There are two small-signal circuit models which are commonly used to analyze JFET circuits.
These are the hybrid-π model and the T model. The two models are equivalent and give identical
results. They are described below.
Let the drain current and each voltage be written as the sum of a dc component and a small-signal
ac component as follows:
iD = ID + id
vGS = VGS + vgs
vDS = VDS + vds
If the ac components are sufficiently small, we can write
where the derivatives are evaluated at the dc bias values. Let us define
The drain current can thus be written
The T model of the JFET is shown in Fig. 5(b). The resistor r0 is given by Eq. (15). The resistor rs is given by
where gm is the transconductance defined in Eq. (14). The currents are given by
The currents are the same as for the hybrid-π model. Therefore, the two models are equivalent.
Small-Signal Equivalent Circuits
Several equivalent circuits are derived below which facilitate writing small-signal low-frequency equations for the JFET. We assume that the circuits external to the device can be represented by Thévenin equivalent circuits. The Norton eqivalent circuit seen looking into the drain and the Thévenin equivalent circuit seen looking into the source are derived. Several examples are given which illustrate use of the equivalent circuits.
Simplified T Model
Figure 6(a) shows the JFET T model with a Thévenin source in series with the gate. We wish to solve for the equivalent circuit in which the source i'd connects from the drain node to ground rather than from the drain node to the gate node. We call this the simplified T model. Aside for the subscripts, the T model in Fig. 5(b) is identical to the T model for the BJT with rx = 0.
Therefore, the simplified T model for the JFET must be of the same form as the simplified T model for the BJT. Because ig = 0, the effective current gains of the JFET are α = 1 and β = ∞. The simplified T model is shown in Fig. 6(b), where i'd and rs are given by
Norton Drain Circuit
The Norton equivalent circuit seen looking into the drain can be used to solve for the response of the common-source and common-gate stages. Fig. 7(a) shows the JFET with Thévenin sources connected to its gate and source. The Norton drain circuit follows directly from the BJT Norton collector circuit with appropriate changes in subscripts and the substitutions α = 1, and β = ∞, and rx = 0. The circuit is given in Fig. 7(b), where id(sc) and rid are given by
id(sc) = Gmg.Vtg − Gms.Vts
The two transconductances Gmg and Gms are given by
For the case r0 >> Rts and r0 >> rs, we can write
id(sc) = Gm (vtg − vts)
Thévenin Source Circuit
The Thévenin equivalent circuit seen looking into the source is useful in calculating the response of common-drain stages. Fig. 8(a) shows the JFET symbol with a Thévenin source connected to the gate. The resistor Rtd represents the external load resistance in series with the drain. The Thévenin source seen looking into the source follows directly from the Thévenin emitter circuit for the BJT with appropriate subscript changes and the substitutions α = 1, β = ∞, and rx = 0. The circuit is shown in Fig. 8(b), where vs(oc) and ris are given by
When Rtd = 0, note that ris = rs//r0.
Summary of Models
Figure 9 summarizes the four equivalent circuits derived above.
Nombre: María José Nieto Cárdenas