## Overall Feedback Versus Local Feedback

It is one of the fundamental principles of negative feedback that if you have more than one stage in an amplifier, each with a fixed amount of open-loop gain, it is more effective to close the feedback loop around all the stages, in what is called an overall or global feedback configuration, rather than applying the feedback locally by giving each stage its own feedback loop. I hasten to add that this does not mean you cannot or should not use local feedback as well as overall feedback–indeed one of the main themes of this book is that it is a very good idea, and indeed probably the only practical route to very low distortion levels.

It is worth underlining the effectiveness of overall feedback because some of the less informed audio commentators have been known to imply that overall feedback is in some way decadent or unhealthy, as opposed to the upright moral rigour of local feedback. The underlying thought, insofar as there is one, appears to be that overall feedback encloses more stages each with their own phase shift, and therefore requires compensation which will reduce the maximum slew-rate. The truth, as is usual with this sort of moan, is that this could happen if you get the compensation all wrong; so get it right, it isn’t hard.

It has been proposed on many occasions that if there is an overall feedback loop, the output stage should be left outside it. I have tried this, and believe me, it is not a good idea. The distortion produced by an output stage so operated is jagged and nasty, and I think no one could convince themselves it was remotely acceptable if they had seen the distortion residuals.

**Figure 3.15** shows a negative feedback system based on that in **Figure 3.1** at the start of the chapter, but with two stages. Each has its own open loop gain A, its own NFB factor b, and its own open-loop error Vd added to the output of the amplifier. We want to achieve the same closed-loop gain of 25 as in **Table 3.1**, and we will make the wild assumption that the open-loop error of 1 in that table is now distributed equally between the two amplifiers A1 and A2. There are many ways the open- and closed-loop gains could be distributed between the two sections, but for simplicity we will give each section a closed-loop gain of 5; this means the conditions on the two sections are identical. The open-loop gains are also equally distributed between the two amplifiers so that their product is equal to column 3 in **Table 3.1** below. The results are shown in **Table 3.4**; columns 1-7 show what’s happening in each identical loop, and columns 8 and 9 give the results for the output of the two loops together, assuming for simplicity that the errors from each section can be simply added together; in other words, there is no partial cancellation due to differing phases, and so on.

This final result is compared with the overall feedback case of **Table 3.1** in **Table 3.5**, where column 1 gives total open-loop gain, and column 2 is a copy of column 7 in **Table 3.1** and gives the closed-loop error for the overall feedback case. Column 3 gives the closed-loop error for the two-stage feedback case.

It is brutally obvious that splitting the overall feedback situation into two local feedback stages has been a bad move. With a modest total open-loop gain of 100, the local feedback system is barely half as effective. Moving up to total open-loop gains that are more realistic for real power amplifiers, the factor of deterioration is between six and forty times–an amount that cannot be ignored. With higher open-loop gains the ratio gets even worse. Overall feedback is totally and unarguably superior at dealing with all kinds of amplifier errors, though in this book distortion is often the one at the front of our minds.

While there is space here to give only one illustration in detail, you may be wondering what happens if the errors are not equally distributed between the two stages; the signal level at the output of the second stage will be greater than that at the output of the first stage, so it is plausible (but by no means automatically true in the real world) that the second stage will generate more distortion than the first. If this is so, and we stick with the assumption that open-loop gain is equally distributed between the two stages, then the best way to distribute the closed-loop gain is to put most of it in the first stage so we can get as high a feedback factor as possible in the second stage. As an example, take the case where the total open-loop gain is 40,000.

Assume that all the distortion is in the second stage, so its open-loop error is 1 while that of the first stage is zero. Now redistribute the total closed-loop gain of 25 so the first stage has a closed-loop gain of 10 and the second stage has a closed-loop gain of 2.5. This gives a closed-loop error of 0.0123, which is about half of 0.0244, the result we got with the closed-loop gain equally distributed. Clearly things have been improved by applying the greater part of the local negative feedback where it is most needed. But…our improved figure is still about twenty times worse than if we had used overall feedback.

In a real power amplifier, the situation is of course much more complex than this. To start with, there are usually three rather than two stages, the distortion produced by each one is level-dependent, and in the case of the voltage-amplifier stage the amount of local feedback (and hence also the amount of overall feedback) varies with frequency. Nonetheless, it will be found that overall feedback always gives better results.

Excerpt from* Audio Power Amplifier Design, 6th edition* by Douglas Self © 2013 Taylor & Francis Group. *All Rights Reserved.*

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