# 2.3 Common Source Amplifier

The common source amplifier is analogous to the common emitter amplifier. The prototype amplifier circuit with device model is shown in Figure 2.3.1 .

This circuit includes a swamping resistor, π_{π} . The input signal is presented to the gate terminal while the output is taken from the drain.

## Voltage Gain

An equation for the voltage gain, π΄_{π£}, is developed as follows. 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.

(2.3.1)

If there is no swamping resistor, the first portion of the denominator drops out and the gain simplifies to βπ_{π}β
π_{πΏ} . The swamping resistor in the source, π_{π}, plays the same role here as it did in the BJT: it helps to stabilize the gain and reduce distortion. It does so at the expense of voltage gain.

## Input Impedance

Referring back to Figure 2.3.1 , the input impedance of the amplifier will be ππΊ in parallel with the impedance looking into the gate terminal, π_{ππ(πππ‘π)}. For the non-swamped case, this will be π_{πΊπ}. At low frequencies π_{πΊπ} is very large, well into the megohms. In most practical circuits, π_{πΊ} will be much lower, hence

Z_{in} = r_G || r_{GS} \approx r_G \](2.3.2)

Theoretically, for swamped amplifiers π_{ππ(πππ‘π)} will be higher than π_{πΊπ} but this is a moot point. In either case, it is relatively easy to obtain a high input impedance, certainly much easier than it is for typical single-device BJT amplifiers.

It might be easy to become complacent and simply assume that π_{πΊ} sets the input impedance and that’s the end of it. This would be a mistake. As mentioned earlier, with impedances this high, we cannot ignore items such as junction capacitance. For example, for a general purpose device a typical value for πΆ_{ππ π } , the total input capacitance, may be in the vicinity of 5 to 10 pF. This capacitance appears in parallel with π_{πΊ}. If this amplifier is used for ultrasonic signals, the capacitive reactance, π_{πΆ}, would be as low as 160 k Ξ© at 100 kHz. Although this is high compared to typical BJT circuits, it’s less than the π
_{πΊ} values commonly used for biasing. At higher frequencies, the situation is even worse as π_{πΆ} decreases with frequency. Also, we are ignoring the Miller effect here which makes the situation even worse than even worse, so perhaps we can say that it’s even worser, which is a claim we could also make regarding the grammar of this sentence.

## Output Impedance

To investigate the output impedance, we’ll refer to Figure 2.3.2 . This circuit is very similar to that of Figure 2.3.1 . The major difference is that the AC load equivalent has been split into its two components, the load itself, π
_{πΏ}, and the drain biasing resistor, π
_{π·}.

From the vantage point of π
_{πΏ}, peering back into the amplifier we see π
_{π·} in parallel with the impedance at the drain. At the drain we find the current source, π_{π·} . The internal impedance of this equivalent current source is very high compared to typical values for π
_{π·} (hundreds ofΒ Ξ© ), therefore we can approximate the output impedance as

*** QuickLaTeX cannot compile formula: \[Z_{out} \approx R_D \label\] *** Error message: Emergency stop.

(2.3.3)

It should be noted that all forms of DC bias discussed in the previous chapter are game here. There are a few limitations to be aware of, though. For example, when using constant voltage bias, swamping is not possible as that bias form does not use a source resistor. In contrast, self bias and combination bias include a source resistor so swamping is a possibility, however, π
_{π} may need to be split and partially bypassed to achieve the desired results. Finally, constant current bias is not well-positioned to use swamping as that would require some additional work to fit in a new π
_{π} along with the current source. More typically, the current source will just be bypassed with a capacitor to produce a non-swamped amplifier.

Example 2.3.1

Determine the voltage gain and input impedance for the circuit shown in Figure 2.3.3 . Assume πΌπ·ππ=15 mA and ππΊπ(πππ)=β3 V.

This is an unswamped common source amplifier with constant current bias. We can determine π_{ππ} via inspection.

To find the voltage gain, we’ll first need to find πΌ_{π·} and π_{π0} in order to find π_{π}.

Knowing the current and maximum transconductance, we can find π_{π} through the use of Equation 10.2.4.

Example 2.3.2

Determine the voltage gain and input impedance for the circuit shown in Figure 2.3.3 . Assume πΌ_{π·ππ}=24 mA and π_{πΊπ(πππ)}=β4 V.

This is an unswamped common source amplifier with self bias. Once again, we can determine π_{ππ} via inspection.

To find the voltage gain, we’ll first need to find π_{π0}. Also, we can take a shortcut and find the normalized drain current from the self bias graph instead of finding πΌ_{π·} itself.

π
_{π} is 1.5 kΞ©, therefore π_{π0}π
_{π}=18. From the self bias graph this produces a normalized drain current of 0.08.

Again, there is no swamping so π_{π}=0. The gain formula reduces to

We will now turn our attention to the effect of swamping. As in the BJT case, we expect to sacrifice gain and in return, see an improvement in distortion. We shall examine this through the use of a simulation.

## Computer Simulation

A common source amplifier using self bias is entered into the simulator as shown in Figure 2.3.5.

Reasonable device values for this model are πΌ_{π·ππ}=40 mA and π_{πΊπ(πππ})=β2.3 V. Based on these we find

Given π
_{π}=1 k Ξ© , the self-bias equation yields

The results of a transient analysis are shown in Figure 2.3.6 for a 100 mV peak input signal.

The input signal was raised to 240 mV peak in order to keep the output signals of the two versions at the same amplitude. The symmetry appears to be better here and the gain works out to β4.85, just a few percent low.

Total harmonic distortion (THD) analysis is performed next. The results are shown in Figures 2.3.8 and 2.3.9 . To keep the comparison fair, the input levels are adjusted to maintain similar output voltages. The non-swamped results are seen in Figure 2.3.8 , and as expected based on the waveform asymmetry, the THD is relatively high at roughly 4%. The swamped version scores better at just over 1.6%, although this is still not stellar performance.

It is interesting to note that while the voltage gain of the swamped amplifier has dropped to 41% of the non-swamped gain, the THD has dropped to 41% of the nonswamped THD. In fact, given the square-law nature of the characteristic curve, we would expect the distortion to be lower if we used smaller signals. To verify this, the THD simulation is run again for the swamped amplifier, but now using an input signal ten times smaller at only 24 mV peak. The result is shown in Figure 2.3.10 .

The resulting THD is markedly lower for an order of magnitude improvement. We’re now at least approaching βhi-fiβ territory.