For a field-effect transistor, if the drain current change is △ID = 1 mA in response to a gate-to-source voltage change of △VGS = 1 V, what is the device transconductance gm?

Introduction / Context:
Transconductance (gm) quantifies how effectively a FET converts an input voltage variation at the gate into an output current change at the drain. It is a key small-signal parameter for gain and bandwidth calculations in analog design.

Given Data / Assumptions:

• △ID = 1 mA.
• △VGS = 1 V.
• Definition: gm = △ID / △VGS, with units of siemens (A/V).

Concept / Approach:
Apply the definition directly. Ensure consistent units: milliamperes per volt yields millisiemens.

Step-by-Step Solution:
gm = △ID / △VGS.Substitute: gm = 1 mA / 1 V = 1 mA/V.Convert units: 1 mA/V = 1 × 10^-3 A/V = 1 mS.

Verification / Alternative check:
Dimensional check: A/V is siemens (S). Milliampere per volt corresponds to millisiemens, confirming the numerical result.

Why Other Options Are Wrong:

• 1 kS: Off by 10^6; unrealistically large for discrete FETs.
• 1 kΩ and 1 mΩ: These are resistance units, not transconductance.

Common Pitfalls:

• Mixing up transconductance (S) with resistance (Ω) or conductance (also S but of a resistor, not a transfer parameter).
• Forgetting to convert milliamps to amps when required.

Final Answer:
1 mS