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EE 220
Operational Amplifiers
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Operational Amplifiers (Op Amps)
1. Op Amp Characteristics
2. Ideal Op Amp
3. Inverting Amplifier
4. Non-Inverting Amplifier
5. Summing Amplifier
6. Difference Amplifier
7. Voltage Follower
8. Cascaded Op Amps
9. MOSFET
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What is an Op Amp?
It is an electronic circuit that behaves like a
voltage-controlled voltage source.
It is often used to perform mathematical
operations such as inversion, addition, subtraction,
multiplication, division, differentiation and integration.
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Inside The Op Amp
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Operational Amplifier
Two input terminals, positive (non-
inverting) and negative (inverting)
One output
Power supply V+ , and
Op Amp showing power supply Op Amp with power supply not shown (which is how we usually display op amp circuits)
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Op Amp Gain
Key important aspect of op amp: high voltage gain output,
◦ A is the op-amp gain (or open-loop gain)
◦ Linear response
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Op Amp Equivalent Circuit
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Circuit Analysis With Ideal Op-Amps
Use nodal analysis as before.
N
Do not apply KCL at op amp output
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Non-Inverting Amplifier
in
f
o vR
Rv
1
1
9
Non-inverting amplifier is designed to produce positive
voltage gain.
Vo = (1+R1/R2)vs
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KCL at Node a:
KCL at Node b:
2
210
R
RR
v
vG
s
For infinite A:
= 4.999975
= 5
Node a
Node b
Non-Inverting Amplifier
Example 1:
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Inverting Amplifier
i
f
o vR
Rv
1
11
An inverting amplifier reverses the polarity of the input signal while amplifying it.
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Inverting Amplifier
Example 2:
Refer to the op amp circuit below. If vi = 0.5V, calculate the output voltage vo and the current in the 10 k resistor.
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Answer: (a) -1.25V; (b) 50μA
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Summing Amplifier
3
3
2
2
1
1
vR
Rv
R
Rv
R
Rv
fff
o
13
Summing Amplifier is an op amp circuit that combines
several inputs and produces an output that is equal to the
weighted sum of the inputs.
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Summing Amplifier
Example 3:
Calculate vo and io in the op amp circuit shown below.
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Answer: -3.8V, -1.425mA
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Difference Amplifier
1 if , )/1(
)/1(
4
3
1
2121
1
22
431
212
R
R
R
Rvvvv
R
Rv
RRR
RRRv oo
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Difference amplifier is a device that amplifies the difference
between two weighted inputs.
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Voltage Follower/Buffer
depends on load resistor.
is immune to load resistor.
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Cascaded Op Amps
It is a head-to-tail arrangement of two or more op amp
circuits such that the output to one is the input of the
next.
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Cascaded Op Amps
Example 4:
Find vo and io in the circuit shown below.
18Answer: 350mV, 25μA
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Cascaded Op Amps
Example 5:
Find vo in terms of v1, v2 and v3.
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Practice Problems (Chap. 4)
Solve the following problems: 4, 8, 12, 16,
20, …, 52.
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Another Transistor: the MOSFET
A MOSFET (metal-oxide semiconductor field-effect transistor) is
a voltage-controlled electronic switch.
A MOSFET has three terminals: the gate (G), the source (S),
and the drain (D).
Because the gate G is separated from the rest of the transistor
by the thin insulating layer, no dc current can flow from G to
either D or S.
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MOSFET Equivalent Circuit
Characteristic curves Idealized response
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MOSFETs in Digital Circuits
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Vout
B
4-bit ROM
NAND Gate
A
Vout
AB
NOR Gate
A
BOut
A
BOut