This is not a homework question but from a lecture note. There isn't any explanation on the lecture note so I am wondering how it is derive from the small signal model?

The one highlighted in red

 

It appears to be simply the node equation with substitutions for the control voltages.

 

If you are asking where the SS model itself comes from, you need to start with the equation for the large signal model (including the body effect) and then take the partial derivatives with respect to the various voltages and then convert that into the equivalent circuit.

 

If you are asking where the SS model itself comes from, you need to start with the equation for the large signal model (including the body effect) and then take the partial derivatives with respect to the various voltages and then convert that into the equivalent circuit.

Hi What I mean is the equation(The one highlighted in red) that is derive from the SS model.

Like why is Vbs1 = - Vout ? ( why is Vout negative? )

 

Hi What I mean is the equation(The one highlighted in red) that is derive from the SS model.

Like why is Vbs1 = - Vout ? ( why is Vout negative? )

Who says Vout is negative? Vout is whatever Vout is.

What is Vbs1? It's Vb - Bs (review double-subscript notation, if you need to) which is the body voltage relative to the source voltage. The body voltage is 0V and the source voltage is Vout. So what is 0 V - Vout?