Operational Amplifiers

The operational amplifier, also know as an op amp, is essentially a voltage amplifier with an extremely high voltage gain.One of the building blocks for the construction of analog electronics systems.It may be combined with various external components for a wide variety of purposes.

Operational Amplifiers

They are usually fabricated as an integrated circuit, an array of transistors, resistors, and capacitors, on a single silicon chip.DIP – dual in-line package is the most common package form.

Operational Amplifiers

invout vAv

An ideal amplifier is defined as:

Ideal Operational Amplifiers

An op amp is built as a differential amplifier, where the output voltage is defined as the product of the gain with the voltage difference between of the amplifier’s two inputs.This means that any stray noise appearing on both inputs are cancelled, and only the voltage difference is amplified.

Ideal Operational Amplifiers

It has two inputs: v+ - the non-inverting input; v- - the inverting input.

The currents through the inputs are zero, due to fact that an ideal op amp’s has infinite input resistance.The output voltage given by the open loop gain is defined below:

Negative Feedback

Negative feedback is required to make a large class of useful circuits with op amps. It is achieved when the output voltage, vo , is connected through a network to the inverting input of the op amp.

Negative Feedback

The provision that the open loop gain approaches infinity and negative feedback, allow us to assume that the voltage at the “-” input terminal is driven to to same voltage as that applied at the “+” input terminal.

vv

Closed Loop Gain

The negative feedback connection closes the loop, which allows us to compute the closed-loop gain, AF , for circuits containing such feedback loops.

Power Supply Voltage Constraint

The output voltage of an op amp cannot exceed the supply voltage applied to operate the op amp.

DDoSS VvV

Summary

An ideal op amp with feedback, assumes: i+ = i- = 0 v- = v+

Vo is bounded by the power supply voltage.

Non-inverting Amplifier

The input of the amplifier is made to the non-inverting input.The closed loop gain is:

The output is not inverted.

1

21R

RAF

Unity Gain Buffer

The input of the amplifier is made to the non-inverting input.The closed loop gain is:

The output is not inverted.

1FA

Inverting Amplifier

The input of the amplifier is made to the inverting input.The closed loop gain is:

The output is inverted.

1

2

R

RAF

Differential Amplifier

The input of the amplifier is made to both inputs.The closed loop gain is:

The output is inverted.

211

2 vvR

Rvo

Summing Circuit

The input of the amplifier is made to the inverting input.The closed loop gain is:

The output is inverted.

iB

BiA

Ao v

R

Rv

R

Rv

1

2

1

2

Integrator Circuit

The input of the amplifier is made to the inverting input.The closed loop gain is:

The output is inverted.

t

oio vdtvCR

v0

1

01

Active Filters

Filter is a network that is frequency selective.Passive filters uses only passive components such as: resistors, capacitors, and inductors.Active filters uses amplifiers to achieve higher performance.

Active Filters

The complex voltage gain is the ratio of the phasor transforms of the output and input voltages.

CR

CRjRR

A

RZ

RCj

Z

Z

Z

v

vA

HI

F

i

oF

2

2

1

2

11

2

2

1

2

1 Where

1

11

Current-to-Voltage Converter

Some applications require that a current be converted to a voltage, and this can be accomplished with an op-amp.

Riv

ii

io

fi