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Standard XII

Physics

Photodiode

Consider an n...

Question

Consider an n-channel MOSFET having width $W$ , length $L$ , electron mobility in the channel $μ_{n}$ and oxide capacitance per unit area $C_{o x}$ . If gate-to source voltage $V_{G S} = 0.7 V$ , drain-to-source voltage $V_{D S} = 0.1 V, (μ_{n} C_{o x}) = 100 μ A / V_{2}$ , threshold voltage $V_{T h} = 0.3 V$ and $(W / L) = 50,$ then the transconductance $g_{m} (i n m A / V)$ is

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Solution

Given that,
$V_{G S} = 0.7 V, V_{T H} = 0.3 V, V_{D S} = 0.1 V$
$V_{G S} - V_{T H} = 0.4 > V_{D S}$
$\Rightarrow$ MOSFET is in linear region,
$I_{D} = K_{n} [2 (V_{G S} - v_{T H}) V_{D S} - V_{D S}^{2}]$ Transconductance,
$g_{m} = \frac{δ I_{D}}{δ V_{G S}} = 2 K_{n} V_{D S}$
$K_{n} = \frac{K_{n}^{'}}{2} (\frac{W}{L}) = \frac{μ_{n} C_{o x}}{2} (\frac{W}{L})$
So, $g_{m} = 2 K_{n} V_{D S} = μ_{n} C_{o x} (\frac{W}{L}) V_{D S}$
$= 100 \times 50 \times 0.1 μ A / V$
$= 0.5 m A / V$

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Given that, VGS=0.7V,VTH=0.3V,VDS=0.1V VGS–VTH=0.4>VDS ⇒ MOSFET is in linear region, ID=Kn[2(VGS−vTH)VDS−V2DS] Transconductance, gm=δIDδVGS=2KnVDS Kn=K′n2(WL)=μnCox2(WL) So, gm=2KnVDS=μnCox(WL)VDS =100×50×0.1μA/V =0.5mA/V