how to derive step response from frequency response

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Fractional-N

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is there any relationship between frequency response of a circuit and its time domain step response?
I mean, if in the frequency response there is a certain amount of gain peaking, does it tell us that step response of the circuit must have ringing?
 

Fractional-N said:
is there any relationship between frequency response of a circuit and its time domain step response?
I mean, if in the frequency response there is a certain amount of gain peaking, does it tell us that step response of the circuit must have ringing?
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1.) Of course, there is a fixed relationship. However, it strongly depends on the pole and zero location of the transfer function (i.e. on its order).
Some formulas are available for a 2nd order TF.

2.) Yes, there are some graphs for a 2nd order system which connects gain peaking and overshoot in the time domain.
More than that, there is a starting value and final value theorem which give you - based on the transfer function - two values for the step reponse:
(a) The value for t=0
(b) The value for t approaching infinite.
 

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