# Op-amps

## The Operational Amplifier

### Introduction

The operational amplifier is one of the most useful analog IC available, and one of the most daunting for beginners and experienced engineers. This page is to introduce some of the uses, and how to calculate values for the various configurations.

• While for these examples it is fine to assume an ideal amplifier. Many op-amps do not go rail to rail and have varying amounts of linearity.

## Theory

The operational amplifier can operate in many difrent ways because of its gerral characteristics.

### Virtual-Ground concept

When the positive input of an op-amp is grounded, the negative input undergoes a state called the virtual-ground. In this state the DC level at the negative input is extremely close to ground.

This is the basis for many for many functions preformed by an operational amplifier, and many of the equations are derived from this mode. R1 is the feedback resistor. Because the negative input appears to be grounded R2 is the basis for input impeadance. The closed loop gain can be derived by the following equation.

where a equals open loop gain

## Voltage Follower

A voltage follower uses the the properties of the op-amp to make the input equal to output. It does this because the op amp wants the negative and positive inputs to be equal. It will adjust the output according to the values on the inputs, since the output is directly tied to the negitive(or inverting) input, the op-amp acts like an analog buffer.

## Simple non inverting

Below is a diagram of an op-amp in a closed loop non inverting configuration. Probably the most used configuration. Lets assume this is an ideal amplifier. To calculate output use the following formula.

R3 can be calculated by the following.

### Example 1

In order to bring a 1V peak input to a 5v range we would need R2=5k and R1=1k and R3=833

and for R3

lets graph it.

### Example 2

Lets say that you want to measure a 12 volt max signal with a 3.3v a/d converter. Using the same formulas as before and standard resistor values.

and for R3

lets graph it.

## Summing amplifier

The summing amplifier will take voltages on the inputs and output the negitive of sum of the voltages.

In the above circuit you will find a basic summing amplifier, with 4 inputs and a single output. What this circuit does is adds the voltages V1 to V4. Lets assume for now that there is unity gain(no gain) and R1 through R4 equal 1000 ohms and the feed back resistor Rf = 1000 ohms and Rom = 200 ohms. This will add the voltages in the following way.

the following is the equation for the above circuit.

This would be useful but if the op-amp is powered by a single +5V, the output would not swing above 5v, But what if you want to add and scale the sum to be within 0 to 5 volts? This is where the math gets more complicated, lets assume the same values as before except Rf=250 and Rom=125 and the previous formula for Vout will change to

plug in the values for V1 through V4 = 5V Why does Rom and Rf change, and what are their relationships to the output? Rf is the feed back resistor and is one half of how the gain is determined. R1 through R4 could have been changed just as easily.

The values for Rom can be derived by

## Latex equations

This is a history of the LATEX formatted equations on this page:

• Virtual Ground
\mathit{gain}=\left({R}_{1}/{R}_{2}\right)\left\lbrack : 1/\left(1-\left(1/a\right)\right)\left(1+{R}_{1}/{R}_{2}\right)\right\rbrack
• Non inverting
example 1
math>\frac{5000}{1000}\ast \mathrm{1V}=\mathrm{5V}[/itex]
math>\frac{1000\ast 5000}{1000+5000}=833[/itex]
example 2
math>\frac{220}{860}\ast \mathrm{12V}=\mathrm{3.06V}[/itex]
math>\frac{860\ast 220}{860+220}=175[/itex]
• summing

by no means is this a complete list.