1. Saturated transistor
When a transistor (BJT) going into the saturation region a injection of charge taken to start into the emitter region, due to the high numbers of minority charge into the emitter region you've also a high injection of charge into the collector region and the final effects is to collapse the resistance of the collector region, as a final result the voltage across the transistor into the saturation is more smaller than the other region. This phenomenon are know as "modulation of the conducibility".
2. Swith Mode Power Supply
Analysis of switch mode power supply into the steady-state condition can be did by using the fact that average voltage on inductor must be equal to 0 and average current into capacitor must be qual to 0 otherwise you aren't into the steady state condition.
After this assumption is easy found the dc-dc transfer function of every converter.
Dynamical analysis is another story and can be carried in several ways, from state space averaging (Middlebrook) or by using the switch averaging way (Vatché Vorpérian), of course dynamical analysis will show same result of steady-state analysis when you look the relation for a frequency equal to 0.
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Basic forumula is just a approximation of the real converter behaviour, as example try to derive the simple Buck formula for the duty-cycle ration by considering also the effect of the diode voltage drop, you'have another formula with inside the averaged diode forward voltage drop and so on... basical formula is widely used to design the power cell under the assumption that the parasitics components of the converter will be minimized by carefully choice of converter components.
Hope it help
Best regards
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