FINDING MOSFET CIRCUIT GAIN USING INTRINSIC GAIN METHOD

Here in this post, I'll help build your basics of the MOSFET incremental model and try to find some parameter values, which will be used extensively to find out the gain of any MOSFET circuit.

There are three method to find out the gain of the amplifier

• Conventional Method (using the small-signal method)
• Intrinsic gain method approach
• \(G_{m}, R_{out}\)  method

Here in this tutorial, We will only be discussing the second method in this post. For this you only need to remember three expressions along with a voltage divider equation and some basic methods of finding equivalent impedance (from inspection) at any node. 

That's all!

(There will be a separate tutorial dedicated to the last method.)

First, we shall define the intrinsic gain of different configurations (CS, CD, CG) and find their value once.

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Let's start-------

                   Configuration                     Intrinsic Gain                  

                 Common Source                    $-g_{m}r_{0}$

              

                 Common Drain                          $\frac{g_{m}r_{0}}{M}$

                  Common Gate                            $ M $

But what is $M$ in the expressions? 
Well, I call it Mirroring Factor. For the time being just remember its expression  $M= (1+g_{m}r_{0})$. ( It will be explained in the subsequent blog.)

Other than above 3 expressions you have to remember the Thevenin's equation.

$Actual \, Gain = Intrinsic \, Gain \times \frac{R_{L}}{R_{L}+R_{out}}$ 

$R_{L}$= Actual load seen by the circuit

$R_{out}$= Output impedance seen into the circuit >

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Without justifying the above equation, let's just jump into one of the simplest MOSFET amplifier circuit.

Observation: Common Source Configuration

So, $\frac{v_{out}}{v_{in}}= A_{Intrinsic}\times \frac{R_{L}}{R_{L}+R_{out}}$

            $ = -g_{m}r_{0} \times \frac{R_{D}}{R_{D}+r_{0}}$

            $ = -g_{m} \times \frac{r_{0}R_{D}}{r_{0}+R_{D}}$

            $ = -g_{m}(r_{0}||R_{D})$

This is a very well known result, doesn't seem surprising to us.

You will appreciate this, as we are going to solve quite a complex amplifier circuit. I promise, you will never have any fear while dealing with MOSFET Circuits ever again. 

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In the upcoming lectures, We will discuss more about the basics of intrinsic Gain. So get ready!

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