# Deriving the small signal model of this transistor

Given that the current equation for a graphene transistor is given by equation (1) I'm trying to find the small signal model of the transistor.

$$(1)\space \space i_D(V_{GS},V_{DS})=\frac{W}{L}μ(C_{ox}V_{GS}+a)V_{DS}\\ i_G=0$$

Small signal models were always given in the courses I've had. So, a problem like this is unusual for me. I gave it a go though. I used the Taylor series around the bias point for two variables and ignored the non-linear terms:

$$i_D(V_{GS},V_{DS})=i_{bias}+(V_{GS}-V_{GSbias})(\frac{\partial _{i_D}}{\partial V_{GS}})_{V_{GS}=V_{GSbias}}+(V_{DS}-V_{DSbias})(\frac{\partial _{i_D}}{\partial V_{DS}})_{V_{DS}=V_{DSbias}}\\ Δi=ΔV_{GS}(\frac{\partial _{i_D}}{\partial V_{GS}})_{V_{GS}=V_{GSbias}}+ΔV_{DS}(\frac{\partial _{i_D}}{\partial V_{DS}})_{V_{DS}=V_{DSbias}}\space \space (2)$$

I'm confident that this is the small signal equation for the current. However, this equation is causing me some confusion.

What is the transconductance gm and the resistance ro for this model?

## 1 Answer

This is your general formula 2 which is valid for all fets which have source, gate and drain

The red partial derivative is the transconductance. The green one is the output conductance.

To get the actual transconductance formula calculate the red partial derivative from your model equation (it seems quite simple, like an ordinary silicon mosfet, I guess graphene transistors have more complex models) .