In this script, we will discuss the most important topic of Operational Amplifier, we have already discussed this topic in another script

Now we will discuss

  • What is  Inverting Amplifier
  • Configuration of Inverting Amplifier
  • Math

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Inverting Amplifier

In this section, we consider some useful op-amp circuits that often serve as modules for designing more complex circuits. The first of such op amp circuits is the inverting amplifier. Inverting Amplifier used constant gain amplifier circuit. An inverting op-amp is part of an operational amplifier circuit. Inverting amplifier is output voltage changes in the opposite direction as the input voltage. It can also be said out of phase by 180o

Figure: Inverting Amplifier

That reason is it is called inverting amplifier. we use two external resistors to create a feedback circuit and make a closed-loop circuit across the amplifier.

Configuration of Inverting Amplifier:


We show this circuit, that the noninverting input is grounded, V1 is connected to the inverting input through R1, and the feedback resistor Rf is connected between the inverting input and output. The output is obtained by multiplying the input by fixed or contain connections. In this configuration, we can see that  there are two very important rules 
  • 1)No Current Flows into the Input Terminals
  • 2) V1 = V2 = 0 (Virtual Earth)

Then by using the first rules we can derive the equation for calculating the closed-loop gain of an inverting amplifier.

There are two types of gains 

        1)Closed-loop voltage gain = Av

        2)Open -loop voltage gain = A

Applying KCL at node 1

$$ {i1 = i2 }$$
$${Vi-V1} = {V1-Vo}$$
$$\text{When V1=V2=0 for an ideal open,}$$
$${Vi-o\over R1}={o\over R2}-{V1\over Rf}$$
$${Vi\over R1}= {- Vo\over Rf}$$
$${Vo\over Vi}= {- Rf \over R1}$$

An inverting amplifier reverses the polarity of the input signal while amplifying it.

Problem: 1
  Find out op-amp in Fig.If vi = 0.5 V, calculate: 
(a) the output voltage vo,
 

 (b) the current in the 10-㏀ resistor.

Solution:
(a)We know that,
$${Vo\over Vi}= {- Rf \over R1}$$
$${Vo\over Vi}= {- 25 \over 10}$$
$${Vo}= {- 2.5Vi}$$
$${Vo}= {- 2.5(0.5)}$$
$${Vo}= {- 1.25v}$$
The output voltage vo = -1.25v (Answer)

(b) The current through the 10-㏀ resistor is 
$${i}= {Vi\over R1}$$
$${i}= {0.5\over 10㏀}$$
$${i}= {50ⲘA}$$