## A high Feedback Amplifier Example.

The diagrams show the effects of feedback on the output stage distortion of my MJR6 mosfet amplifier. This circuit uses high feedback loop gain to reduce distortion to very low levels. For now ignore input and driver stage distortion, and suppose there was distortion D at the output. Looking at the voltage gain round the feedback loop we find that after passing round the feedback loop the distortion at the input of the output stage is 10,000 times the output distortion D.

There are two ways we can specify the output stage distortion. One is the distortion percentage at the output of the output stage for an undistorted sinewave applied to its input. The second, and more useful specification is the distortion we need to add at the input of the output stage so that its output is an undistorted sinewave. These two distortion figures can be expected to be about the same percentages, but the frequency spectra can be very different. An extreme example of this difference is for a square-law amplifier stage, such as a single undegenerated fet. In this case an undistorted sinewave input will produce an output distortion consisting entirely of the second harmonic (plus a d.c. term), but if we want to produce an undistorted sinewave output the required input is given by a square-root function, and includes an infinite series of harmonics.
In a closed loop amplifier neither of these two options are correct because neither input nor output of the output stage is undistorted, but the example of the MJR-6 has output stage distortion 10,000 times higher at the input than the output, so the second alternative is in this case by far the more useful.

Suppose we use a moderately sensitive speaker producing 90dB/watt, and the sound level of the music signal is 90dB at a certain instant, then the output voltage will be about 3V. At this level the distortion of the MJR6 output stage would be around 5%.

Returning to our 3V output, the signal at the input of the output stage will also be close to 3V, with distortion 5% = 150mV = 10,000D
From this we find D = 15uV, the distortion at the amplifier output, which heard alone would have a sound level of -16dB, well below the nominal 0dB threshold of hearing.

The 'threshold of hearing' is in practice not a very precise level. I tried my own experiment using a test subject with excellent hearing, and found that using one of my MS20 speakers and listening at 1 metre distance to a 3kHz sinewave the minimum audible level was produced by 300uV across the speaker, so the 15uV mentioned above would be 26dB lower than this, and would be accompanied by the undistorted part of the signal at 90dB, so it seems safe to assume the distortion is far below audibility.

The assumption that input stage distortion is small can be justified by looking at the signal levels in the circuit shown next:

Here we have the same output of 3V, and to achieve this with an open-loop gain of 200,000 the signal at the input of the input stage is just 15uV. The cfp input stage used in the MJR6 is highly linear at this signal level, and even the open-loop distortion will be low . Add the distortion reduction from 80dB negative feedback and the contribution from the input stage becomes insignificant.

The distortion levels rise above 5kHz where the loop gain starts to fall, but the sensitivity of our ears falls at high frequencies, and the distortion will remain below the threshold of hearing.

The frequency spectrum of the output distortion D is the same as that at the input of the output stage apart from being 10,000 times lower, so the closed-loop distortion has almost exactly the same frequency spectrum as the signal needed at the input of the output stage to give a zero distortion output. This is another way of understanding the widely mentioned example of how adding feedback to a square-law amplifier adds high order harmonics which were not there with no feedback. In this case the high order harmonics are just those needed at the input to reduce output distortion, and it just happens that the inverse of a square-law is a square-root-law, which gives an infinite sequence of harmonics. If we wanted to avoid feedback we could first pass the signal through a stage with a square-root transfer function, which would add high order harmonics, and then apply this to the square-law device to achieve a distortionless output. Matching the two functions to an accuracy of one part in 10,000 would be virtually impossible, but this is what can be achieved automatically by the application of high levels of overall feedback. Only that small one part in 10,000 remains as output distortion.

In conclusion, high levels of overall negative feedback can be a highly effective way to reduce output distortion. The common objections to feedback include the addition of high order harmonics, but this is merely the difference between input distortion for an undistorted output and output distortion for an undistorted input, and although the frequency spectra are widely different in the case of a square-law amplifier, they need not be so different for other more common amplifiers. Other objections to feedback include PIM, TID etc, all of which involve input stage nonlinearity. The example given here reduces input stage signal to typically 15uV, where the stage can be made highly linear, while in comparisson a zero feedback amplifier will have an input stage signal of 150mV at the same output level, and therefore needs to handle a signal 10,000 times greater. If we were to use the same input stage in both cases its second harmonic would be 10,000 times greater and its third harmonic 100,000,000 times greater for the zero overall feedback case. With high feedback input stage distortion can easily be reduced to insignificant levels.

In practice, in the high feedback example, some of the linearity can be traded for higher stage gain, and in the MJR-6 the input stage will clip with an input of about 10mV, which is no problem because the actual signal at the input base, even with a full level square-wave input, is a small fraction of a mV. Very high frequency inputs such as those in square wave signals or in radio frequency interference could easily overload this input stage because there will be far less feedback available to reduce the level, which is one good reason for including a low-pass filter at the input. The MJ-6 circuit includes two capacitors at the input (560p and 390p) to give good attenuation of unwanted high frequencies, but still it is a good idea to pay attention to screening and layout to minimise interference pickup.

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