How Negative Feedback eliminates crossover distortion

First, listen to the following .wav files to hear the difference of an audio signal played through an amplifier with crossover-distortion and another one played through a negative feedback linearized amplifier.

1. Linearized (Negative Feedback): Piano

2. Crossover distortion (no Negative Feedback): Piano

3. Linearized (Negative Feedback): Beethoven's 9th Symphony, Part I
4. Crossover distortion (no Negative Feedback): Beethoven's 9th Symphony, Part I

Hear the difference? Very annoying and unpleasing the sound of crossover distortion. Amongst audiophiles, low amounts of crossover distortion is far worse than large amounts of audio clipping.
(If you are not interested in electronics, go to the end of the post where crest factor is explained.)

(Note: output .wav files were produced through an LTSpice amplifier circuit. This experiment alone, proves the consistency of basic negative feedback theory.)

Now, we will see how negative feedback efficiently works to linearize non-linear components in the forward path of a signal and especially how it decreases the crossover distortion of an amplifier.

Consider a Class B push-pull amplifier output stage with complementary NPN/PNP transistors used in emitter-follower configuration (Fig. 1).

Fig.1 Basic class B amplifier

 We know that all transistors have an inherent turn-on base-emitter voltage Vbe, that need to be overpassed in order the transistor to come into the active region of its operation. Working in a Class B topology, this Vbe, causes a problem; a dead-zone when the input signal is smaller that Vbe and thus not amplified because transistors are in their cutoff region. Of course this causes distortion in the output signal, the so called crossover-distortion (because it occurs when the signal crosses the x-axis in the time domain), which is very audible and annoying and huge efforts are given to eliminate it in audiophile amplifiers. Fig.2 shows the simulation of the output of the amplifier  for 1kHz sine-wave at 1Vrms.

Fig.2 Crossover distortion in Class B amplifier

Notice the dead-zone that occurs at around 0 μsec, 500 μsec ανδ 1 μsec and its duration is the time the sine wave spends below Vbe (NPN) or -Vbe (PNP).

Consider now the topology in seen in Fig.3, enhanced with a differential input stage and global negative feedback.

Fig.3 Class B with NFB

In Fig.4 is the simulation of the output. We see that there is no crossover distortion in the output waveform and that is because the global negative feedback worked to linearize the output in order to accurately follow the input signal (basic feedback theory).

Fig.4 Output of the amplifier with NFB

This does not mean that the turn-on voltage of the transistors (the dead-zone) is gone, but the negative feedback with the differential input stage created an error signal at point in2 in Fig.3, which has such a shape to customize the output. Lets see in Fig.5 what is the waveform of the output of the input stage (in2). We can metaphorically say the error signal is the complementary of the open-loop output signal (with no negative feedback) and when they sum they create the linearized output that is an amplified version of the input.

Fig.5 Output of the differential input stage.

Combining error, open-loop output and closed-loop output signals we get the plot at Fig.6.

Fig.6 Combined plot

Coming back to the music (.wav files in top of this post), we see that cross-over distortion has a larger effect on signals that are of low amplitude, because they spend most time in the transistors dead-zone. So, listening to piece of classical music for example, which has a lot of dynamics in playing (many low passages, etc), very little amount of crossover distortion can ruin the whole listening experience. The song parts that are low in amplitude (pianissimo) are never heard, because they are in the dead-zone and silence has taken their place. In Fig.7 and Fig.8 the two waveforms of a part of Beethoven's 9th Symphony are compared. The former being the output of a circuit with negative feedback and thus no crossover distortion and the latter the output of a circuit with crossover distortion.

Fig.7 No crossover distortion

Fig.8 Crossover distortion

Notice the low passages of the musical piece as seen in Fig.7; they are disappeared in Fig.8 and almost silence has taken their place. In practice it will be even worse; there will be no silence in their place but noise, thus affecting the SNR ratio of the whole waveform. In Fig.7, noise is overpassed by the signal (greater SNR ratio). On the other hand, listening to a song that is compressed to be as loud as possible (low dynamics), less information is lost, because the signal spends most time in the active region of the transistors (close to saturation). Thus, the missing of information because of the crossover distortion is determined by the crest factor of the waveform of the audio recording. Crest factor is the ratio of peak values to the rms value of amplitude of the waveform.
$$ C=\frac{|V|_{peak}}{V_{rms}} $$