**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

**Unit :**Transistors

## Conductance and Transconductance of the MOSFET

**Conductance of the MOSFET:**

In this analysis the depletion charge Q_{d} in the threshold voltage V_{T} is simply the value with no drain current. This is an approximation, since Q_{d}(x) varies considerably when V_{n} is applied, to reflect the variation in V_{x}. However, Eq of the drain current is a fairly accurate description of drain current for low values of V_{D, }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 Q_{d}(x). Performing the integration of these equations for Q_{n}(x) one obtains:

Integration of this

The drain current is described by Eq. above for low V_{D. }Initially the channel appears as an essentially linear resistor, dependent on V_{G }.The conductance

of the channel in this linear region can be obtained with V_{D}<(V_{G}-V_{T}):

**Transconductance:
**

As the drain voltage is increased, the voltage across the oxide decreases near the drain, and Q_{n} 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 V_{D} into this equ,

The transconductance in the saturation range can be obtained approximately by differentiating the above equ with respect to the gate voltage: