n-channel DMOSFET and JFET transconductance

Working of n-channel D-MOSFET

The n-channel depletion MOSFET has a p-type substrate, n⁺ source and drain, and a thin n-type channel built in between them, covered by SiO₂ and a metal gate.

      S      G      D
      |   +--||--+  |
   +--+---+-------+--+---+
   | n+   n-channel  n+  |
   |   p-type substrate  |
   +---------------------+

• VGS = 0: electrons flow through the built-in channel when VDS is applied: ID = IDSS.
• VGS negative: the gate repels electrons, the channel is depleted (narrower), and ID < IDSS. At VGS = VP the channel is cut off (ID ≈ 0). This is the depletion mode.
• VGS positive: the gate attracts more electrons, the channel widens, and ID > IDSS. This is the enhancement mode.
• At small VDS, ID varies linearly with VDS (ohmic); at VDS ≥ VGS - VP, the channel pinches off at the drain end and ID saturates: ID = IDSS (1 - VGS/VP)².
• The insulated gate gives a very high input resistance (about 10¹⁴ Ω), and the gate may be driven positive or negative.

Characteristics:

 ID (drain)                      ID (transfer)
  |    ____ VGS = +1             |             /
  |  _/____ VGS = 0              |          _.'
  | / /____ VGS = -1             |    IDSS .-'
  |/ /_____ VGS = -2             |      .-'
  +----+---- VDS                 +--+------+---- VGS
                                  VP      0

Transconductance of JFET (derivation)

gm = ∂ID/∂VGS at constant VDS. In the saturation region:

ID = IDSS (1 - VGS/VP)²

gm = dID/dVGS = 2 IDSS (1 - VGS/VP) · (-1/VP)
   = (2 IDSS/|VP|) (1 - VGS/VP)       (VP is negative)

gm = gm0 (1 - VGS/VP) ,     gm0 = 2 IDSS/|VP|

Using ID: gm = gm0 √(ID/IDSS). It is maximum at VGS = 0 and zero at VGS = VP. Example: IDSS = 10 mA, VP = -4 V: gm0 = 5 mA/V.