DC gain of the closed loop, Kv is defined as,
Kv = KpKoKn
and the transfer function has a natural frequency,
ωn = Kv/t1 + t2)1/2
and a dampning factor,
L = (ωn/2) (t2 + 1Kv)
Rewriting the above equations and solving for the ML13176
with L = 0.707 and ωn = 5.0 k rad/sec.
Kv = KpKoKn = (30) (0.91 X 106)(1/32) = 0.853 X 106
t1 + t2 = Kv/ωn2 = 0.853 X 106/(25 X 106) = 34.1 ms
t2 = 2L /ωn = (2)(0.707)/(5 X 103) = 0.283 ms
t1 = (Kv/ωn2) –t2=(34.1–0.283) = 33.8 ms
Page 7 of 16
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