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Drain and Transfer Characteristics

Two n-channel...

Question

Two n-channel MOSFETs, $T 1$ and $T 2$ , are identical in all respects except that the width of $T 2$ is double that of $T 1$ . Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage $(V_{G S} - V_{T H})$ of $T 2$ is double that of $T 1$ , where $V_{G S}$ and $V_{T H}$ are the gate-to-source voltage and threshold voltage of the transitors, respectively. If the drain current and transconductance of $T 1$ are $I_{D 1}$ and $g_{m 1}$ respectively , the corresponding values ofthese two parameters for $T 2$ are

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Solution

Ans :(b)

$W_{2} = 2 W$
$V_{G S_{2}} - V_{T_{2}} = (V_{G S_{1}} - V_{T_{1}})$
$\frac{I_{D_{2}}}{I_{D_{1}}} = \frac{W_{2}}{W_{1}} \times {(\frac{V_{G S_{2}} - V_{T_{2}}}{V_{G S_{1}} - V_{T_{1}}})}^{2}$
$= 2 \times 4 = 8$
$I_{D_{2}} = 8 I_{D_{1}}$
$\frac{g_{m_{2}}}{g_{m_{1}}} = \frac{W_{2}}{W_{1}} \times \frac{V_{G S_{2}} - V_{T_{2}}}{V_{G S_{1}} - V_{T_{1}}} = 2 \times 2 = 4$ $g_{m_{2}} = 4 g_{m_{1}}$

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