Understanding why R_E is in parallel with g_m in a BJT

[kl055]

Homework Statement

Why is R_E in parallel with 1/g_m1?
I drew the small signal model but it does not make sense to me

Homework Equations

The Attempt at a Solution

 

[kl055]

I get that V_A is given by a voltage divider, but why is R_E in parallel with 1/g_m1?

 

[rude man]

Q3 is just a diode so g_m3 can't play a role.

What is r₂₃? What is V_A? You need to define some of these parameters. I assume g_m = β but am not sure ...

I analyzed the circuit assuming β → ∞. Why? Because any circuit that is β-dependent is not a good circuit.

So I got what looks like your expression if g_m → ∞. I know that's not what you are trying to find out - sorry.