Consider the Large and small signal model of the MOSFET amplifier,

^{simulate this circuit – Schematic created using CircuitLab}

How is this transformation valid, I get the linearization of the MOSFET, but then how can a source become a short and how can we reason the simplifications of other elements. I mean, the original circuit looks totally different from the small signal model. Please provide an intuitive answer, as I get the math part (i.e.) for small signal variations, the behavior of various elements are studied and then approximated, My question is how is this valid? For example, the small signal model of a resistor is simply the resistor itself because the resistor produces a corresponding voltage drop during the small wiggle that we supply, similarly wouldn't the Voltage source be unaltered during the 'wiggle', so shouldn't the small signal model of the Voltage source be itself ?