Equation for output noise voltage of CS stage

We model the thermal and flicker noise of $M_1$ by 2 current ->
$\hspace{2cm}\bar{I_{n,th}^2}=4KT(\frac{2}{3})g_m$
$\hspace{2cm}\bar{I_{n,1/f}^2}=\frac{Kg_m^2}{C_{OX}WLf}$

We also represent thermal noise of $R_D$ by current source.
$\hspace{2cm}\bar{I_{n,R_D}^2}=\frac{4KT}{R_D}$

The output noise voltage per unit BW=
$\bar{V_{n,out}^2}=\Big( 4KT\frac{2}{3}g_m+\frac{Kg_m^2}{C_{OX}WLf}+\frac{4KT}{R_D} \Big)R_D^2 \hspace{2cm}$.......(1)

We have,
$\bar{V_{n,in}^2}=\frac{\bar{V_{n,out}^2}}{A_v^2}$
$=\Big( 4KT\frac{2}{3}g_m+\frac{Kg_m^2}{C_{OX}WLf}+\frac{4KT}{R_D} \Big)R_D^2 \,\, \frac{1}{g_m^2\,R_D^2}\,\hspace{2cm}$

Input reffered noise:
$\therefore\,\,\,V_{n,in}^2=\Big( 4KT\frac{2}{3g_m}+\frac{K}{C_{OX}WLf}+\frac{4KT}{g_m^2\,R_D} \Big)\hspace{2cm}$.......(2)