Consider the N-channel MOS transistor in Figure 3.1 and
assume that it is saturated.
Then the drain-source current is given by:
where is the mobility of the charge carriers, COX is the gate-oxide
capacitance per unit area, W and L are channel width and length,
is the channel length modulation factor,
is the
substrate effect factor,
is the Fermi potential, and VT0
the threshold voltage at VBS=0.
Small variations of VGS will result in small variations of
IDS. The correlation is described by the
transconductance of the transistor determined by differentiating
(3.2) with regard to VGS:
Similarly, small variations of VBS will result in small
variations of IDS. This is described by the
back-bias transconductance gmb of the transistor. Using
(3.2-3.5) we get:
Finally, VDS variations will also influence IDS. The output
conductance of the transistor is obtained by differentiating
(3.1) with regard to VDS:
The obtained small-signal parameters, gm, gmb and gds,
describe the behaviour of the MOS transistor at low frequencies, and the
corresponding small-signal equivalent diagram is shown in
Figure 3.2. Note that the model is valid at low frequencies
only.
Figure 3.2: Small signal LF equivalent diagram for the MOS transistor.