BJT bipolar vs FET unipolar; MOSFET transconductance

Bipolar vs unipolar

• A BJT is called bipolar because its current is carried by both types of charge carriers, electrons and holes: the emitter injects majority carriers into the base, where they are minority carriers, and the current in the device depends on minority carriers as well as majority carriers (e.g. electrons and holes in an npn).
• A FET is called unipolar because the current is carried by only one type of carrier, the majority carriers (electrons in an n-channel, holes in a p-channel) flowing through the channel; minority carriers do not take part.

Transconductance of MOSFET (n-channel enhancement, saturation)

ID = k (VGS - Vt)²           (k in A/V²)

gm is defined as gm = ∂ID/∂VGS at constant VDS. Differentiating:

gm = d/dVGS [k (VGS - Vt)²] = 2k (VGS - Vt)

Using (VGS - Vt) = √(ID/k):

gm = 2√(k ID) = 2 ID/(VGS - Vt)

(If ID = ½ kn'(W/L)(VGS - Vt)², then gm = kn'(W/L)(VGS - Vt).)

For a depletion MOSFET or JFET, ID = IDSS(1 - VGS/VP)² gives gm = (2 IDSS/|VP|)(1 - VGS/VP). Example: k = 0.5 mA/V², VGS - Vt = 2 V gives gm = 2 mA/V.