Filter translation into base band...

I have a say 100% efficiency (class E) RF modulator which is 100% pulse modulated through its supply. Between the 0/100% supply pulse and the modulator supply rail I have a pulse shaping filter.

That amplifier is designed to spec with a real 50R load and works nicely. But now I have to study and tune its RF pulsed performances with the actual loads which are tuned magnetic loops. Those loops are perfectly matched to the 50R impedance... at the carrier frequency, but the loop being pulse spectrum being pretty wide... Well you know...

What I'd like to do is translate the RF domain output filter and load impedance to the baseband domain as a load impedance seen on the supply rail.

All that in order to properly design the shaping filter and avoid a tedious and iterative guess work...

Of course I can take some measurement on the system and do identification but that'll require to build it entirely. (and that's cheating :-)

Any lead about how to approach that pb?

DSP design software usually has that capability. Also really expensive math software but then they often nickel and dime you for extra "toolboxes" you must buy:

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The search term would be "baseband equivalent".

I never do that for my stuff. Recently I had to design a balun/iso/filter module for pulsed power RF. Steep filter. It needed a notch for a harmonic as well, and then baseband gets ugly. So I did it the usual way. Used the filter handbook as a starter, threw it on SPICE, nudged it all towards catalog component values, optimized some more to have reasonable sensitivity to tolerances, then layout. Built it last Thursday (after my right front paw had healed from some serious poison oak swelling), hooked it up to the network analyzer and the plot was almost verbatim like the SPICE plot.