I don't think the problem is as simple and straightforward as it looks.
Let us take some examples:
The amplifiers have a gain of -1, and the distortion is small enough (let's say 1%) to render higher intermodulation products negligible.
In this case, the second amplifier will add harmonics in antiphase with that of the first, and the final result will be ~0%.
Another example: the amplifiers have a gain of 1, and the distortion consist purely of clipping.
In this case, once the signal has been clipped, it will pass unchanged through the other stage.
Etc etc
I doubt it is possible to find a correct generalization.
Let us take some examples:
The amplifiers have a gain of -1, and the distortion is small enough (let's say 1%) to render higher intermodulation products negligible.
In this case, the second amplifier will add harmonics in antiphase with that of the first, and the final result will be ~0%.
Another example: the amplifiers have a gain of 1, and the distortion consist purely of clipping.
In this case, once the signal has been clipped, it will pass unchanged through the other stage.
Etc etc
I doubt it is possible to find a correct generalization.
It is very complex. However you can calculate the total distortion mathematically, if you have time enough....
The simplest example is an amplifier with purely second harmonic distortion. This is input to the next amplifier (also with purely second harmonic distortion). The output is the wanted squared gain (first harmonic), a second harmonic (also a function of the gain in the amplifier), and a third and fourth harmonic (both gain dependent, in different ways). In other words: it is a nonlinear function, and you cannot predict the distortion in a general manner without knowing the spectral properties of the distortion.
The simplest example is an amplifier with purely second harmonic distortion. This is input to the next amplifier (also with purely second harmonic distortion). The output is the wanted squared gain (first harmonic), a second harmonic (also a function of the gain in the amplifier), and a third and fourth harmonic (both gain dependent, in different ways). In other words: it is a nonlinear function, and you cannot predict the distortion in a general manner without knowing the spectral properties of the distortion.
THD alone does not give you enough information. However, you could make an estimate, given certain vaguely reasonable assumptions.
Assume the THD is pure second harmonic. Then the two together would give either 20% or 0% second harmonic, depending on whether the amplifer inverted or not. You would also get 1% third harmonic and 0.1% fourth harmonic in either case.
This shows the limitations of distortion cancellation. It always introduces higher order distortion, so better to design for low distortion in each stage.
Assume the THD is pure second harmonic. Then the two together would give either 20% or 0% second harmonic, depending on whether the amplifer inverted or not. You would also get 1% third harmonic and 0.1% fourth harmonic in either case.
This shows the limitations of distortion cancellation. It always introduces higher order distortion, so better to design for low distortion in each stage.
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As an example: Here is a 2SK170 FET amplifier fed with 5mV (peak). The output is scaled down to feed a new 2SK170 FET amplifier with about the same amplitude. As you can see, the distortion of the last amplifier is much lower due to cancellation. But remember that in reality, the second amplifier normally would have the output signal of the first amplifier as an input signal....
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