GAIN OF AN OPERATIONAL AMPLIFIER.
Welcome back with a new exercise of Online Technologies For Beginners.
It is assigned a classic amplifier circuit based on the use of an operational amplifier.
The operational amplifier is supplied with a voltage indicated by Vi, and the voltage output to the amplifier is indicated with Vo.
The amplifier circuit consists of two resistors (R1 and R2), and it is requested to calculate the resistance value to be assigned to the resistor R1 in order to obtain a voltage gain equal to 3.5, knowing that the resistor R2 has a value of 10 kilo-Ohms.
SOLUTION
To solve the exercise, it can be observed that the circuit under analysis is a classic non-inverting amplifier configuration.
From theory we know the voltage gain formula of this configuration.
In general, we have that the voltage gain, which we denote with the letter G, is equal to the ratio between the output voltage Vo and the input voltage Vi. In the case of our configuration, this gain is equal to 1 plus the ratio between R2 and R1.
Replacing the known values, we have that G is equal to 1 plus 10 kilo-Ohms divided by the value of R1, which is unknown. Furthermore, the text of the exercise tells us that G is equal to 3.5 and therefore we report it as a result of the expression.
Analyzing this relationship, we note that the only unknown term is R1, and we can therefore invert the expression in order to calculate the value of it.
The steps are very simple.
We first move the term 1 to the right.
We therefore have that the ratio between 10 kilo-Ohms and R1 is now equal to 3.5 minus 1.
At this point, we have that R1 is equal to the ratio between 10 kilo-Ohms and 3.5 minus 1, the latter equal to 2.5.
We therefore have that R1 is equal to 4 kilo-Ohms.
Finally, we have that by using a 4 kilo-Ohms resistor for R1 and a 10 kilo-Ohms resistor for R2 in a non-inverting operational amplifier configuration, we obtain a voltage gain equal to 3.5.
Well, with this last observation we have completed the exercise.
Thanks for your attention by Online Technologies For Beginners.
