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Operational Amplifier Gain

Show how an ideal Operational Amplifier with an open loop gain = A can be used to provide:
i) a non-inverting amplifier with gain= +6v/v.
ii) an inverting amplifier with gain= -3v/v.
iii) an integrator with gain= +3.

Explain the purpose of every component in your circuits.

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Prob 1

Figure 1: Inverting amplifier circuit.

Figure 2: Noninverting amplifier circuit.

The way that you define the gain is by setting the ratio of R1 to R2. Neither of these resistors will ever have much power going thru them, so these can be very tiny - often 1/4 or 1/8 watt resistors are used. To keep power consumption down, as well as noise introduced by cheap carbon resistors, we will use resistors in a range of 10,000 Ohms thru 1 Meg Ohm.
If R2 is equal to R1, then we have Unity Gain, or a 1X Amplifier - This is a 1:1 ratio. if R2 is twice the resistance of R1, we have an Amplifier with a gain of 2 - a 2:1 ratio. To build the 2X gain amplifier, lets pick resistor values that will set the 2:1 ratio - R2 = 20,000 ohms and R1 = 10,000 ohms (20000:10000 = 2:1). That really wasn't that hard to do.
A(i) Non Inverting Amplifier :

Gain = 1 + R2/R1
6 = 1+ R2 / R1
R2 /R1 = ...

Solution Summary

Solution presents Operational Amplifier as non inverting, inverting and integrator.