**Generalized FET Amplifier Circuit:**

The analysis of a common source amplifier with a source resistance R_{S}, a common gate amplifier and a common drain amplifier at low frequencies may be made by considering the Generalized FET Amplifier Circuit given in Fig. 13.55. The Generalized FET Amplifier Circuit consists of three independent signal sources (V_{in} in series with the gate, V_{s} in series with the source, and V_{a} in series with the drain).

For common source amplifier V_{a} = V_{s} = 0, and the output V_{out1}Â is taken at the drain terminal D, as shown. For common gate circuit V_{in} = V_{a} = 0, the input signal is V_{s} with a source resistance R_{S}, and the output V_{out1}Â is again taken at the drain terminal D. For the common drain (or source follower) R_{D} = 0, V_{s} = V_{a} = 0, the input signal voltage is V_{in} and the output V_{out2}Â is taken at the source terminal, as shown in Fig. 13.55. The signal-source resistance is ineffective as it is in series with the gate which draws almost no current.

Thevenin’s equivalent circuit from drain to ground and from source to ground are given in Figs. 13.56 (a) and 13.56 (b) respectively. From the circuit given in Fig. 13.56 (a) it is concluded that “looking into the drain” of the FET it is seen (for small signal operation) an equivalent circuit consisting of two generators in series, one of -Î¼ times the gate signal voltage V_{in }and the second (Î¼ + 1) times the source-signal voltage V_{s} and the resistance r_{d}+(Î¼ + 1) R_{S}. Note that the source-signal voltage V_{s }and the resistance in the source lead are both multiplied by the same factor, (Î¼ + 1).

**1. Common Source Amplifier With An Unbypassed Source Resistor:**

In Fig. 13.56 (a) substituting V_{a} = V_{s} = 0, we have

Voltage gain

Note that, for R_{S} = 0, the above equation reduces to that Eq. (13.41). The minus sign indicates a phase shift of 180Â° between input and output.

Resistance R_{out}, looking into the drain is increased by (Î¼ + 1)R_{S}Â from its value r_{d} for R_{S} = 0. The net output resistance Râ€²_{out} taking R_{D} into account is given as

It is observed that with the addition of R_{S}, voltage gain is reduced while the output impedance is increased. The input impedance is extremely high (100 MÎ© or so) since gate junction is reverse biased.

**2. Common Gate Amplifier: **

In Fig. 13.56 (a) substituting V_{in}Â = V_{a}Â = 0,Â we have

Voltage gain,

Since A_{v} is positive, there is no shift between input and output. Also since g_{m} â‰« g_{d}, the magnitude of amplification is approximately the same as for the common source amplifier circuit with R_{S}Â â‰ 0.

The output resistance is given by Eq. (13.53), and unless R_{S} is quite small, output resistance will be much larger than r_{dÂ }|| R_{D}.

The input impedance Z_{in}, between source and ground is obtained from seeing Fig. 13.56 (b)

The common gate amplifier with its low input impedance and high output impedance has few applications.

**Output From Source:** From Fig. 13.56 (b) it is concluded that “looking into the source” of the FET it is seen (for small-signal operation) an equivalent circuit consisting of two generators in series, one of value Âµ/(Âµ + 1) times the gate-signal voltage v_{in} and the second 1/Î¼ + 1 times the drain-signal voltage v_{a} and a resistance r_{d}Â + R_{D}/Î¼ + 1.

**3. Common Drain Amplifier:**

Substituting V_{s} = V_{a} = 0 and R_{D} = 0 in Fig. 13.56 (b), we have

Voltage gain,

The output impedance Z_{out} of the source follower at low frequencies (with R_{D} = 0 and with R_{S} considered external to the amplifier) is, from Fig. 13.56 (b),