In a common-source MOSFET amplifier, what describes the intrinsic gain and the role of ro?

• A. Gain ≈ -gm * Rc // ro; ro limits gain and provides finite output resistance.
• B. Gain ≈ -gm * (Rc // ro); ro limits gain and provides finite output resistance, affecting the high-frequency response.
• C. Gain ≈ gm * Rc; ro has no effect on gain.
• D. Gain is independent of ro.

Answer: (B)

The main idea is that the drain load in a common-source MOSFET amplifier is the parallel combination of the external drain resistor and the transistor’s own output resistance ro. The small-signal drain current is gm times vgs, and this current flows into the load at the drain, giving a output voltage of vout = -gm·vgs · (Rc // ro). The negative sign comes from the inverting nature of the common-source stage.

Because ro is finite, the effective load is smaller than Rc alone, so the gain magnitude is reduced from -gm·Rc to -gm·(Rc // ro). ro also sets the stage’s finite output resistance, which is Rc // ro, rather than an ideal infinite resistance. If ro were infinite, you’d get the ideal -gm·Rc; with ro finite, the gain is limited by the parallel combination.

Ro can also influence high-frequency behavior through its interaction with drain capacitances to form RC paths that shape the bandwidth, though the dominant factors for frequency response are the capacitances themselves.