4.2. Transistor Variable Incremental Relationships
As illustrated previously diagrammatically, for example, in Fig. 3.2, the MOSFET is a four-terminal device. The four-terminal version of the schematic symbol is repeated here in Fig. 4.2. The terminals again are the source, drain, gate, and body. The drain current and the three terminal-pair voltages are all interdependent such that iD = f(vDS, vGS, vSB). Use of the three-terminal schematic symbol for the transistor, as in Fig. 4.1, conveys the assumption that the body and source are connected. For an applied incremental Vgs, for example, there will be, in response, incremental drain current Id and incremental voltages Vds and Vsb. The linear model is based on relating the current to the three voltages. This is
Equation 4.1
Figure 4.2. Four-terminal NMOS schematic symbol in a common source configuration.
The linear-model representation is shown in Fig. 4.3. Figure 4.3(a) shows a current-source version. The body-effect parameter, gmb, is defined as positive. The minus sign is required as the partial derivative in (4.1) is negative. In Fig. 4.3(b) the body-effect current source is reversed to eliminate the minus sign, and the current source associated with gds is replaced with a resistance. The latter is possible as the voltage-dependent current source is between the same nodes as the voltage.
Figure 4.3. (a) Linear model that includes all contributions to the signal drain current, Id, as given in (4.1). The body-effect parameter, gmb, is a positive number such that current from the current source is in the direction opposite the arrow. (b) Current source of body effect is reversed to eliminate the minus sign, and a resistor replaces the gds current source.
In the following units, using the detailed functions (3.8) and (3.14), which relate the four variables, expressions, as used in SPICE, will be obtained for the three proportionality constants: transconductance parameter, gm, output conductance parameter, gds, and body-effect transconductance parameter, gmb. The results will be used to obtain numerical results for the circuit transconductance, Gm, for various cases.