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Analyze the following circuit to get voltage gain equation if M2 is twice as wide as that of M1 and Vin1 = Vin2.

Subject: CMOS VLSI Design

Topic: Differential Amplifiers

Difficulty: High

cvd • 977  views
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$(\frac{W}{L})_1=2(\frac{W}{L})_2$

$\therefore\,\, I_{D_{2}}=2I_{D_{1}}\,\,\,=\gt\,\,\,g_{m_{2}}=2g_{m_{1}}$

Therefore, small signal voltage is given by,

$|A_v|=\frac{2R_D}{\frac{1}{g_{m_{1}}}+\frac{1}{g_{m_{2}}}}=\frac{2R_D}{\frac{1}{g_{m_{1}}}+\frac{1}{2g_{m_{1}}}}=\frac{2R_D}{\frac{3}{2g_{m_{1}}}}=\frac{4}{3}g_{m_{1}}\,R_D$

$\therefore\,\,\,|A_v|=\frac{4}{3}g_{m_{1}}\,R_D$