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LECTURE 11 - THE OP-AMP
• Op-Amp: “Operational Amplifier”
• Circuit Symbol:
Power
Supply +
• Reality:
8
7
OUT
6
5
LM741
1
2
_
3
4
Power
+ Supply
-
THE DIFFERENTIAL AMPLIFIER
Differential Amplifier
V+
V
+
A

V0  A(V  V )
V0
Circuit Model in linear region
Ri
“Differential”
+

V1
+

AV1
+

 V0 depends only on difference (V+  V-)
“Very high gain”  A  
But if A ~ , is the
output infinite?
The output cannot be larger than the supply voltages. It will limit or
“clip” if we attempt to go too far. We call the limits of the output the
“rails”.
V0
WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL
HIGH-GAIN DIFFERENTIAL AMPLIFIER ?
• Circuit model gives the essential linear part
VIN +

+

V0
• But V0 cannot rise above some physical voltage related to
the positive power supply VCC (“ upper rail”)
V0 < V+RAIL
• And V0 cannot go below most negative power supply, VEE
i.e., limited by lower “rail”
V0 > V-RAIL
Example: Amplifier with gain of 105, with max V0 of 3V and min V0 of 3V.
(a)
I-V near
origin
(b)
I-V over wider
range
3
V0 (V)
0.2
0.1
3 2 1
.2
V0 (V)
upper “rail”
2
1
1
2
3
VIN(V)
lower “rail”
30 20 10
1
2
3
10 20 30
VIN(V)
NEGATIVE FEEDBACK

+
VIN
THE VOLTAGE FOLLOWER
Negative feedback
 Stabilizes the output
V0
NEGATIVE FEEDBACK
Familiar examples of negative feedback:
Thermostat controlling room temperature
Driver controlling direction of automobile
Fundamentally
pushes toward
stability
Photochromic lenses in eyeglasses
Familiar examples of positive feedback:
Microphone “squawk” in room sound system
Mechanical bi-stability in light switches
Thermonuclear reaction in H-bomb
Fundamentally
pushes toward
instability or
bi-stability
EASY WAY TO GET ANSWER
FOR OP-AMP CIRCUITS
“Ideal Op-Amp Technique”:
iIN(-)
(1) V @ V
A
V0
+

iIN(+)
Why?
V0 CANNOT  , BUT
A   V+  V() in
order that V0 = A (V+  V)
Finite
(2) i IN   0
i IN   0
infinite must be zero
Why? (a) RIN large by design
(b) V+  V()  voltage
difference across RIN 0
With ideal op-amp technique we can analyze all sorts of negative feedback
EXAMPLES USING IDEAL OP-AMP TECHNIQUE
Vp
Vn
+
Vout
_
Vin
R2
R1
I
The non-inverting amplifier
EXAMPLES USING IDEAL OP-AMP TECHNIQUE
C
R2
R1
Vin
Vn
Vp
+
Vout
_
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