# 2.4 Common Drain Amplifier

The common drain amplifier is analogous to the common collector emitter follower. The JFET version is also known as a source follower. The prototype amplifier circuit with device model is shown in Figure 2.4.1 . As with all voltage followers, we expect a non-inverting voltage gain close to unity, a high π_{ππ} and low π_{ππ’π‘}.

The input signal is presented to the gate terminal while the output is taken from the source. Many bias circuits may be used here as long as they do not have a grounded source terminal such as constant voltage bias.

## Voltage Gain

In order to develop an equation for the voltage gain, π΄_{π£}, we follow the same path we took with the common source amplifier earlier in this chapter. First, we start with the fundamental definition, namely that voltage gain is the ratio of π£_{ππ’π‘} to π£_{ππ}, and proceed by expressing these voltages in terms of their Ohm’s law equivalents.

(2.4.1)

Equation 2.4.1 is very similar to the gain equation derived for the swamped common source amplifier; the notable changes being the lack of the minus sign indicating that this circuit does not invert the signal, and π_{πΏ} replacing π_{π} in the denominator. It is worth remembering that π_{πΏ} here is the AC source resistance while in the common source amplifier π_{πΏ} is the AC drain resistance. To avoid potential confusion, this equation could also be written as

(2.4.2)

In any event, the goal is to make sure that π_{π}π_{π}β«1 . By doing so, the voltage gain will be very close to unity.

## Input Impedance

The analysis for common drain input impedance is virtually identical to that for the swamped common source amplifier. The result is replicated here for convenience.

(2.4.3)

## Output Impedance

In order to investigate the output impedance, we’ll separate the load resistance from the source bias resistor, as shown in Figure 2.4.2.

From the position of π
_{πΏ}, looking back toward the source we find π
_{π} in parallel with the impedance looking back into the source terminal. The voltage at this node is π£_{πΊπ} and the current entering this node is π_{π·}. The ratio of the two must yield the impedance looking into the source.

(2.4.4)

Therefore, the output impedance is

(2.4.5)

We can expect this value to be much smaller than the output impedance of typical common source amplifiers.

Example 2.4.1

For the follower shown in Figure 2.4.3 , determine the input impedance and output voltage. Assume π_{ππ}=100 mV, πΌ_{π·ππ}=30 mA, π_{πΊπ(πππ)}=β2 V.

This is a follower using self bias. We’ll find π_{π} via the self bias graph.

π
_{π} is 1 k Ξ© , yielding 30 for π_{π0}π
_{π} . The normalized drain current from the self bias graph is approximately 0.05.

Thus π_{ππ’π‘} is 71.6 mV. By inspection, π_{ππ} may be approximated as 2.2 M Ξ© .

Example 2.4.2

For the circuit shown in Figure 2.4.4 , determine the input impedance and output voltage. Assume π_{ππ}=100 mV, πΌ_{π·ππ}=36 mA, π_{πΊπ(πππ)}=3 V.

This follower uses combination bias with a P-channel JFET. Note that the source is at the top. We’ll find π_{π} via the combination bias graph for π=3 ( π=π_{ππ}/_{ππΊπ(πππ)}) .

π
_{π} is 1.8 kΞ©, yielding 43.2 for π_{π0}π
_{π}. The normalized drain current from the π=3 combination bias graph is approximately 0.17.

Thus π_{ππ’π‘} is 86.4 mV. By inspection, π_{ππ} may be approximated as 390 k Ξ© .