Question

Why there is no dynamic input resistance in the equivalent circuit of the MOSFET
(compared to the BJT)?

Answer 1

The difference is due to the nature of operation and physical structure of the devices

A BJT essentially acts like a current controlled current source. Amount of current flowing into the base, I_B controls the output characteristics of the device.

Whereas MOSFET is essentially a voltage controlled current source. The current flowing through the channel (drain-source terminals) is controlled by the gate-source voltage(V_GS)

So you can say that there is no current flowing into the gate terminal of a MOSFET whereas there is always a current flowing into the base of BJT.

This is why we draw open circuit between gate and source when we draw the small signal equivalent circuit of the MOSFET,

as open circuit represents no current flow. We cannot do this for a BJT as there is actually some current flowing into the base, however small it may be.

Another reason is due to the physical structure of the devices

In a BJT, all the terminals are made of doped semiconducting materials and will have pn junctions associated with them. Even when the pn junctions are reversed biased, small current flows through it (thermally generated carriers).

A MOSFET device has metal-oxide-semiconductor structure (MOS capacitor) at its heart. The oxide material is essentially an insulator and does not allow any current flow.

Note that if you physically measure the resistance across the MOSFET gate, you will measure some value in order of MegaOhms but it can be treated as an open circuit for all practical purposes.