ISRO EC 2025 Q.38: solution and answer

ISRO 2025 · ECQ.38 · 1 mark · MCQ

In a common source amplifier using an NMOS transistor, what is the impact of increasing the channel length modulation parameter ( $λ$ )?

(A)
Output resistance increases
(B)
Gain increases
(C)
Output resistance decreases
(D)
There is no change in output characteristics

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Answer and solution

ANSWER

Increasing the channel length modulation parameter $λ$ decreases the output resistance, option (c).

Official answer: CSource: ISRO's final answer key of 15 May 2026

In saturation, channel length modulation makes the drain current rise slightly with $V_{D S}$ : $I_{D} = \frac{1}{2} μ_{n} C_{o x} \frac{W}{L} (V_{GS} - V_{T H})^{2} (1 + λ V_{D S})$ . Write $I_{D}^{'} = \frac{1}{2} μ_{n} C_{o x} \frac{W}{L} (V_{GS} - V_{T H})^{2}$ for the current without the $(1 + λ V_{D S})$ factor.
The small-signal output conductance is $\frac{\partial I _{D}}{\partial V _{D S}} = λ I_{D}^{'}$ , so the output resistance is $r_{o} = \frac{1}{λ I _{D}^{'}} \approx \frac{1}{λ I _{D}}$ (since $λ V_{D S} ≪ 1$ ).
Hence $r_{o} \propto 1/ λ$ . A larger $λ$ means a steeper $I_{D}$ - $V_{D S}$ curve in saturation, so $r_{o}$ decreases. This is option (c).
Check the other options. (a) is the opposite of the result. (b) The common source gain is $A_{v} = - g_{m} (r_{o} ∥ R_{D})$ , and a smaller $r_{o}$ lowers $r_{o} ∥ R_{D}$ , so the gain magnitude falls rather than rises. (d) is wrong because the output characteristics become less flat as $λ$ grows.
Therefore the output resistance decreases.

KEY IDEA

Output resistance of a MOSFET in saturation is $r_{o} = 1/ (λ I_{D})$ , so it is inversely proportional to $λ$ : a larger $λ$ gives a steeper $I_{D}$ - $V_{D S}$ curve and a lower $r_{o}$ .

WATCH OUT FOR

Thinking that more channel length modulation means a better or higher output resistance, or that the gain rises. The gain $- g_{m} (r_{o} ∥ R_{D})$ actually drops because $r_{o}$ drops.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 2 ISRO Amplifiers questions, with notes