# 4.3 MOSFET Common Drain Followers

As discussed under the section on JFETs, the common drain amplifier is also known as the source follower. The prototype amplifier circuit with device model is shown in Figure 4.3.1 . As with all voltage followers, we expect a non-inverting voltage gain close to unity with a high π_{ππ} and a low π_{ππ’π‘} .

As is usual, the input signal is applied to the gate terminal and the output is taken from the source. Because the output is at the source, biasing schemes that have the source terminal grounded, such as zero bias and voltage divider bias, cannot be used.

## Voltage Gain

The voltage gain equation for the common drain follower is developed as follows: We begin with the fundamental definition 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. The load is now located at the MOSFET’s source, and thus can be referred to as either π_{πΏ} or π_{π} .

(4.3.1)

or, if preferred

If ππππβ«1 , the voltage gain will be very close to unity; a desired outcome.

## Input Impedance

The analysis for source follower’s input impedance is virtually identical to that for the common source amplifier. The same commentary applies regarding the simplification of gate biasing resistors to arrive at the value of π_{πΊ} .

(4.3.3)

## Output Impedance

In order to determine the output impedance, we modify the circuit of Figure 4.3.1 by separating the load resistance from the source bias resistor. This is shown in Figure 4.3.2 .

Looking back into the source from the perspective of the load we find that the source biasing resistor, π
_{π}, is in parallel with the impedance looking back into the source terminal.

To find π_{π ππ’πππ} , note that the voltage at the source is π£_{πΊπ} and the current entering this node is π_{π·} . The ratio of the two will yield the impedance looking back into the source.

(4.3.4)

Therefore, the output impedance is

(4.3.5)

Looking at Equation 4.3.5 it is obvious that the higher the transconductance, the lower the output impedance. As noted earlier, a large transconductance also means that the voltage gain will be close to unity. As a general rule then, a large transconductance is desired for the source follower.

Time for a few illustrative examples.

Example 4.3.1

For the circuit of Figure 4.3.3 , determine the voltage gain and input impedance. Assume π_{πΊπ(πππ)} = β0.8 V and πΌ_{π·ππ} = 30 mA.

This amplifier uses self bias so we need to determine π_{π0}π
_{π} .

The DC source resistance is the 270 Ξ© biasing resistor resulting in π_{π0}π
_{π} = 16.2. From the self bias equation or graph this produces a drain current of 2.61 mA.

The voltage gain is

Finally, for the input impedance we have

Example 4.3.2

For the circuit of Figure 4.3.4 , determine the voltage gain and input impedance. Assume π_{πΊπ(πππ)} = β2.5 V and πΌ_{π·ππ} = 80 mA.

This follower uses a P-channel device with combination bias. Note that the source terminal is toward the top of the schematic. First, determine π_{π0}π
_{π} and the bias factor, π . Then the combination bias equation can be used to determine the drain current.

The DC source resistance is the 1.8 k Ξ© biasing resistor resulting in π_{π0}π
_{π} = 115.2. The bias factor is π_{ππ}/π_{πΊπ(πππ)} , or 4. The combination bias equation (Equation 10.9) yields πΌ_{π·} = 6.67 mA.

We can now find the transconductance and voltage gain.

The voltage gain is

Lastly, the input impedance is