Question

i was wondering. when you find the transfer function of an RC circuit. could be in the form of an opamp or something. And you are asked to find the cut off frequency using the transfer function, how is that done? is there a general way of doing it?

Answer 1

Yes there is a general way. Cut off frequency is one of the corner frequencies. Corner frequency is the value of the frequency at which the Bode magnitude plot changes its slope.

For a first order filter , let's take an example of a transfer function : T(s)= 1/(s+10)

For this : the corner frequency can be found using the the poles of the TF, for w= 10rad/s the Bode magnitude plot changes its value. So, the safest shortcut is to take the TF in time constant form (1+as) form then find corner frequency by taking inverse of coefficient of s, w= 1/a

Eg: T(s)= 5/(s+2) = 2.5/(0.5s+1)

Coefficient of s= 0.5, hence corner frequency , w = 1/0.5=2 rad/s

P.S. TF= transfer function =T(s)