Input reffered noise voltage of CS Stage,

we model the thermal and flicker noise of m_1 by 2 current sources.

$\bar{I^2_{n,th}}=4KT(2/3)gm$

$\bar{I^2_{n,1/f}}=\frac{Kgm^2}{C_{OX}WL\,f}$

Thermal noise of $R_D$ by current source,

$\bar{I^2_{n,R_D}}=\frac{4KT}{R_D}$

The output noise voltage per unit BW=

$\bar{V_{n,out}^2}=(4KT(2/3)gm+\frac{K}{C_{OX}WL}\,\frac{1}{f}\,gm^2+\frac{4KT}{R_D})R_D^2 \hspace{1.5cm}$ -(1)

We have, $\bar{V_{n,in}^2}=\frac{\bar{V^2_{n,out}}}{A_v^2}$

$\hspace{2.4cm}=\frac{(4KT(2/3)gm+\frac{K}{C_{OX}WL}\,\frac{1}{f}\,gm^2+\frac{4KT}{R_D})R^2_D}{gm^2\,R^2_D}$

$\bar{V_{n,in}^2}=4KT(\frac{2}{3})\frac{1}{gm}+\frac{K}{C_{OX}WL}\,\frac{1}{f}\,gm+\frac{4KT}{R_D\,gm^2}\hspace{1.5cm}$ -(2)

Eq (1) -> output noise voltage of CS stage.

Eq (2) -> input noise voltage of CS stage.