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In the small signal model of a MOSFET, the current from the drain to the source (for an n channel MOSFET) is a function of the gate to source voltage only.

But, if a positive voltage was not applied at the drain, the current wouldn't flow in the first place.

So, why is the drain to source voltage not considered?

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    \$\begingroup\$ I would review how a small signal model is derived- that would give you the answer. \$\endgroup\$ – isdi Oct 23 '18 at 20:36
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A small-signal model is only valid around a certain operating point. Your particular model makes the assumption that the DC bias voltage on the drain is such that the model is valid, and the AC drive voltage at the gate is small enough that the gm approximation works.

As an example, the Id vs VGS characteristic for a particular FET is shown below with Vds=15V. Graphic from here. If your gate is biased at the point on the diagram where the slope of the curve is gm, then those would be the conditions around which your small-signal model would be valid.
enter image description here

For different DC conditions you may have different values of gm and output resistance.

enter image description here

You can Google all kinds of detailed explanations of how to derive a small-signal model and the assumptions made.

Here's one example: Small-signal derivation Here's another: MOSFET Small Signal Modelling

Maybe after reviewing what you can find with Google you could post a new question with any specific doubts you have about what you find.

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  • \$\begingroup\$ Thanks, but can you elaborate a bit more on this concept? \$\endgroup\$ – Curiosity Oct 23 '18 at 20:38
  • \$\begingroup\$ That is to say, what assumption is made about the DC bias voltage? \$\endgroup\$ – Curiosity Oct 23 '18 at 20:39
  • \$\begingroup\$ @Curiosity Elaborated. \$\endgroup\$ – John D Oct 23 '18 at 21:01
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    \$\begingroup\$ A small signal model is only valid for a biased MOSFET, so a drain current MUST flow. The behavior of a MOSFET when Vds = 0 isn't modeled/considered in the small signal model. It would be pointless to do so because when Vds = 0 the MOSFET cannot "do" anything with a signal. \$\endgroup\$ – Bimpelrekkie Oct 23 '18 at 21:01
  • \$\begingroup\$ @Bimpelrekkie: Well, you could make a small-signal model of a MOSFET with 0V drain to source. Depending on V_GS and whether it's enhancement or depletion mode, it'd either be a couple of capacitors, or a capacitor and (be still, my beating heart) a resistor from drain to source. Note that I'm not saying it'll be an interesting model. \$\endgroup\$ – TimWescott Oct 24 '18 at 0:29

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