Subject: CMOS VLSI Design

Topic: Single Stage Amplifier

Difficulty: Difficult

Using Miller's theoram,

$C_{GS}$ can be shifted to input and output side.

Modified circuit using Miller's theoram,

Input => Total capacitance seen from (X) to ground,
$\hspace{1cm}=C_{GS}+(1-A_v)C_{GD}\hspace{3cm}$.........$A_v=-g_mR_D$
$\therefore\,\,$ Input cutoff frequency,
$\hspace{1cm}\omega_{in}=\frac{1}{R_{in}C_{in}}=\frac{1}{R_S[C_{GS}+(1+g_mR_D)C_{GD}]}$

Output => Total capacitance w.r.t ground,
$\hspace{1cm}=C_{DB}+(1-A_v^{-1})C_{GD}$
$\hspace{1cm}\approx C_{DB}+C_{GD}$
$\hspace{1cm} \therefore\,\omega_{out}=\frac{1}{R_D(C_{DB}+C_{GD})}$

$\therefore\,\,\,T.F=\frac{V_{out}}{V_{in}}(s)=\frac{-g_mR_D}{\Big( 1+\frac{S}{\omega_{in}} \Big)\Big( 1+\frac{S}{\omega_{out}} \Big)}$

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