# LTI system and step input

I would like to study how a system responds to a step input of 3V.

My idea was to use Laplace transform. So I need to get an LTI system of my system which is not linear. To make it linear I need to go into small signal analysis. As around a DC point I can say that it is linear if the coming input of the system is small.

And then to get the response of the system, I transform the step input with Laplace and then multiply the transfer function of my LTI system and the step into the laplace domain to get response of my system into the Laplace Domain. Then I used the inverse laplace to get it in time domain.

What is strange to me is that a step input is not a small signal ? it is rather a large signal ? So how can the response could be correct ?

(Suppose a step input of 3V cannot not be considered as small signal for the system. In other word the system will not react linearly to this step input)

Thank you :)

• What prevents you from making a very small step signal? I.e. a 1mV step, or even 1µV if you wanted. Commented Jan 20, 2023 at 16:40
• A step is as big as you want it to be. The resulting output will be scaled in line with the step amplitude. Commented Jan 20, 2023 at 16:55
• @JonathanS. You re right ! I will edit the post for saying that I want a step input of let's say 3V :D
– Jess
Commented Jan 20, 2023 at 17:58
• @Andyaka I am not sure to understand what you say. I do not think that all system will react according to the small signal transfer function to a large step input
– Jess
Commented Jan 20, 2023 at 18:03
• @Jess then you can't realistically apply Laplace to the problem because of non-linearities. Commented Jan 20, 2023 at 18:06