f(L)=1/(2*pi*Req*Cs)

To do this, I'm supposed to reduce the circuit "seen" by capacitor Cs to an equivalent RC circuit where Req would be the equivalent resistance seen by Cs.

Employing Thevenin's Theorem, open-circuiting all current sources and short circuiting all voltage sources gives me the equivalent resistance as:

Req=R

_{S}||((R

_{L}||R

_{D})+r

_{d}) which simpifies into the equation:

Req=R

_{S}/(1+(R

_{S}/(R

_{D}R

_{L}+r

_{d})))

But the real equation stated in the internet and text books is:

Req=R

_{S}/(1+(R

_{S}(1+g

_{m}r

_{d})/(R

_{D}R

_{L}+r

_{d})))

So, I am missing the factor (1+g

_{m}r

_{d}) in my equation. Please help me figure out what I am doing wrong.