GATE EE 2025 Set 1 — Question 38
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Analog & Digital Electronics → Amplifiers & Feedback → Small-Signal Equivalent Circuits
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Question
In the circuit, is an ideal current source. The transistors and are assumed to be biased in saturation, wherein is the input signal and is fixed DC voltage. Both transistors have a small signal resistance of and trans-conductance of . The small signal output impedance of this circuit is
Correct answer
(C) gₘ r_(ds)² + 2r_(ds)
Solution
To find the small-signal output impedance , set the input signal to zero (), keep and at small-signal ground, apply a test voltage at and find the test current : . is a common-source device whose gate is driven by , and is stacked on it with its gate at the fixed voltage , so acts as a common-gate (cascode) device. The output is taken at the drain of .
1.Resistance seen below . With , , so the controlled source of is zero and looks like its output resistance from its drain to ground. This is the resistance in the source of : .
2.Looking into the drain of . For a MOSFET with source degeneration and gate at small-signal ground,
(the source voltage gives , and ).3.Substitute equal parameters. With and :
4.Effect of . The ideal current source connects to (small-signal ground), so it is in parallel with . Its small-signal impedance is infinite, so it does not reduce the output impedance:
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