Linearity of Transistor Amplifier Stages

This article demonstrates the impact of source impedance on a succeeding stage lacking negative feedback. It will be shown that a small amount of negative feedback (NFB) works wonders for maintaining a linear response. Added source impedance also helps (when necessary), but negative feedback is superior.

This LTspice experiment was inspired by the article Linearity of the Transistor Amplifier, from Wireless World May 1972.

Consider a pair of almost equal common emitter stages, with identical ramp signals going into both. Q1 has no emitter resistor, so will have a maximum gain depending upon the transistor's Beta. Q2 does have a low valued emitter resistor, effectively giving it some negative feedback. The gain of this stage is reduced to about 40 (20k/500).

Both Q1 and Q2 are fed by a signal source with a source resistance of 25 ohms (quite low). This might happen if these transistors were being fed by an emitter follower stage, for example. What the simulation will show is that stage Q1 will experience much higher distortion than Q2.

The linearity problem resolves around the fact that the input impedance of the Q1 stage (especially) changes as it's collector current changes (or that the transistor has an exponential response). If we assume the midpoint Q1 collector current value of 280uA, the Q1's re (internal transistor emitter resistance) is about 89 ohms:

Assuming about 300 ohms for rb, and Beta=300, this causes the Q1 input impedance ri to be:

But as Q1 collector current increases near saturation, re becomes:

Re-evaluating the input impedance for Q1, we get:

The input impedance for Q1 has changed from 27k ohms to 12.6k ohms near maximum conduction. The input impedance changed to less than half of it's original at the midpoint! This impacts the amplification of the signal as we'll see next.

The red plot shows the voltage being injected into the base of each transistor. It is a slowly rising ramp, with the plot starting just below the transistor's initial conduction point.

The yellow plot is the current in the collector of Q1, which is shown as I(R1). You can immediately see how the plot is exponential in nature, and thus very non-linear. The final half of Q1's current excursion is the most linear, but the initial (lower) half is not.

Finally, the blue plot shows the collector current for Q2. It starts out non-linear as the transistor starts to conduct, but then quickly straightens out as the transistor moves into it's active region.

Q2's amplifying response clearly shows less gain (lower slope) than Q1 but also is clearly is very linear. This was achieved because as Q2 begins to conduct, a small amount of amplified signal voltage appears across Q2's emitter resistor. Doing so causes the voltage between it's base and emitter to be reduced, effectively causing negative feedback.

The negative feedback is what is responsible for taking a non-linear amplifying stage and correcting it so that the output result is a faithful reproduction of the input signal. The Q2 stage has become linear in operation.

If we modify the circuit to bias both transistors about midway through their active regions and supply a 22mV sine wave signal, we can examine the outputs for distortion.

The plots at right show the results of a 60Hz sine wave being amplified by both Q1 and Q2. The upper plot shows the result of analyzing the output of Q1. Notice the fundamental signal at 60Hz, but then the added distortion products to the right of it.

Q2's output on the other hand looks very clean, as expected.

If you absolutely must avoid negative feedback (maybe for fewer parts and high gain), then the only alternative is to increase the source resistance.

We calculated an approximate midpoint input impedance of 27k. If we multiply that by about 10 as a starting point and then add a resistor in series with the base of 270k ohms (R6), we substantially improve the stage's linearity at the expense of gain.

From the spectrum plot at left, you can see some improvement, though the result is still inferior to Q2's result.

Increasing the source resistance makes the signal source appear as a current source flowing into a lower impedance input. However, as more input resistance is added, the more the stage gain is lowered and noise increases.

One final observation is the fact that there is an even order harmonic (the fundamental is 60Hz, and the next harmonic is at 120Hz). Even harmonics only show when the generated wave form is asymmetrical. This tells use that the sine wave is experiencing a different distortion in one half of the wave form from the other half. From what we saw earlier, it is the negative half of the input wave that gets the most distorted. This is the region where the exponential curve was most pronounced.

• The Linearity of the Triode Tube
• The Linearity of the Pentode Tube