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Two identical nMOS transistors M1 and M2 are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. Vbias and VD are adjusted so that both transistors are in saturation. The transconductance of this combination is defined as gm = ∂iD/∂vGS, while the output resistance is ro = ∂vDS/∂iD, where iD is the current flowing into the drain of M2. Let gm1, gm2 be the transconductances and ro1, ro2 be the output resistances of transistors M1 and M2, respectively. Which of the following statements about estimates for gm and ro is correct?

1. gm ≈ gm1 + gm2·ro2 and ro ≈ ro1 + ro2.
2. gm ≈ gm1 + gm2 and ro ≈ ro1 + ro2.
3. gm ≈ gm1 and ro ≈ ro1·gm2·ro2.
4. gm ≈ gm1 and ro ≈ ro2.

Correct answer: gm ≈ gm1 and ro ≈ ro1·gm2·ro2.

Solution

The correct option indicates that the transconductance gm is primarily determined by the first transistor M1, while the output resistance ro is influenced by both transistors, specifically the output resistance of M1 combined with the effect of M2's transconductance and output resistance, reflecting the interaction in the amplifier configuration.

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