## Friday, April 22, 2022

### Hawksford's Error Corection and "Distortion Selector"

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

Hawksford's error correction (H.ec, see my previous post) compares the output signal of a (near-unity gain) output stage with that at its input and adds the difference back to the input, thus correcting the error $\epsilon$ that the output stage introduces:

H.ec is equivalent to the following structure, which sometimes is called a "distortion selector":

"Equivalent" here means that the two schematics above have the same signal transfer function $$STF={H \over {1-B+HB}}$$ and error transfer function $$ETF = {{1-B} \over {1-B+HB}}$$

Ideal compensation in H.ec (i.e. $B \rightarrow 1$) corresponds to an infinite loop gain ${B \over {1-B}} \rightarrow \infty$ of the distortion selector.

Naturally, both H.ec and the distortion selector can be applied not only to a unity gain output stage, but to any amplifier with gain $1 / K$; one just needs to scale appropriately the output signal:

If H is an amplifier with feedback, there is no need to use a separate scaler K; one can use the existing feedback network of H:

It looks a bit complicated, but one practical implementation is straightforward:

Here, A is the "main" amplifier, R1R2 is its feedback network, and C is the distortion selector. Two of the four voltage adders are inside A and C, respectively, and the remaining two are implemented with R1R2.

The distortion selector C by itself is not distortion free, which can be ameliorated by giving it its own distortion selector:

Along the same lines, one can add C3, C4 and so on.

Obviously, in such a structure the stability problem arises. One possible solution was devised by John D. Yewen and described in his article "High-precision composite op-amps", published by Electronics & Wireless World in February 1987. In my next post, I will have a closer look at Yewen's solution.