## Introduction to Operational Amplifiers (Op-Amps)

In summary, the op-amp is a voltage amplifier, typically with two inputs, and a single output. For the sake of simplification, most op-amps can be simplified into the following model.

http://en.wikipedia.org/wiki/Operational_amplifier |

**V+**This is the noninverting input

**V-**This is the inverting input

**Vout**This is the output terminal

**Vs+**This pin is attached to a high voltage source

**Vs-**This is the grounding pin

However, usually they are drawn as follows

http://hyperphysics.phy-astr.gsu.edu/ |

We do not explicitly show the power-supply connections (Vs+ and Vs-) in circuit diagrams.

It is assumed that the Vout voltage is made in relation to the circuit's ground.

The op-amp multiplies the difference between V+ and V-, and multiplies it by Aol, the open loop gain.

i.e.

**Vout**= |(

**V+**-

**V-**)| x

**Aol**

This gain parameter, Aol is very large, and is assumed to be infinite, in the case of an ideal op-amp.

For the simplicity of calculation, we simply assume that, because Vout is real,

**Vout**/

**Aol**= |

**V+**-

**V-**|

i.e.

**V+**=

**V-**

This concept is known as the summing point constraint.

This is the default assumption we make whenever calculating feedback loops for ideal op-amps.

By making this assumption, we can apply standard circuit analysis principles.

While there is a difference between V+ and V-, we have to assume that they are the same value for the sake of calculation, such as the following cases demonstrated below.

## Using the Op-Amp in circuits

Inverting amplifiers - negative feedback

Inverting amplifiers - positive feedback

Noninverting amplifiers

Non inverting amplifiers always have negative feedback.

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