Subject: CMOS VLSI Design

Topic: CMOS analog building blocks

Difficulty: Medium

Small signal drain current of $M_1=g_{m_1}V_{in}$

$I_{D_1}=I_{D_2}$ $\therefore\ \ I_{D_2}=g_{m_1}V_{in}$

$M_2\ \ \&\ \ M_3$ forms Basic current mirror

$\therefore I_{D_3}=\frac{(\frac{W}{L})_3}{(\frac{W}{L})_2}I_{D_2}$

$\therefore I_{D_3}=\frac{(\frac{W}{L})_3}{(\frac{W}{L})_2}g_{m_1}V_{in}$

$V_{out}=R_L I_{D_3}$

$\therefore V_{out}=R_L \frac{(\frac{W}{L})_3}{(\frac{W}{L})_2}g_{m_1}V_{in}$

$\therefore A_v=\frac{V_{out}}{V_{in}}=R_L \frac{(\frac{W}{L})_3}{(\frac{W}{L})_2}g_{m_1}$