4.4. Body-Effect Transconductance Parameter
For circuits in which the signal Vsb is nonzero, there will be an additional component of Id, gmbVsb. An example is the circuit of Fig. 4.1 but with body terminal connected to ground. This feature is added to the circuit as shown in Fig. 4.4. The proportionality constant for this case, gmb, is the body-effect transconductance. It is defined as
Equation 4.9
Figure 4.4. Signal circuit with the addition of a current source due to the body effect. In this example, Vb = 0 V and Vsb = IdRS.
which is [with (3.8) and (3.14) for iD and Vtn]
Equation 4.10
The minus sign is consistent with a current source in the opposite direction from that of Fig. 4.4 (as shown in Fig. 4.3) as iD is defined as positive into the drain. The preference is to turn the current source around as in Figs. 4.3 and 4.4 and use positive gmb. The result for gmb is a factor, η, times gm, that is
Equation 4.11
For γn = 0.5 V1/2, VSB = 5 V, and 2ΦF = 0.7 V, gmb = 0.1gm (η = 0.1). Note that gmb is not zero even with the source connected to the body [i.e., with VSB = 0 in (4.11)]. However, signal Vsb is zero in such a case, such that gmb does not have to be taken into account. In general, even with VSB ≈ 0 it is possible for Vsb ≠ 0, in which case, gmb must be included in the model (e.g., in Project 8 on the study of the source-follower stage, at the low end of the bias current scan).