GATE EC 2016 Set 3 — Question 51
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Analog Circuits → BJT & MOSFET Amplifiers → Small-Signal & Hybrid-Pi Model
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Question
In the circuit shown in the figure, the channel length modulation of all transistors is non-zero (). Also, all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain () of the circuit is
Correct answer
(C) -gₘ₁ (rₒ₁ (1gₘ₂ rₒ₂) rₒ₃)
Solution
In the small-signal model:
The small-signal voltage gain is:
This matches option (C).
1.Transistor is the driver NMOS with transconductance and output resistance .
2.Transistor is a PMOS with its gate at a constant bias (AC ground). Its small-signal resistance is .
3.Transistor is a diode-connected PMOS (gate connected to drain). Its small-signal resistance is .
All three resistances are in parallel at the output node . The total output resistance is:The small-signal voltage gain is:
This matches option (C).
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