FET as amplifier

Similar to the Bipolar junction transistor, JFET can also be taken in use as an amplifier. The equivalent circuit of AC of a JFET is shown in the figure 1.

Figure 1

The resistance in between the gate and the source R_GS is quite high. The drain of a JFET behaves like a current source with the value of g_m V_gs. This model is applicable at the low frequencies.

From AC equivalent model

Amplification factor µ for FET can be defined as

When V_GS = 0, gm has its maximum value. The maximum value is designated as g_mo.

Again consider the equation,

As V_GS increases, g_m decreases linearly.

Measuring I_DSS and g_m, V_GS(off) can be determined

Figure 2, shows the common source amplifier.

Figure 2

When a small AC signal is coupled into the gate it creates variations in gate source voltage. This generates sinusoidal drain current. As the AC current flows through the drain resistor. The amplified AC voltage is obtained at output. Increase in the gate source voltage generates more drain current, which shows that the drain voltage is decreasing. As the positive half cycle of input voltage generates the negative half cycle of output voltage, we obtain the phase inversion in a CS amplifier.

The AC equivalent circuit is shown in the figure 3.

Figure 3

The AC output voltage can be given as                v_out = - g_m, v _gS R_D

Hear the negative sign means phase inversion. Because the AC source is directly connected between the gate source terminals hence the AC input voltage equals

V_in = V_gs

The voltage gain can be given by

The further simplified model of the amplifiers is shown in the figure 4.

Figure 4

Hear Z_in is the input impedance. At the low frequencies, this is the parallel combination of R₁|| R₂|| R_GS. Since R_GS  is quite large, it is parallel combination of R₁  & R₂. A Vin  is output voltage and RD  is output impedance.

Because of the nonlinear transductance curve, the JFET distorts large signals, as shown in the  figure 5.

Given a sinusoidal input voltage, we obtain a non-sinusoidal output current in which the positive half cycle is elongated and negative cycle is compressed. This kind of distortion is called as Square law distortion because transductance curve is parabolic.

                                  Figure 5                                                                                                    Fig. 6

The distortion is undesirable for an amplifier. One method to minimize this is to keep the signal small. In that case the part of curve is used and operation is nearly linear. At times swamping resistor is taken in use to minimize the distortion and gain constant. Now source is no longer AC ground as shown in the figure 6.

Drain current through r_S produces an AC voltage in between the source and ground. If r_S is large sufficiently the local feedback can swamp out non-linearity of the curve. Then the voltage gain reaches the ideal value of R_D / r_S.

Since R_GS  reaches  infinity thus, all the drain current  flows through r_S  producing a voltage drop of g_m V_gS r_S. The Ac equivalent circuit is shown in the figure 7.

Fig. 7

The voltage gain decreases but voltage gain is quite less effective by making change in gm. r_S  should be greater than 1 / g_m only then

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