Operational Amplifiers
A Linear IC circuit
Operational Amplifier (op-amp)
• An op-amp is a high-gain amplifier that has high
input impedance and low output impedance.
• An ideal op-amp has infinite gain and input
impedance and zero output impedance.
• An integrated circuit (IC) contains a number of
components on a single piece of semiconductor.
• Most op-amps are IC chips.
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The 741 Operational Amplifier
Op-Amp Input/Output
• We consider the op-
amp as a single
component with input
and output
characteristics.
• Two signal inputs:
 Inverting
 Non-inverting
• Two dc power supply
leads (+ and −)
• One output lead
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Op-Amp Packages
The Operation of Op-amps
• The input stage of an op-amp is a
differential amplifier.
• The op-amp amplifies the difference
between the two input terminal voltages.
Vdiff =V2 −V1
V1
−
V2
+
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Op-Amp Output
• The output of the amplifier is determined by




The gain of the amplifier.
The polarity relationship between V1 and V2.
The values of the supply voltages, +V and -V.
The load resistance
Op-Amp Gain
• The maximum possible gain of an op-amp
is called the open-loop gain AOL.
• Generally AOL is greater than 10,000.
• Typical values are on the order of 200,000.
• An ideal op-amp would have infinite gain.
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Input/Output Polarity
• The output polarity follows the sign of Vdiff.
• If V2 – V1 > 0 the output polarity will be positive.
• If V2 – V1 < 0 the output polarity will be negative.
V1
−
V2
+
Supply Voltages
• The supply voltages determine the limits of output
voltage swing. No matter what the gain and input
voltages the output value can not exceed +V or
–V.
• In practice the maximum output voltage is slightly
less than the supply voltages.
 For resistive loads > 10kΩ the output voltages are
about 1V “less” than the supply voltages.
 For resistive loads > 2kΩ the output voltages are about
2V “less” than the supply voltages.
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Open Loop Op-amp Use
• As the open loop gain of most op-amps is
extremely large the output of an open-loop circuit
is either the maximum positive or negative
voltage.
+15 V
V1
−
V2
+
#+ 14 V
Vout = "
!$ 14 V
V2 > V1
V2 < V1
-15 V
Feedback Circuits
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Feedback
• Most op-amp circuits are designed to use
feedback.
• Feedback is defined as taking a portion of the
output of a circuit and coupling or feeding it back
into the input.
• If the output fed back is in phase with the input
then the circuit has positive feedback.
• If the output fed back is out of phase with the
input then the circuit has negative feedback.
Negative Feedback
• Most amplifiers use negative feedback.
• Disadvantages:
 decreased gain.
• Advantages:
 increased circuit stability,
 increased input impedance,
 decreased output impedance,
 increased frequency bandwidth at constant
gain.
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Negative Voltage Feedback
•
A fraction B < 1 of the output voltage is subtracted from the
input voltage.
v" = vin ! Bvout
v′
Σ
vin
AOL
vout
-B
Negative Voltage Feedback
•
The closed loop gain, Av, is defined as
•
The closed loop gain can be calculated from two equations
v′
vin
AOL
Σ
vout
-B
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Negative Voltage Feedback
•
Solving for Av gives
•
Usually the open-loop gain is so large that we can approximate:
v′
vin
AOL
Σ
vout
-B
Negative Feedback
• The gain of the amplifier circuit
depends only on B, the fraction
of output voltage fed back.
• B can be made very constant so
that the amplifier has great gain
stabilization.
• Example: B could be determined
by two resistors in a voltage
divider relationship.
vout
R1
Bvout
R2
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Negative Feedback Impedance
• The input and output impedance is also
changed by the feedback.
Op-Amp Circuits With Negative
Feedback
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Non-Inverting Amplifier
• Using Kirchoff’s rule, Ohm’s Law, and our knowledge of
op-amps we can derive a closed loop-voltage gain for the
non-inverting amplifier circuit shown below.
i2
R2
i1
i´
R1
vin
v1
vout
v2
Non-Inverting Amplifier
• As the input resistance of the op-amp is very large we can
neglect i´.
• The output voltage is given by the voltage difference and
the open-loop gain.
i2
R2
i1
i´
R1
vin
v1
vout
v2
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Non-Inverting Amplifier
• Combining the previous equations we find:
Av =
v out
AOL (R1 + R2 )
=
v in (AOL + 1)R1 + R2
• If the open-loop gain is very large:
!
i2
R2
i1
i´
R1
v1
vin
vout
v2
Inverting Amplifier
• Using Kirchoff’s rule, Ohm’s Law, and our knowledge of
op-amps we can derive a closed loop-voltage gain for the
inverting amplifier circuit shown below
i2
R2
i1
R1
vin
i´
v1
vout
v2
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Inverting Amplifier
• The output voltage is related to the voltage difference.
• Neglecting i´ and combining the equations gives
i2
R2
i1
R1
vin
i´
v1
vout
v2
Inverting Amplifier
• For a very large open-loop gain
becomes
i2
R2
i1
R1
vin
i´
v1
vout
v2
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The Two Golden Rules of
Op-Amp Circuits
• Notice in both derivations two approximations were made: (1)
the input current i´ flowing into the op-amp was neglected
compared to other currents; and (2) the open-loop op amp gain
AOL was assumed to be very large compared to the gain with
feedback.
• These two approximations can be extended to form two “golden
rules” for analyzing an op-amp circuits with negative feedback.
• Op-Amp Current Rule (OACR): The current into or out of each
op-amp input terminal is approximately zero.
• Op-Amp Voltage Rule (OAVR): The voltage difference between
the two op-amp input terminals is approximately zero.
Op-Amp Current Rule
• The OACR basically says that the input
impedance of the op-amp is much higher
than the external input impedance from the
input terminal to ground.
• For BJT op-amps input impedance is on the
order of 10MΩ.
• For FET op-amps input impedance is on the
order of 1012 Ω.
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Op-Amp Voltage Rule
• The OAVR is the equivalent of saying that the open-loop
gain is infinite.
• The output of the op-amp can never be greater than the
supply voltage (~15V) which means that (v2-v1 ) must be
less that 150 µV for a typical AOL or the output will be
saturated. Therefore if the op-amp is not saturated then the
difference between the input terminals must be nearly zero.
• The rule says that in an actual op amp circuit the negative
feedback plus the high gain of the op-amp effectively zeros
the difference between the two inputs.
Non-inverting Amp
• OACR: i1 = i2
OAVR: v1 = v2 = vin
i2
R2
i1
R1
vin
v1
vout
v2
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Inverting Amp
• OACR: i1 = i2
OAVR: v1 = v2 = 0
i2
R2
i1
R1
vin
v1
vout
v2
Instrumentation Amplifier
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Peak Detection Amplifier
Positive Feedback
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Positive Feedback Circuits
• Rather than placing a portion of the output
back into the inverting input a portion of the
output is sent back to the non-inverting
terminal to produce positive feedback.
Positive Feedback Circuits
• Oscillators
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Positive Feedback Circuits
• Oscillators
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