MOSFET INTRINSIC GAIN

This post will be dedicated to find out the intrinsic gain for 3 different MOSFET amplifier Configurations.

First Consider the small signal model of MOSFET.

Here Body effect on incremental MOSFET model is neglected. 

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Common Source:

Here biasing is not shown and only MOSFET in common source is analyzed.

       $V_{out}=  -g_{m}V_{gs}r_{o}$

   => $V_{out}= -g_{m}V_{in}r_{o}$

 => $\frac{V_{out}}{V_{in}}= -g_{m}r_{o}$ 

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Common Drain:

$V_{out} = g_{m}V_{gs}r_{o}$

   

=>  $V_{out} = g_{m}(V_{in}-V_{out}r_{o})$

=>  $V_{o}(1+g_{m}r_{o}) = V_{in}g_{m}r_{o}$

=> $\frac{V_{out}}{V_{in}} = \frac{g_{m}r_{o}}{M}$ 

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Common Gate:

Vin Voltage source does not draw any current due to unavailability of path to ground. All $g_{m}V_{gs}$ current flows through $r_{o}$

$V_{gs}=V_{in}$

=>$V_{out}= V_{in}- g_{m}(-V_{in})r_{o}$

=>$\frac {V_{out}}{V_{in}}=(1+g_{m}r_{o})$

=>$\frac {V_{out}}{V_{in}} = M$ >

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Extra: If anywhere you want to consider body effect on intrinsic gain expression (Body grounded, where source has some incremental signal nature). 

just Put $M=1+(g_{m}+g_{mb})r_{o}$

This is 2nd post of the series "Finding MOSFET gain". In 3rd post we will learn the intuitive way to find impedances of any MOSFET circuit. From the 4th post onwards we will take different amplifier circuits and try find out their gains and impedances.

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