Short note: transconductance of JFET

Transconductance (gm) of a JFET is the ratio of the change in drain current to the change in gate-source voltage, at constant VDS. It measures how effectively the gate voltage controls the drain current: gm = ∂ID/∂VGS (siemens, mA/V). It is the FET's counterpart of the BJT's gm.

Expression

From Shockley's equation, ID = IDSS (1 - VGS/VP)²:

gm = dID/dVGS = 2 IDSS (1 - VGS/VP) × (-1/VP)
   = (2 IDSS/|VP|) (1 - VGS/VP)

gm = gm0 (1 - VGS/VP)       with  gm0 = 2 IDSS/|VP|  (the value at VGS = 0)

Eliminating VGS: since (1 - VGS/VP) = √(ID/IDSS),

gm = gm0 √(ID/IDSS)

Properties

• gm is maximum (gm0) at VGS = 0 and falls to zero at VGS = VP (cut-off).
• It depends on the dc bias point: it is higher at larger ID.
• Typical values are 1 to 10 mA/V (lower than for BJTs at the same current).
• Example: IDSS = 10 mA, VP = -4 V: gm0 = 5 mA/V; at VGS = -1 V, gm = 5 (1 - 0.25) = 3.75 mA/V.
• The voltage gain of a common-source amplifier is Av = -gm (RD || rd || RL).