A vo=A( v - v )
ECSE 330 Introduction to Electronics Lecture 02: Operational Amplifiers Roni Khazaka
OpAmp Symbol +15V
i1 + v+
+
-
io
A + v-
vo=A( v+ - v- ) + vo
i2
-
-15V
R. Khazaka
ECSE330 Introduction to Electronics
2
1
vo=A( v+ - v- ) v+
+
io vo
A v-
1. 2. 3.
-
Supply voltages are not shown. Supply currents are not shown (Be careful with KCL). Never do KCL at reference node (otherwise need to include supply currents).
R. Khazaka
ECSE330 Introduction to Electronics
3
Ideal OpAmp
vo=A( v+ - v- ) v+
+
io
A v-
R. Khazaka
vo
-
ECSE330 Introduction to Electronics
4
2
Virtual Short Principle
Assuming vO is finite (no clipping), and infinite gain (A is infinite):
R. Khazaka
ECSE330 Introduction to Electronics
5
Inverting Amplifier
Virtual Ground
R. Khazaka
ECSE330 Introduction to Electronics
6
3
Effect of Finite Gain
vO − R2 R1 = v I 1 + 1 + R2 R1
(
Infinite Opamp Gain R. Khazaka
(1 + R
2
)
A
)
R1
OpAmp Symbol +15V
i1 + v+
+
-
io
A + v-
vo=A( v+ - v- ) + vo
i2
-
-15V
R. Khazaka
ECSE330 Introduction to Electronics
2
1
vo=A( v+ - v- ) v+
+
io vo
A v-
1. 2. 3.
-
Supply voltages are not shown. Supply currents are not shown (Be careful with KCL). Never do KCL at reference node (otherwise need to include supply currents).
R. Khazaka
ECSE330 Introduction to Electronics
3
Ideal OpAmp
vo=A( v+ - v- ) v+
+
io
A v-
R. Khazaka
vo
-
ECSE330 Introduction to Electronics
4
2
Virtual Short Principle
Assuming vO is finite (no clipping), and infinite gain (A is infinite):
R. Khazaka
ECSE330 Introduction to Electronics
5
Inverting Amplifier
Virtual Ground
R. Khazaka
ECSE330 Introduction to Electronics
6
3
Effect of Finite Gain
vO − R2 R1 = v I 1 + 1 + R2 R1
(
Infinite Opamp Gain R. Khazaka
(1 + R
2
)
A
)
R1
