Hybrid-pi Model of MOSFET

In the previous post, we studied the key differences between D-MOSFET and E-MOSFET. In this post, we will only analyze the Ac model (small-signal analysis) of E-MOSFET as the working of D-MOSFET is similar to that of JFET so there isn't any significance in studying D-MOSFET. I hope that now you all guys are very much familiar with BJT and its model. We will compare the rπ(r-pi) model of BJT to study the ac analysis of MOSFET.
# R-pi Model of BJT:-

So now as you can see that in BJT all the regions i.e. base, emitter, and collector region are connected to each other and a small current Ib which is in a few micro-amps flows through the base terminal but in the case of E-MOSFET, there is an oxide layer which is present in between the Gate and Substrate which acts as an insulator, therefore, the current Ig flowing through the gate terminal is zero i.e. (Ig = 0mA). 

Now we know that V = I * R,

if Ig = 0mA 

Therefore, R = infinite (∞)

Thus for MOSFET the value of rπ = ∞ so in Ac analysis of E-MOSFET, we open-circuit the path of r-pi resistance indicating that it provides very high resistance. Rest all the things are the same in the hybrid-pi-model of MOSFET. 

# What is Transconductance?

For understanding this first you have to understand its definition. We will break it into 2 words (Trans)  and (Conductance). First, we will understand What is the definition of conductance and then the meaning of trans.

So as you know conductance [g] is inverse of resistance [r] i.e. 

if r = v/i 

then g = 1/r = i/v 

and trans means relation between input and output parameters.Therefore we can say that 

gm = i(output) / v(input).........(1)

Definition of transconductance(gm):-Change in Output current(Ic) with respect to the Input voltage(Vbe) 

Differentiating Id with respect to Vgs

i.e. (gm = dId/dVgs)..........(2)  {From 1}

The image shown below shows the proof of the transconductance parameter.

Now that we had understood the parameters like gm, Vgs, rπ, etc, we are only left with ro parameter. ro is the resistance of the current source gmVgs. This resistance of the current source gmVgs will remain the same in the h-pi model of the MOSFET as well. Thus the overall H-pi model of MOSFET will look as shown in the figure below. 

I had explained the concept quickly and concluded certain things through a short video.

Video:-