CHAPTER 9
Basics of
Operational
Amplifiers
OBJECTIVES
Describe and Analyze:
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Op-Amp Basics
Feedback
Inverting Amplifiers
Non-Inverting Amplifiers
Comparators
Troubleshooting
Introduction
Op-Amps have:
• Differential Inputs: (+) & (-)
• High “Open Loop” Gain: AOL > 100,000
(Open-loop means without feedback. More
on that later.)
• High Input Impedance: Zin > 1 Meg
• Low Output Impedance: Zout  0
Introduction
Some Facts about Op-Amps:
• Op-amps are the most commonly used linear ICs.
• An IC package can have 1, 2, 4, or more op-amps.
• Op-amps come in many varieties based on
parameters such as bandwidth, cost, and transistor
type (BJT, JFET, MOSFET).
Op-Amp Basics
Analysis can be based on two approximations:
• No current flows into or out of the input pins
• The voltage across the input pins is zero
Op-Amp Basics
The front-end of an Op-Amp is a differential amplifier
Voltage Follower
Simplest circuit, illustrates use of negative feedback
Non-Inverting Amplifier
Av = 1 + (Rf / Ri)
Non-Inverting Amp
Gain equation derived as follows:
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Vin applied to (+) input means V(+) = Vin
zero difference across inputs implies V(-) = V(+)
V(-) = V(+) implies V(-) = Vin
Iin = 0 implies V(-) = Vin = [Ri / (Ri + Rf)]  Vout
which leads to Vin / Vout = Ri / (Ri + Rf)
which leads to Vout / Vin = Av = (Ri + Rf) / Ri
which is the same as Av = 1 + Rf / Ri
Non-Inverting Amp
An example calculation:
a)
b)
Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k
Find voltage at (-) input
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Av = 1 + Rf / Ri = 1 + 10k / 5k = 1 + 2 = 3
Vout = Av  Vin = 3  1V = 3 Volts DC
V(-) = V(+) = 1 Volt DC
Negative Feedback
Negative feedback reduces gain to a useable value
Negative Feedback
Besides setting the gain, negative feedback provides
performance improvements such as:
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Makes Zin higher
Makes Zout lower
Increases the usable bandwidth
Reduces distortion in the op-amp
Negative Feedback
It looks complicated, but actually it’s not
Negative Feedback
We can analyze negative feedback as follows:
• Some of the output is fed back to the input:
Vfb = B  Vout where 0 < B < 1
• The signal that gets to the op-amp is the applied
input plus the feedback:
Vx = Vin + Vfb = Vin + B  Vout
• But the output is the open-loop gain of the op-amp
times the signal that gets to the input:
Vout = AOL  Vx = AOL  (Vin + B  Vout)
• Now we can find closed-loop gain: ACL = Vout / Vin
as we will see on the next slide.
Negative Feedback
Start with Vout = AOL  (Vin + B  Vout)
Then Vout = AOL  Vin + AOL  B  Vout
Then Vout – B  AOL  Vout = AOL  Vin
Then (1 - B  AOL )  Vout = AOL  Vin
Then Vout = [AOL / (1 - B  AOL ) ]  Vin
Then Vout / Vin = ACL = AOL / (1 - B  AOL )
Where ACL is the closed-loop gain
Now, if B  AOL >> 1 (which is usually the case)
then ACL  1 / B where B is set by a resistor ratio.
The Inverting Amplifier
Av = - (Rf / Ri) where minus means 180O phase shift
The Inverting Amp
Gain equation derived as follows:
• Vin applied to (-) input through Ri
• zero difference across inputs implies V(-) = V(+)
• (+) input grounded implies V(-)  0
(-) input is a “virtual ground”
• which leads to Iin = Vin / Ri and If = Vout / Rf
• no current into (-) input implies If = Iin
• so Vout / Rf = Vin / Rin and Vout / Vin = Rf / Rin
• If Vin makes Iin flow in, Vout must make If flow out.
So Vout has opposite polarity of Vin: Av = -Rf / Ri
The Inverting Amp
An example calculation:
Find Vout if Vin = 1 Volt DC, Rf = 10k, Ri = 5k
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Av = - Rf / Ri = - (10k / 5k) = - 2
Vout = Av  Vin = -2  1V = -2 Volts DC
Comparators
Very small V between inputs gives a binary output
Comparators
Some Facts about Comparators:
• Comparator output is high or low depending on which input
has the higher voltage applied to it.
• An open-loop op-amp can be used as a comparator.
• Open-loop op-amps go into saturation, and they take a
relatively long time to get out of saturation.
• The output can “chatter” (oscillate high / low) when inputs are
equal. Chatter can be cured with hysteresis.
• There are ICs designed to be comparators. They are better at
the job than op-amps.
Troubleshooting
• Check the power rails: +VCC and –VCC
• Check if the output is in saturation (usually,
saturation is not a good thing).
• Check the input voltages, knowing that voltage
across inputs is supposed to be virtually zero.
• Check that polarity (phase) of output is the same as
input for a non-inverting amplifier.
• Check that polarity (phase) of output is the opposite
input for an inverting amplifier.
• Check signal levels based on gains (look at the
resistor ratios of the feedback loops).