GATE 2022 BM – Question 55
The shown saturation-biased MOSFET has Vth=0.5 V, W=100 μm, L=0.1 μm and μₙCox=100 μA/V². Gate bias is 0.7 V, drain bias 1.25 V, supply 2.5 V; drain and load resistors are each 625 Ω. For a 1 mV small-signal input, find output magnitude in mV to two decimals. Neglect channel-length modulation.
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Correct answer: 6.25 to 6.25
Explanation
Overdrive is VGS−Vth=.7−.5=.2 V. Transconductance gm=μₙCox(W/L)Vov=100×10⁻⁶×1000×.2=.02 S. In small signal the supply is ground and coupling capacitors are shorts, so the drain sees 625||625=312.5 Ω. Gain magnitude=gmR=.02×312.5=6.25. A one-millivolt input therefore produces 6.25 mV.