User manual

page 18
Analog System Lab Kit PRO
V2
V1
Vo= Ao [V1-V2]
+VSS
-VSS
experiment 1
The goal of this experiment is two-fold. In the rst part, we will understand
the application of negative feedback in designing ampliers. In the second
part, we will build an instrumentation amplier.
An OP-Amp [8]canbeusedinnegativefeedbackmodetobuildunitygainampliers,
non-invertingampliersandinvertingampliers.WhileanidealOP-Ampisassumed
tohaveinniteopen-loopgain and innitebandwidth,realOP-Ampshavenite
numbers for these parameters. Therefore, it is important to understand some
limitationsofrealOP-Amps,suchasniteGain-BandwidthProduct(
GB). Similarly,
theslewrateandsaturationlimitsofanoperationalamplierareequallyimportant.
Given an OP-amp, how do we measure these parameters?
1.1 Brief theory and motivation
1.1.1UnityGainAmplier
Figure 1.1: An ideal Dual-Input, Single-Output OP-Amp and its I-O characteristic
Figure 1.2:
A Unity Gain System
(1.1)
(1.2)
(1.3)
(1.4)
(1.5)
(1.6)
(1.7)
Sincethefrequencyandtransientresponseofanamplierareimpactedbythese
parameters, we can measure the parameters if we have the frequency and transient
responseoftheamplier;youcanobtaintheseresponsecharacteristicsbyapplying
sinusoidal and square wave inputs respectively. We invite the reader to view the
recorded lecture [16].
An OP-Amp can be considered as a Voltage Controlled Voltage Source (VCVS) with
the voltage gain tending towards innity. For nite output voltage, the input
voltage is practically zero. This is the basic theory of OP-Amp in the negative
feedbackconguration.Figure1.1showsadierential-input,single-ended-output
OP-Amp which uses dual supply
!Vss for biasing.
In the above equations, A
0
is the open-loop gain; forrealampliers,A
0
is in the
range 10
5
to 10
6
and hence V
1
c V
2
. A unity feedback circuit is shown in the Figure
1.2. It is easy to see that,
In OP-amps, closed loop gain A is frequency
dependent, as shown in the equation below, where
~~
()
1
1
1
VAVV
VV
A
V
V
V
A
A
V
V
as A
A
ss
A
T
A
AsAsAsA
sGBsAsGB
GB A
GB
T
sQs
Q
GB
A
GB
GB
Q
Q
V
VGB
Q
Q
dt
dV
V
1
1
1
11
1
1
1
1
1
1
1
1
1
2
1
2
1
114
2
0
2
2
s
s
dd
dddd
dd
d
d
d
d
p
p
p
0012
12
0
0
0
0
0
0
0
12
0
00102
2
012
02 2
01
2
0
2
2
02
0
0
0
0
""
$
$
$
$
3
1
2
1
~~~
~~
~
~~
~
~
~
~~
p
~
=
=
=
+
=
++
=
=
++ ++
=
+
=
=
=
=
=
~~
~
p
-
-
+
++
++
+
-
__
_
_
`
_
ii
i
i
j
i
and
~~
()
1
1
1
VAVV
VV
A
V
V
V
A
A
V
V
as A
A
ss
A
T
A
AsAsAsA
sGBsAsGB
GB A
GB
T
sQs
Q
GB
A
GB
GB
Q
Q
V
VGB
Q
Q
dt
dV
V
1
1
1
11
1
1
1
1
1
1
1
1
1
2
1
2
1
114
2
0
2
2
s
s
dd
dddd
dd
d
d
d
d
p
p
p
0012
12
0
0
0
0
0
0
0
12
0
00102
2
012
02 2
01
2
0
2
2
02
0
0
0
0
""
$
$
$
$
3
1
2
1
~~~
~~
~
~~
~
~
~
~~
p
~
=
=
=
+
=
++
=
=
++ ++
=
+
=
=
=
=
=
~~
~
p
-
-
+
++
++
+
-
__
_
_
`
_
ii
i
i
j
i
are called the dominant poles of the OP-
amp. This transfer function is typical OP-Amp that
has internal frequency compensation. Please view
the recorded lecture [17] to get to know more about
frequency compensation.
WecannowwritethetransferfunctionTforaunity-gainamplieras,
The term
~~
()
1
1
1
VAVV
VV
A
V
V
V
A
A
V
V
as A
A
ss
A
T
A
AsAsAsA
sGBsAsGB
GB A
GB
T
sQs
Q
GB
A
GB
GB
Q
Q
V
VGB
Q
Q
dt
dV
V
1
1
1
11
1
1
1
1
1
1
1
1
1
2
1
2
1
114
2
0
2
2
s
s
dd
dddd
dd
d
d
d
d
p
p
p
0012
12
0
0
0
0
0
0
0
12
0
00102
2
012
02 2
01
2
0
2
2
02
0
0
0
0
""
$
$
$
$
3
1
2
1
~~~
~~
~
~~
~
~
~
~~
p
~
=
=
=
+
=
++
=
=
++ ++
=
+
=
=
=
=
=
~~
~
p
-
-
+
++
++
+
-
__
_
_
`
_
ii
i
i
j
i
, also known as the gain bandwidth product of the operational
amplier,isoneofthemostimportantparametersinOP-Ampnegativefeedback
circuit. The above transfer function can be rewritten as
VO
VS
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
~ ~
( )
1
1
1
V A V V
V V
A
V
V
V
A
A
V
V
as A
A
s s
A
T
A
A sA sA sA
sGB sA sGB
GB A
GB
T
s Qs
Q
GB
A
GB
GB
Q
Q
V
V GB
Q
Q
dt
dV
V
1
1
1
1 1
1
1
1
1
1
1
1
1
1
2
1
2
1
1 14
2
0
2
2
s
s
d d
d d d d
d d
d
d
d
d
p
p
p
0 01 2
1 2
0
0
0
0
0
0
0
1 2
0
0 01 02
2
0 1 2
0 2 2
0 1
2
0
2
2
0 2
0
0
0
0
" "
$
$
$
$
3
1
2
1
~ ~~
~ ~
~
~ ~
~
~
~
~~
p
~
=
=
=
+
=
+ +
=
=
+ + + +
=
+
=
=
=
=
=
~ ~
~
p
-
-
+
+ +
+ +
+
-
_ _
_
_
`
_
i i
i
i
j
i
Goal of the experiment