Figure 841
the Cascode Current Source in Fig$\mu \mathrm{m}$ CMOS Process for Which

Question

Figure 841 
the Cascode Current Source in Fig$\mu \mathrm{m}$ CMOS Process for Which

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The Answer is $Figure 8.4.2 \begin{aligned} V_{S G} & =\left|V_{t p} ight|+\left|V_{O V} ight| \ & =0.5+0.2=0.7 \mathrm{~V} \end{aligned} Minimum required voltage V_{S D}=\left|V_{O V} ight|=0.2 \mathrm{~V} . From Fig. 8.4.2, we see that \begin{aligned} V_{G 1} & =+0.9 \mathrm{~V} \ V_{G 2} & =+1.1 \mathrm{~V} \ v_{O \max } & =+0.9+0.5=1.4 \mathrm{~V} \ I_{D} & =\frac{1}{2}\left(\mu_{p} C_{o x} ight)\left(\frac{W}{L} ight)\left|V_{O V} ight|^{2} \ 50 & =\frac{1}{2} imes 100 imes \frac{W}{L} imes 0.2^{2} \ \Rightarrow \frac{W}{L} & =25 \ R_{o} & =R_{o 1}=\left(g_{m 1} r_{o 1} ight) r_{o 2} \end{aligned} where \begin{aligned} g_{m 1} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.05}{0.2}=0.5 \mathrm{~mA} / \mathrm{V} \ r_{o 1} & =r_{o 2}=\frac{\left|V_{A} ight|}{I_{D}}=\frac{\left|V_{A}^{\prime} ight| L}{I_{D}} \end{aligned} For R_{O}=1 \mathrm{M} \Omega , \begin{aligned} 1000 & =0.5 r_{o}^{2} \ \Rightarrow r_{o} & =44.72 \mathrm{k} \Omega \ 44.72 & =\frac{6 L}{0.05} \ \Rightarrow L & =0.37 \mu \mathrm{m} \end{aligned}$
Figure 8.4.2

\begin{aligned}V_{S G} & =\left|V_{t p} ight|+\left|V_{O V} ight| \& =0.5+0.2=0.7 \mathrm{~V}\end{aligned}

Minimum required voltage

V_{S D}=\left|V_{O V} ight|=0.2 \mathrm{~V}

.
From Fig. 8.4.2, we see that

\begin{aligned}V_{G 1} & =+0.9 \mathrm{~V} \V_{G 2} & =+1.1 \mathrm{~V} \v_{O \max } & =+0.9+0.5=1.4 \mathrm{~V} \I_{D} & =\frac{1}{2}\left(\mu_{p} C_{o x} ight)\left(\frac{W}{L} ight)\left|V_{O V} ight|^{2} \50 & =\frac{1}{2} imes 100 imes \frac{W}{L} imes 0.2^{2} \\Rightarrow \frac{W}{L} & =25 \R_{o} & =R_{o 1}=\left(g_{m 1} r_{o 1} ight) r_{o 2}\end{aligned}

where

\begin{aligned}g_{m 1} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.05}{0.2}=0.5 \mathrm{~mA} / \mathrm{V} \r_{o 1} & =r_{o 2}=\frac{\left|V_{A} ight|}{I_{D}}=\frac{\left|V_{A}^{\prime} ight| L}{I_{D}}\end{aligned}

For

R_{O}=1 \mathrm{M} \Omega

,

\begin{aligned}1000 & =0.5 r_{o}^{2} \\Rightarrow r_{o} & =44.72 \mathrm{k} \Omega \44.72 & =\frac{6 L}{0.05} \\Rightarrow L & =0.37 \mu \mathrm{m}\end{aligned}

Figure 841
the Cascode Current Source in Fig $\mu \mathrm{m}$ CMOS Process for Which

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Figure 841 the Cascode Current Source in Fig μm\mu \mathrm{m}μm CMOS Process for Which

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Figure 841
the Cascode Current Source in Fig $\mu \mathrm{m}$ CMOS Process for Which

Correct Answer:
Verified