Download 1E6 Electricity and Magnetism

6. Operational Amplifier Applications: Part I
Properties:
The operational amplifier is an integrated amplifier which is manufactured
specifically for the purposes of designing negative feedback amplifiers as shown in
Fig. 1. It is a differential amplifier having two input terminals so that two separate
input voltages can be applied to it. Its main properties are as listed below:
+
Ve
AO
_
V+
VO = AOVe
V-
Fig. 1 An Operational Amplifier
Property
Ideal
Practical
Open Loop Gain
∞
2 x 105 to 106
Input Resistance
∞
> 2 MΩ
Output Resistance
0
< 500Ω
Bandwidth
∞
1 – 100 MHz
Output Current
∞
10 mA typical
Note: A very high input resistance means that the input current demanded by the
op-amp is negligible and can be ignored in analyses. Some properties, such as the
output resistance, are substantially reduced by the use of negative feedback.
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A Non-Inverting Amplifier:
The schematic diagram of a non-inverting amplifier is shown in Fig. 2, where the
resistors, R1 and R2 , are used to provide the negative feedback. A non-inverting
amplifier is one in which the output signal is in the same sense as the input signal.
+
Ve
_
AO
IO
R2
VO
Vi
Vf
R1
Fig. 2 Schematic Diagram of a Non-inverting Amplifier
Since the input resistance of the amplifier is very high, it can be assumed that the
input current required into either input, V+ or V- is negligible and can be taken as
zero for the purposes of analysis.
In addition, if the loop gain, AOβ >>1, the error voltage at the op-amp input, Ve ,
can be taken as zero. This means that the inverting and non-inverting input
terminals can be taken as being at the same potential, i.e. V+ = V-. This is also
useful for the purposes of analysis.
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From Ohm’s Law, the current flowing into the feedback network is given as:
VO
IO 
R 1  R 2 
But the feedback voltage is:
Vf  IO R1
Substituting gives:
R1
Vf 
VO
R1  R 2 
But if V+ = V- then:
Vf  Vi
so that:
R1
Vi 
VO
R 1  R 2 
Or
VO

R1  R 2 

V
R1
3
i
The closed loop voltage gain is then given as:
VO R 1  R 2 
R2
AV 

1
Vi
R1
R1
Note:
R1
Vf 
VO
R1  R 2 
and
Vf
R1


VO R 1  R 2 
Then from previous analysis:
VO R 1  R 2 
R2
AV 

1
Vi
R1
R1
This shows that the analysis above, based on circuit principles agrees with the
previous analysis of the general block diagram, so that there is consistency.
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Unity Gain Buffer:
A special case of the non-inverting amplifier exists where R1 = ∞ and R2 → 0 as
shown in Fig. 3. In this case full feedback is applied to the amplifier with β = 1 and
Vf = VO .
+
Ve
_
AO
VO
Vi
Vf = VO
Fig. 3 Schematic Diagram of a Unity-Gain Buffer
VO R 1    R 2 0 R 1
AV 


1
Vi
R 1  
R1
In this case:
This provides a buffer amplifier, which has a very high input resistance which
demands no current and so does not cause any attenuation effect on an input signal
applied. The output of the op-amp, on the other hand, can supply several mA of
current to a modest load. The unity-gain buffer can provide an interface between a
transducer with significant internal source resistance and a load of similar
resistance to avoid attenuation of the signal, even when gain is not required.
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Case Study 5:
Design a non-inverting amplifier to have a voltage gain of 11.
+
_
AO
R2
VO
Vi
R1
Simply:
VO
R2
AV 
1
 11
Vi
R1
Therefore:
R2
 10
R1
One resistor can be chosen arbitrarily and should have a value between 1 – 100kΩ.
Then if choose:
R 2  10kΩ and R1  1kΩ
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The Inverting Amplifier:
It is also possible to apply the input signal to the inverting input of the op-amp to
generate an output signal which is of opposite sense to the input signal. Since the
negative feedback must also be applied to the inverting terminal of the op-amp, the
non-inverting input is simply connected to ground. In this case with Ve → 0V and
V+ = V-, the inverting and non-inverting inputs can be considered as being at the
same potential so that the inverting terminal can be considered to be a ‘virtual
earth’ point, i.e. V+ = V- → 0V. The schematic diagram of the inverting amplifier is
shown in Fig. 4.
R2
R1
Ii
If
_
AO
Ve
+
Vi
VO
Fig. 4 Schematic Diagram of the Inverting Amplifier
If the input resistance of the amplifier is taken as infinite, then this means that
whatever current flows into the input resistor, R1 , must also flow through the
resistor in the feedback path, R2 and then into the output terminal of the amplifier.
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That is:
Ii  If
But:
Vi  V
Ii 
R1
V  VO
If 
R2
-
and
Then:
V  VO
Vi  V

R1
R2
-
-
But if the inverting input terminal can be taken as a virtual earth point, V- → 0V so
that:
VO
Vi

R1
R2
So that:
VO
R2
AV 

Vi
R1
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Note that if:
Vi
Ii 
R1
Then:
Vi
Ri 
 R1
Ii
This is the input resistance seen by the source, Vi , which is usually considerably
lower than the input resistance of the op-amp itself.
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Case Study 6:
Design an inverting amplifier to have a gain of – 5 and an input resistance of 20kΩ.
R2
R1
_
A
+
O
Vi
VO
The input resistance is:
R i  R1  20kΩ
Then:
R2
A V  5  
R1
Therefore:
R 2  5R1  5 x 20kΩ  100kΩ
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