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For an ideal op-amp, the inverting amplifier gain is given simply by

when Rf =R1:
Vout/Vin = -1
For equal resistors, it has a gain of -1, and is used in digital circuits as an Inverting buffer.

Non-Inverting Amplifier
Circuit Diagram

Operational Amplifier
An operational amplifier (Op-Amp) is a differential amplifier that amplifies the difference of voltages applied to its two input terminals (differential input), and provides a single-ended output.

Inverting Amplifier
Operational Amplifier
Introduction
Introduction
Types of op-amp
Inverting Amplifier
Non-inverting Amplifier
In this circuit the signal is applied to the non-inverting input of the op-amp. However the feedback is taken from the output of the op-amp via a resistor to the inverting input of the operational amplifier where another resistor is taken to ground. It is the value of these two resistors that govern the gain of the operational amplifier circuit.

For an ideal op-amp, the non-inverting amplifier gain is given by

Vout/ Vin = - Rf/ R1
Vout/Vin = 1 + Rf/R1
bbv
Properties of op-amp
practically ideally

High input impedance
Low o/p impedance
Large band width
High gain
High slew rate

Infinite input impedance
Zero o/p impedance
Infinite band width
Infinite gain
Infinite slew rat
Applications of Op amp
Summing Amplifiers
An operational amplifier with several voltage inputs and one voltage output
It add the input voltages. The output is the negative sum of the inputs.

Types:

1-Inverting Summers

2-non-inverting summers

3-mixer summers

Thr circuit shows a three input inverting summing amplifier circuit providing a mean of algebraically adding three voltages each multiplied by its constant gain factor. The expression is shown as
Difference Amplifier (Subtractor)

Difference amplifier – A summing amplifier that provides an output proportional to the difference between two input voltages. Also called a subtractor.

In order to work properly,Resistances are equal (R = R and RA = RA) then the output voltage is as given and the gain is +1. If the input resistance are unequal the circuit becomes a differential amplifier

summing Amplifier
subtractor Amplifier
Integrator Amplifier
Differentiator Amplifier
For node N,

Vs3/R3 +Vs2/R2 +Vs1/R1= -V0/Rf
V0= -(Rf/R1 Vs1 + Rf/R2 Vs2 +Rf/R3 Vs3 )
V0= -Rf/R1 (Vs1 +Vs2 + Vs3)
if Rf = R1
V0= -Rf/R1 (Vs1 +Vs2 + Vs3)
circuit diagram
Combining these gives us the overall output equation:

The differentiator is the circuit whose output wave form is the differential input wave form.

The differentiator may be constructed form the basic inverting amplifier
Here we replace the input resistor by a capacitor.

Differentatior

A circuit whose output is proportional to the rate of change of its input signal

circuit diagram:
R2
-
+
R2
R1
R1
I
V2
V1
circuit diagram
The current through a capacitor depends upon the rate of change of voltage across it and the capacitor value.

Input is applied to inverting terminal of the op-amp.
Non inverting terminal is grounded.
If sin wave is applied terminal then the output will be cosine wave.

Circuit Diagram

Integrator
Equating gives

Input

The input is cosine wave the output become sine wave

Output=

The circuit in which the output wave form is the integral of input wave form is known as an integrator

Such type of circuit is obtained by using basic inverting amplifier configuration where we use a capacitor in feed back
Others Applications op-amp
D/A Converter
Audio Amplifier
Precision Rectifier
Instrumentation amplifier

Digital-to-analog (D/A) converter
One summing amplifier application is as a digital-to-analog (D/A) converter.

Digital-to-analog (D/A) converter – A circuit that converts digital circuit outputs to equivalent analog voltages.
Audio Amplifier

The final audio stage in low-power communications receivers, used to drive the speakers.

Precision Rectifier

A clipper that consists of a diode and an op-amp. The circuit can clip extremely low-level input signals.

References
[1] R. L. Boylestad and L. Nashelsky, ”Operational Amplifiers and Op-amp Applications”, in Electronic Devices & Circuit Theory,8th ed.,Ed.New Delhi :Prentice Hall, 2004 pp.594-651.

[2]  D.A.Bell., “ Operational Amplifier Parameters and Op Amps as DC Amplifiers," in Operational Amplifiers and Linear Ics, 2nd ed., Ed. New Delhi: Prentice Hall , 2003, pp. 20-54.

[3] G.Clayton and S.Winder,”Applications : linear circuit,” in Operational Amplifiers ,5th ed. ,ed.Bulington: Elsevier, 2003  pp.82-106.

[4] W.Jung., Op Amp Applications Handbook. : Newness, 2006.

[5] Dr.C.Saritha. (2012). Application Of Op Amps [PowerPoint slides]. Retrieved from Slide share.net.com.
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