# Does the impulse response of a system include both its transient response and steady state response?

Suppose you connect a circuit containing passive elements like resistors, inductors and capacitors to a voltage source. Now you provide an impulse to the circuit. Is the response by the circuit the impulse response, a transient response, or is it the sum of two (i.e. transient response and steady state response). Do we call this sum the impulse response or what?

I know how to calculate impulse response, and I have an idea about convolution. I am expecting a more intuitive answer than a mathematical one. I want to understand what exactly is going in the circuit.

• An impulse response is caused by an impulse. A transient response is not defined; it could be due to an impulse, or a step, or a ramp (for instance). Dec 20, 2022 at 13:57
• No. You're mistaking the impulse response for solutions to the partial differential equation. Dec 20, 2022 at 14:17
• "Impulse response", "transient response", and "steady-state response" are three different things, yet you seem to be equating "impulse response" and "steady-state response" in your question. What are you really asking? Dec 20, 2022 at 17:45
• I think pointing out the fact that "transient response and steady-state response are not the same thing" or arguing about their definitions is wasting time on a technicality. What the OP wanted is simply a physical intuition, and the real question is "Does an impulse response measurement of a passive linear circuit contain enough information to allow the determination of its steady-state behavior?" And the answer should be clear. Dec 20, 2022 at 17:49
• Yes, exactly . That's what I am asking. Dec 21, 2022 at 1:03

For example, for the following lowpass filter, the impulse response comes in the form of $$\e^{-t\alpha}\$$, where $$\\alpha\$$, depends on the R and C values. One could say that the output voltage exhibits transient behaviour for about $$\5\alpha\$$ seconds. After that the steady state response is 0.
The circuit below acts as an integrator (note the current source is the input). In this case, the impulse response of the circuit comes in the form of $$\u(t)\$$ (look up unit step if you haven't seen this notation before). The steady-state portion of impulse response is an output voltage that depends on the C value. This might cause some blowback from mathematicians, but I'd argue that there is no transient portion of this response. The unit step function is 0 at t=0-, and is 1 at t=0+. There is no time where the output is changing continuously.