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.
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WW .100Y.C M.TW
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SLAS136B − APRIL 1996 − REVISED JANUARY 2002
W
WW .100Y.C M.TW
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.
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1
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WW .100Y.C M.TW
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WW .100Y.C M.TW
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WW .100Y.C M.TW
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WW
WW .100Y.C M.TW
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WW .100Y.C M.TW
O
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Y.C
0
WW POST
0
5
W.1 OFFICE BOX 655303 • DALLAS, TEXAS 75265
W
W
W
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W
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WW .100Y.C M.TW
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SLAS136B − APRIL 1996 − REVISED JANUARY 2002
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WW .100Y.C M.TW
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W
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.
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W.1 Y.COM W
W
W
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W.1 Y.COM W
W
W
W
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W
00
W
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O
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WTEST CONDITIONS
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W
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WW .100Y
.100
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WW 00Y.CO
WPOST
6
OFFICE
W.1 BOX 655303 • DALLAS, TEXAS 75265
WW
W
M.T
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.
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WW .100Y.C M.TW
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SLAS136B − APRIL 1996 − REVISED JANUARY 2002
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WW .100Y.C M.TW
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.100OFFICE BOX 655303 • DALLAS, TEXAS 75265
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f osc − VCO Oscillation Frequency − MHz
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12
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WW POST
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13
W.1 OFFICE BOX 655303 • DALLAS, TEXAS 75265
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M.T
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WW .100Y.C M.TW
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SLAS136B − APRIL 1996 − REVISED JANUARY 2002
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WW .100Y.C M.TW
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WW 00Y.CO
WPOST
14
OFFICE
W.1 BOX 655303 • DALLAS, TEXAS 75265
WW
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M.T
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.
W
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M.T
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WW .100Y.C M.TW
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SLAS136B − APRIL 1996 − REVISED JANUARY 2002
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WW .100Y.C M.TW
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M
.
.TW
M
O
W
M
O
W the feedback for phase is unity
byWonly
The difference
that
WWthe divider
.CO .Tfrequency
0Y.Cthe fact
WWarises
.T
W
0from
0Y.CN value.
.TW
1
0
M
.
1
00Y
M
.
O
1
W
M
.
while the feedbackW
for frequency
O is 1/N.
WW .100Y.C M.TW
WW 00Y.CO .TW
WW .100Y.C M.TW
O
1
O 17(a) for phase isWW
function of.C
Figure
OM Hence, the transfer
W.
W
Y.C
WW
C
W
.
0
Y
W
W
W
0
0
Y
W
T
.
W
M.T
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10
00
M
.
O
1
W
M
.
O
W
C
O
W
Y.C
WW .100Y.
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WW .100ȱ
.TW
WW .100Y.C M.TW
M
M
O
W
O
O
W
W
Y.C ȧ .TW
WW
KW
W
0Y.C M.TW 1 ) s @WT2
p @ K V .10ȧ
F2(s)
100
WW .100Y.C M.T
M
.
W
(4)
W ) ȧ Y.CO
.COȧ .TW
O F1(s) + N (T1W
W
W
Y
C
W
.
0
W
W
)
T2
W
0@K ȧ M
0
Y
@ W
TKp@K @T2
.
K
1
0
0
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T
.
.
1
0
p
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M
.
O
1
V
V
W
W s2 Y
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OM
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W.
)
).CsO 1 ) W
00Y ȴ M.TW
(T1)T2)
WW Ȳ
.TN@(T1)T2) W N@
1
00
WW .100Y.C M.TW
.
1
M
.
O
W
O
W
O
W
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
W
andOthe transfer function for
frequency isO
W
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
WW .1ȳ00Y.C M.TW
ȱWWWW.100Y.COOM.TW
WW .100Y.C M.TW
O
W
W
W
Y.C
W
.CO .TW
0
Y.C
WW ȧ
K p @ K ȧWW
0
0
T
.
1
0
WW .100FYOUT(s)
M.T
.
1
V
1O
)M
s @ T2
.
O
W
M
W
C
+
(5)
.
O
W
WKW ȧ.100Y
(T
T1
.TW
W) T2) ȧ WW .100YK.Cp@KM@.TT2W
Y.C
K
WW .10F0REF(s)
M
.
@
p
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ȧ
O
V W
W 1 ) Y.CO V
OM
W
s@
W) N@(T1)T2)
WW .100Y.C M.TW
0
W
T
N
(T1)T2)
.
0
WW .100Y.C M.TW
@
1
Ȳ
ȴW
O
OM
W.
O
W
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
2
The standard
denominator isWDW
= s2 + 2Yζ.CωO
the coefficients
WW
W
Y.C of .the
n s + ωT
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.CO2-pole
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W
TWdenominator
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0
0
Y
W
.
1
0
0
WW of equation
T
M
.
.
1
0
M
.
(4)
and
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with
the
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gives
the
following
results.
O
1
W
O
W
OM
W.
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
W
(6)
@ KV
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .1w0n0Y
+
O
W
M
O
W
ON @ (T1 ) T2)
W
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
O
W for T1 + T2
Solving
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
OK
WW 00Y.CO .TW
W
WW 00Y.CO .TW
C
K
.
W
W
W
Y
@
W
p
W T1.)
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100T2 + OM.TV
W.1 Y.COM W
OM
W
W
W
C
.
2
W
C
W
Y
W
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00
W
WW .100Y. N @Mw.nTW
M.T
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W.1 Y.COM W
O
W
O
W
W
C
.
W
Y
W
W
.T
00
Y.C
W (6) .the
.TW is
.TW
100damping
and W
by using .this
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Mfactor
100 valueOfor
W.1 Y.COM W
MT1
O
W
W
W
C
.
W
W
.T
WW .100Y
WW .100Y.C M.TW
.100
M.T
OM
W
O
W
C
.
O
w
W
W
C
Y
NW
.C
W
.TW
WW .100Y.
.TW
WzW+ 2n.1@
T
M(7)
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00YT2 ) KM.@
M
O
W
K
O
W
C
.
O
p
W
W
V
WW .100Y
WW .100Y.C M.TW
WW .100Y.C M.TW
M.T
O
W
O
W
C
solving forWT2
WW .100Y.
WW 00Y.CO .TW
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WW .100Y.C M.TW
M
O
1
W
M
.
O
W
O
2W
z
WW .100Y.C (8)M.TW
W
WW .100Y.C M.TW
0Y.C M.TW
T2 W
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O
W
O
W
WKp @ K O
WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100YV.C M.TW
O
WW 00Y.CO .TW
Wfor T2 in
WW 00Y.CO .TW
then by substituting
equation
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C
.
W
W
W
Y
W
W
M
.1
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00
M
.1
K @ KW
WW 00Y.CO .TW
p .1 2 z .COM
WW 00Y.CO .TW
N
W
W
W
Y
W
T1 + V
–
)
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.T
00
W.1 Y.COM W
N @ w n2W.1w n .KCpO@MK V
WW 00Y.CO .TW
W
W
W
W
0
W
.T
0
W
M
.1
.T
00Y
W.1 Y.COM W
WW 00Y.CO
W.1 Y.COM W
W
W
W
W
.T
00
W
.1
.T
00
W.1 Y.COM W
WW
W.1 Y.COM W
W
W
W
W
.T
W
.100
M.T
.100
OM
W
O
W
C
.
W
C
W
Y
W
W
WW .100Y.
M.T
.100
M.T
O
W
O
W
C
.
W
Y
W
WW .100Y.C M.TW
.100
W
O
W
WW
WW .100Y.C M.TW
O
W
WW .100Y.C M.TW
O
W
Y.C
0
WW POST
0
15
W.1 OFFICE BOX 655303 • DALLAS, TEXAS 75265
W
W
ƪ
ƪ
Ǹ
ǒ
Ǔ
ƫ
ƫ
W
M.T
O
C
W
Y.
M.T
.100
O
W
WW .100Y.C M.TW
O
W
SLAS136B − APRIL 1996 − REVISED JANUARY 2002
W
WW .100Y.C M.TW
T
.
OM
WW 00Y.CO .TW
W
Y.C
WINFORMATION
0
T
APPLICATION
.
0
W.1 Y.COM W
W.1 Y.COM W
W
W
W
.T
W
.T
100
00 the M
From the circuit constants
OM
W.then
Oinitial design parameters
W.1 and
C
.
W
C
.
Y
W
W
.TW
W
.TW
100
00Y
M
.
.TW
1
M
.
O
W
M
O
z WW N 0Y.C1
.CO .TWR2 + 2W
WW .100Y.C M.TW
.TW
0
*
1
00Y
M
.
(10)
O
1
W
w
M
.
KW K
C1O
n W
WW .100Y.C M.TW
WW 00Y.CO .TW
W p @.10V0Y.C M.TW
WW 00Y.CO .TW
W.1 Y.COM W
WW 00Y.CO .TW
W
W
W
W
M
.1
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00
M
.1
WW 00Y.CO .TW
2z
W.1 Y.COM W ȱKp @ KvWW
.C
NO ȳ T
1W
Y
W
W
0
W
R1
+
*
)
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ȧ .C1
M
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(11)
00
w 10
WW 00Y.CO .TW
W.1 Y.COM WȲw n 2 @ N WWn. K0pY@.CKOVM
ȴ
W
W
W
W
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0
W
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00
W.1 Y.COM W
W.1 Y.COM W
OM
W
W.1 Y
W
C
.
W
W
allow
W chosen
.1T µF and 0.1 µF to W
W
M.T resistor values and
.100for reasonable
.TW C1, is usually
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00 The capacitor,
M
.
O
1
M
.
O
W
C
.
O
W
W
physical capacitor size.
W
Y
W
WW .100Y.C M.TW
WW .100Y.C M.TW
M.T
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O
W
O
W
C
O
W
W
WW .100Y.
WW .100Y.C M.TW
WW .100Y.C M.TW
M.T
O
W
O
W
O
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
O
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
O
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WW .100Y.C M.TW
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WW 00Y.CO .TW
W
WW 00Y.CO .TW
C
.
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WW 00Y.CO .TW
W
W
W
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M
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W.1 Y.COM W
W
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W.1 Y.COM W
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O
W
W
W
C
.
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W
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WW .100Y
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W.1 Y.COM W
M.T
OM
W
O
W
W
C
.
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C
W
Y
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00
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WW .100Y.
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W.1 Y.COM W
M.T
O
W
O
W
W
C
.
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W
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WW .100Y
WW .100Y.C M.TW
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M.T
OM
W
O
W
C
.
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C
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WW .100Y.
WW .100Y.C M.TW
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O
W
O
W
C
.
O
W
W
W
Y
W
WW .100Y.C M.TW
WW .100Y.C M.TW
M.T
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O
W
O
W
C
O
W
W
WW .100Y.
WW .100Y.C M.TW
WW .100Y.C M.TW
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W
O
W
C
O
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WW .100Y.
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WW .100Y.C M.TW
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O
W
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WW .100Y.C M.TW
WW .100Y.C M.TW
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W
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WW .100Y.C M.TW
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WW 00Y.CO .TW
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WW 00Y.CO .TW
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.
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WW 00Y.CO .TW
W
W
W
W
M
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WW 00Y.CO .TW
W.1 Y.COM W
W
W
W
W
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00
W
M
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00
W.1 Y.COM W
WW 00Y.CO .TW
W.1 Y.COM W
W
W
W
W
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00
W
W.1 Y.COM W
M.T
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W.1 Y.COM W
O
W
W
W
C
.
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W
00
W
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WW .100Y
.100
W.1 Y.COM W
M.T
OM
W
O
W
W
C
.
W
C
W
Y
W
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W
00
W
WW .100Y.
M.T
.100
W.1 Y.COM W
M.T
O
W
O
W
W
C
.
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WW .100Y
WW .100Y.C M.TW
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M.T
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W
O
W
C
.
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C
Y
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WW .100Y.
WW .100Y.C M.TW
.100
M.T
W
O
W
O
W
W
W
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
WW .100Y.C M.TW
WW .100Y.C M.TW
O
W
O
W
WW .100Y.C
WW .100Y.C M.TW
W
O
W
WW
WW .100Y.C M.TW
O
W
WW .100Y.C M.TW
WW 00Y.CO
WPOST
16
OFFICE
W.1 BOX 655303 • DALLAS, TEXAS 75265
WW
ƪ
ƫ
Normalized Gain Response
W
M.T
O
C
.
W
00Y
M.T
.1
O
W
WW .100Y.C M.TW
O
W
SLAS136B − APRIL 1996 − REVISED JANUARY 2002
W
WW .100Y.C M.TW
T
.
M
O
W
O
C
.
W
W
Y
W
Y.C
W INFORMATION
M.T
.100
M.T APPLICATION
.100
O
W
O
W
C
.
W
W
W
Y.C
WW .100Y
M.T
1.9 W
M.T
.100
O
W
O
W
C
WW .100Y.
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WW .100Y.C M.TW
M
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O
W
M
O
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WW .100Y.C M.TW
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1
00Y
M
.
O
1
W
M
.
O
W
z = 0.1
WW .100Y.C M.TW
WW 00Y.CO .TW
WW .100Y.C M.TW
O
W
W.1 Y.COM W 1.7
W
Y.C
WW 00Y.CO .TW z = 0.2 WW
0
W
0
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W
M.T
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1
00
M
.
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1
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.
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C
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WW .100Y.
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WW .100Y.C M.TW
WW .100Y.C M.TW1.6
M
O
W
O
W
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WW .100Y.C M.TWz = 0.3 W
100
WW .100Y.C M.TW
M
.
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1.5
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
=
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WW 00Y.CO .TW
W
WW 00Y.CO .TW
C
.
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T
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W
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C
.
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C
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00
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WW .100Y.C M.T
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WW .100Y
WW .100Y.C M.TW
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WW .100Y.
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WW .100Y.C M.TW
WW .100Y.C1 M.TW
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WW .100Y.C M.TW
WW .100Y.C M.TW
O
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .1000.9Y.C M.TW
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W.1 Y.COM W
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WW .100Y.
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WW .100Y.C M.TW
WW .100Y.C M.TW
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WW .100Y.C M.TW
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1
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WW .100Y.C M.TW
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WW .100Y.C M.TW
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0.3
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WW 00Y.CO .TW
W
W
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W
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WW 00Y.CO .TW
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0.2 WW
W
M
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WW 00Y.CO .TW
W.1 Y.COM W
W
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W
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M
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WW 00Y.CO .TW
W.1 Y.COM W
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W
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W.1 Y.COM W
M.T
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C
.
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WW .100Y
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3 OM
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11
12 WW
13
.
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.
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WW .100Y.
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WW .100Y.C M.TW
WW .100Y.C M.TW
WW .100Y.C M.TW
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Step Response
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WFigure 18.OType 1 Second-Order
WW .100Y.C
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WW .100Y.C M.TW
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WW
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WW 00Y.CO .TW
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.
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