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Chapter III

Operational Amplifiers

Objectives

• To introduce Operational Amplifiers as linear circuit elements.

• To identify the I-V characteristics of the operational amplifiers.

• To write KCL and KVL equations for the common amplifier

circuits.

• To calculate the gain of cascaded amplifiers’ circuits.

Pin Assignment

Ideal OPAMPs

Ideal Op Amp Applications

The most widely used op amp applications are,

1. The inverting amplifier.

2. The non inverting amplifier.

3. The summing amplifier.

4. The difference amplifier.

5. The voltage follower.

Inverting Amplifier

Vp = Vn = 0

0−𝑣𝑖

𝑅1+ 0−𝑣𝑜

𝑅𝑓

+ 0 = 0

𝑣0

𝑣𝑖= -

𝑅𝑓

𝑅1

The Non-Inverting Amplifier

+

–

vin

+

–

vout

R1

R2

+

–

• Hence, the non-inverting amplifier has a

gained output (> unity) relative to the

resistance ratio

Summing Amplifier

–

+vb+

–

vo

R2

RfR1

va

+

–

+

–

The Difference Amplifier

Voltage Follower

What is the point?

Vo = Vin

Example

• Calculate Vo assuming

• ideal OPAMP

Example

• Show that

The Integrator

The Differentiator