# unit step response of RC high pass filter

#### amangupta1219

Joined Oct 18, 2012
19
what is the unit step response of a high pass RC filter ?
I want to calculate using transfer function approach.
My solution :
Y(s)/X(s) = RCs/(1+sRC)

X(s)=1/s
Y(s)=RC/(1+sRC)
taking inverse laplace transform we should get
y(t)=exp(-t/RC)

But if we consider Y(s)=RC/(1+sRC)
RCsY(s) + Y(s) = RC
then this is a non homogeneous equation
so the solution should contain a dc term also which is a complementary function.
but the previous solution i have written above does not contain the dc term.

#### electron_prince

Joined Sep 19, 2012
96
First Check whether your RC high pass filter is a LTI system or not?

if it's LTI system then check for it's unit impulse response. Once unit impulse response is known, use convolution techniques to find unit step response of that system. That's all i know.

But if i forgot all theories that i have learned from books, then i see unit step signal as a dc signal. and high pass filter won't give any output for it.

Your first solution appears logical because at time t = 0, it will give output 1 (capacitor behave like a short circuit) and as time proceeds, the output exponentially approach towards zero.

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