Low frequency model (saturation)

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, C_OX 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 V_T0 the threshold voltage at V_BS=0.

Small variations of V_GS will result in small variations of I_DS. The correlation is described by the transconductance of the transistor determined by differentiating (3.2) with regard to V_GS:
 
Similarly, small variations of V_BS will result in small variations of I_DS. This is described by the back-bias transconductance g_mb of the transistor. Using (3.2-3.5) we get:
 
Finally, V_DS variations will also influence I_DS. The output conductance of the transistor is obtained by differentiating (3.1) with regard to V_DS:
 
The obtained small-signal parameters, g_m, g_mb and g_ds, 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.