Input impedance of an SMPS?

Hello,
What is the equation for the dynamic input impedance of an smps?

The following , and many others, do not state it...
https://www.intusoft.com/lit/psbook.pdf

The following seems to state it...
https://www.smpstech.com/filter00.htm
...according to this, for a buck converter, dynamic input impedance (dVin/dIin) = -((1/D)^2) * Vout/Iout
..but surely that can't be right?..it doesn't take into account the feedback loop bandwidth?


We are cascading SMPS's, and as you know, if the 'downstream' smps has an input impedance less than the output impedance of its input filter, then it will oscillate. Though what is the equation for dynamic input impedance of an SMPS?

The DC value of the smps input impedance is given on page 11 of the above , but its the dynamic input impedance that is needed.
Does SMPS input impedance decrease with increasing feedback loop bandwidth?

Also, regarding the rule that the input impedance of an smps must be higher than the output impedance of its own input filter.....does that mean, "bigger negatively"?....because as you know, the dynamic input impedance of an smps is negative.

it doesn't take into account the feedback loop bandwidth?

Click to expand...

Won't that be inherently taken account of by the Vout/Iout value?

The Vout/Iout value is just a static DC thing, its not including the dynamics of the feedback loop

The dynamic input impedance of a SMPS is usually dominated by the input filter.

I don't think so...it depends on the crossover frequency...just like the output impedance of an smps is equal to 1/2.pi.f.c where f = crossover frequency; c = output cap