Operational Amplifier (Op-Amp)

Operational Amplifier is an integrated circuit used to amplify the input voltage to high output voltage.

Following picture shows the Op-Amp.

There are total 8 pins in 741 a common operational amplifier.

Following picture shows the Op-Amp circuit.

Basically operational amplifier is contain transistors,resistors,capacitors and diodes.And it's generally notified as

 
Mathematics of Operational Amplifier:

The gain of the operational amplifier is calculated using the following formula 

G = Vout  / (V+ – V-)

When we used operational amplifier in the circuits then the voltage gain calculated as using the following formula

Av = Vout / Vin

Characteristics of Operational Amplifier:

Following picture shows the internal configurational circuit. 

In ideal case its gain is infinite but in practically it's typically over 9000. Closed loop fain is much smaller.In Ideal its internal resistance is infinite but in practically it is in Mega Ohms.In Ideal its (Rout) output resistance is zero but it is very small in practically.

Analysis of the ideal Operational Amplifier:
To analyse an op-amp feedback circuit:
When no current flows into the input terminal of the amplifier its mean there is also no current in the output terminals.
V+ = V-

There are different categories of amplifier.

1-Inverting amplifier
Following picture shows the inverting amplifier and as well as its formula.

2-Non-Inverting Amplifier
Following picture shows the inverting amplifier and as well as its formula.

Operational amplifier can also be used as a Buffer Amplifier as well as unity gain amplifier.

Following picture shows the Buffer amplifier.

Operational Amplifier can also be used as differentiator,integrator and summing amplifier.Following picture shows the these different amplifiers and its formulas.

Following picture shows the Difrentiator amplifier.

Following picture shows the integrator amplifier.

Following picture shows the Summing amplifier.

This is the general information related to operational amplifier and its mathematical relations.It is used in many circuits to enhance the gain of the system.Op-amp used to overcome the overshoot, damping and maintain the speed of the motor.

Source:

Georiga Tech

Writer:

Ihtasham Zahid