User manual

page 28
Analog System Lab Kit PRO
experiment 3
The goal of the experiment is to understand the advantages and
disadvantages of using integrators or dierentiators as a building block in
solving
++
N
AGBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
sRC
sRC
Q
ss
sRC
GB
V
V
V
RC
VT
Tf
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
0
GB RC$
$
$
$
~
~
~
~
=
=
=
++
=
++
=
=
-
-
-
a
b
b
k
l
l
order dierential equations or building an
++
N
AGBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
sRC
sRC
Q
ss
sRC
GB
V
V
V
RC
VT
Tf
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
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GB RC$
$
$
$
~
~
~
~
=
=
=
++
=
++
=
=
-
-
-
a
b
b
k
l
l
order lter.
Integratorsand dierentiators can be used as a building block for lters. Filters
form the essential block in analog signal processing to improve signal to noise
ratio.AnOP-Amp can be used toconstructanintegratorora dierentiator.This
experiment is to understand the advantage of integrators as building blocks instead
ofdierentiators.Dierentiatorsarerejectedbecauseoftheirpoorhigh-frequency
noise response.
AdierentiatorcircuitthatusesanOP-AmpisshowninFigure3.2.
FixtheRCtimeconstantoftheintegratorordierentiatorsothatthephaseshift
andmagnitudevariationoftheidealblockremainsunaectedbytheactivedevice
parameters.
Transient Response - Apply the step input and square wave input to the
integrator and study the output response. Apply the triangular and square
inputtothedierentiatorandstudytheoutputresponse.
Frequency Response - Apply the sine wave input and study the phase error
andmagnitudeerrorforintegratoranddierentiator.
An integrator circuit that uses an OP-Amp is shown in Figure 3.1.
Assuming
++
N
AGBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
sRC
sRC
Q
ss
sRC
GB
V
V
V
RC
VT
Tf
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
0
GB RC$
$
$
$
~
~
~
~
=
=
=
++
=
++
=
=
-
-
-
a
b
b
k
l
l
,
3.1 Brief theory and motivation
3.1.1 Integrators
3.1.2Dierentiators
3.2Specications
3.3 Measurements to be taken
Goal of the experiment
+ +
N
A GBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
s RC
sRC
Q
s s
sRC
GB
V
V
V
RC
V T
T f
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
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GB RC$
$
$
$
~
~
~
~
=
=
=
+ +
=
+ +
=
=
-
-
-
a
b
b
k
l
l
+ +
N
A GBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
s RC
sRC
Q
s s
sRC
GB
V
V
V
RC
V T
T f
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
0
GB RC$
$
$
$
~
~
~
~
=
=
=
+ +
=
+ +
=
=
-
-
-
a
b
b
k
l
l
C
R
V
I
VO = -VI/SCR
Figure 3.1: Integrator
Figure 3.2: Dierentiator
The output goes to saturation in practice. For making it work a high valued resistance
across
++
N
AGBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
sRC
sRC
Q
ss
sRC
GB
V
V
V
RC
VT
Tf
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
0
GB RC$
$
$
$
~
~
~
~
=
=
=
++
=
++
=
=
-
-
-
a
b
b
k
l
l
must be added in order to bring the OP-Amp to the active region where it
can act as an integrator.
(3.1)
(3.2)
Theoutputofthedierentiatorremainsatinputoset(approximately0).However,
any sudden disturbance at the input causes it to ring at natural frequency
++
N
AGBs
V
V
GB
s
sCR
C
V
V
GB
s
GB
sRC
sRC
Q
ss
sRC
GB
V
V
V
RC
VT
Tf
f
1
1
1
1
1
2
1
th
i
i
pp
p
pp
p
0
0
2
0
0
2
2
0
GB RC$
$
$
$
~
~
~
~
=
=
=
++
=
++
=
=
-
-
-
a
b
b
k
l
l
.
C
R
VI
VO = -SCRVI
1
2