An operational amplifier is an integrated circuit with wide applications in analog electronics. (Though it can also be used in digital circuits)
Ideally, its properties are:
Infinite Input Impedance
Zero Output Impedance
Infinite Voltage Gain
One interesting application of the op amp is it can perform addition and subtraction.
Given the circuit, calculate
NOTE: The inputs of the opamp are the + and - sign, the output is connected to the vertex of the triangle.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The three properties of the ideal op amp will lead to these implications:
Infinite Input Impedance - No current will flow into the input terminals
Zero Output Impedance - The output will be unaffected by the load
Infinite Voltage Gain - The voltages in the input terminals are equal
From the third implication, the current through each of the resistors in the input side are:
I i = R i V i − V a
V a = V b = 0 V
I i = 2 i R V i − 0
I i = 2 i R V i eq.(1)
By Kirchhoff's Current Law on b and by the first implication:
∑ i = 0 ∞ I i − I ′ = 0
From eq.(1):
∑ i = 0 ∞ 2 i R V i = I ′
By infinite geometric series:
R 2 V i = R 0 − V o
Hence,
V i − V o = 2