#
**Operational Amplifiers**

Operational Amplifier Stages
Inverting Amplifier
Non-Inverting Amplifier
Summing Amplifier

## Introduction

The name operational amplifier was originally adopted for a series of high performance

**DC** amplifiers used in analog computers. These amplifiers were used to perform

**mathematical operations** applicable to analog computation such as

**summation** ,

**scaling**,

**subtraction**,

**integrating**, etc .

## Equivalent Circuit for an Ideal Operational Amplifier

**(1)** The voltage gain is infinity,

** A**_{vo} = ∞ .

**(2)** The input resistance is infinity,

**r**_{in} = ∞ .

**(3)** The output resistance is zero,

**r**_{o} = 0 .

**(4)** The bandwidth is infinity,

**BW = ∞** .

**(5)** There is zero input offset voltage,

**E**_{o} = 0 if E_{in} = 0 .

## Input Stage

The input stage is a

**dual input**,

**balanced output differential amplifier**.
It has 2 inputs V

_{in1} and V

_{in2} which are applied at the bases B1 and B2
of transistors Q

_{1} and Q

_{2} .The output V

_{0} is measured between the two collectors
C

_{1} and C

_{2} which are at the same dc potential.Because of the equal dc
potential at the two collectors with respect to ground, the output is
referred to as balanced output.

##
Intermediate Stage

The next stage is

**dual input, unbalanced output difference amplifier**.
Here two input signals are used however the output is measured at only
one of the two collectors with reference to ground. The output is
referred to as an

**unbalanced** output because the collector at which
the output voltage is measured is at some finite dc potential with
reference to ground. In other words, there is some

**dc voltage** at the
output terminal without any input signal applied

One of the most common applications is the simple inverting amplifier.
The output is inverted, and the gain is determined by the

**ratio** of the

**feedback** resistor

**(R**_{f}) to the

**input** resistor

**(R**_{in}).

Another common configuration is the non-inverting amplifier, where the output
signal is

**not inverted** . In this circuit, the input voltage is applied to the
positive input of the op amp, and a fraction of the output signal is applied
to the negative input from the

**(R**_{f}) -

**(R**_{in}) **voltage divider** .

This is a special case of the inverting amplifier, as it gives an inverted output
which is equal to the weighted

**algebraic sum** of all inputs. If the input resistors,
and the feedback resistor are chosen to be

**equal** , the output is simply the

**negative
sum** of the inputs. Since there is no interaction between inputs, the operations
of summing and weighting is very easily done.

R5 = R1 || R2 || R3 || R4