Conductance and Transconductance of the MOSFET
Conductance of the MOSFET:
In this analysis the depletion charge Qd in the threshold voltage VT is simply the value with no drain current. This is an approximation, since Qd(x) varies considerably when Vn is applied, to reflect the variation in Vx. However, Eq of the drain current is a fairly accurate description of drain current for low values of VD, and is often used in approximate design calculations because of its simplicity. A more accurate and general expression is obtained by including the variation of Qd(x). Performing the integration of these equations for Qn(x) one obtains:
Integration of this
The drain current is described by Eq. above for low VD. Initially the channel appears as an essentially linear resistor, dependent on VG .The conductance
of the channel in this linear region can be obtained with VD<(VG-VT):
Transconductance:
As the drain voltage is increased, the voltage across the oxide decreases near the drain, and Qn becomes smaller there. As a result the channel becomes pinched off at the drain end, and the current saturates. The saturation condition is approximately given by
The drain current at saturation remains essentially constant for larger values of drain voltage. Substituting the value of VD into this equ,
The transconductance in the saturation range can be obtained approximately by differentiating the above equ with respect to the gate voltage: