High-pass RC circuit as Differentiator:
Adding some ‘salt and pepper’ over high pass RC circuit will give differentiator.In differentiator output voltage, Vout is proportional to the rate of change of input.
Circuit diagram:
As in the case of integrator, when the high pass circuit obey some condition, it act as a differentiator. Shall we see how it is?
Lets write the equation for output voltage.
//output is taken across R and R+1/CS is the total resistance of the circuit. So applying voltage divider rule, Vout = Vin{ R/(Total resistance) } //
Laplace transform s=jw (w=2πf) and RC is the time constant.
Rearranging,
Take the condition that RCw << 1, then
// When RCw << 1, then 1/RCjw become large, so 1+1/RCjw is approximately equal to 1/RCjw. Now the equation become
We know jw = S, Laplace transform. So
therefore, Vout = RC S Vin
The above equation is a Laplace equation and we take inverse Laplace, then equation become,
Equation shows that output voltage is proportional to derivative of input voltage. So the circuit represents a differentiator circuit.
OK!! then go through output of the differentiator circuit for different inputs.
//In lab hours, select different R and C and check output.Also check output just by changing input frequency(by adjusting front nob of signal generator) //
If we make a chicken fry, what is next?. Check its taste, whether salt, chilly etc are ok. Likewise if an output is obtained some people check its different properties and we people study it. So two properties of output wave form.
Rise time (tr): The time taken for the output voltage to rise from 10% to 90% of final value.
//if peak is 100 v, then how much time the wave will take to rise from 10 v to 90v.//
Delay time (td): The time taken for the output voltage to rise from 0 to 10% of its final value.
Low pass RC - integrator and high pass RC - differentiator are very important in lab exams. It will ask in combination with Rectifiers. For theory exams it is not a usual question. Something bigger is going to happen...
Come back with some interesting circuits..