7.3. Body Effect and Source-Follower Voltage Transfer Relation
Suppose now, as in Fig. 7.3, that the body terminal is connected to VSS, which is signal ground. Following the definition of the body-effect transconductance, gmb, the component of Id due to source-body voltage Vsb is [from (4.1)]
Equation 7.9
Since the body is at zero potential (signal), this is
Equation 7.10
This component of current can be included in the circuit, as shown in Fig. 7.3, with an additional resistance in parallel with RS of value 1/gmb. That is, the body-effect contribution to the drain current is a voltage-dependent current source, where the voltage is the same as that across the current source.
Figure 7.3. Source-follower signal equivalent circuit with body connected to VSS, which is signal ground. The body effect is taken care of for this case with a resistance of magnitude 1/gmb placed in parallel with RS along with rds = 1/gds.
With the body-effect addition, the source-follower gain expression is modified to the following:
Equation 7.11
The body-effect parameter is related to gm by [(4.11)]
gmb = ηgm
with
With the substitution of (4.11) in (7.11), the gain is
Equation 7.12
In modern integrated circuits, resistor RS will be replaced with a current-source output resistance, which is significantly greater than RS. The source-follower gain is, in this case, approximately (with no external load)
Equation 7.13
Parameter η will typically be in the range 0.1 < η < 0.2.
Note that the body effect degrades the “gain” significantly below the ideal unity. In the project on the source-follower circuit, we measure the voltage transfer function of the source follower for a range of dc drain current with body and source connected and with the body connected to VSS. The resulting curves will be compared to demonstrate the body effect on the transfer function. A curve fit of the SPICE equation to measured data will provide for an alternative determination of parameter γn. This value should be close to the value obtained from dc measurements.