Single pole system time delay calculation

[santosh_475]

Hi all
when I'm studying the first-order system, a question arose about how the rise time of input pulse affects the delay of the circuit? is there any mathematical model for it?

 

[KlausST]

Hi,

define "delay".

in a first order system the output waveform differs to the input waveform. (usually in every filter system).
Thus you can´t expect the waveform to be shifted ... by a fixed delay time t_d.

Knowing this you maybe try "until the output voltage meets the input voltage".
This - in a pure step response - never happens. So the delay is considered "infinite" in this case.

You see: the answer is not a simple one.

Klaus

 

[santosh_475]

Hi KalusST
Thanks for your response, I got that point to reach 100% of its final value its needs an infinite amount of time actually my point here is how a rise time will affect the t_dealy.
my observation by simple RC ckt simulation in cadence was actually 50%rise time of input also part of that delay, i want some more support or knowledge to justify my answer.
thanks

 

[Dominik Przyborowski]

Convolution of step with finite rise time (t<0,v=0;t>0 & t<t0, v=at; t>t0, v=vamp) and single pole transfer function gives your expression.
Use Laplace transform.