This kind of depends on the circuit used.
The spectral growth argument doesn't occur over all topologies.
Degeneration certainly does affect spectral growth but feedback doesn't always have this affect.
Give this topology a try too.
https://sound-au.com/tcaas/EWW3-89.gif
Use cascoded p channel jfets at input.
https://sound-au.com/tcaas/EWW3-89.gif
Use cascoded p channel jfets at input.
Itsmee,
Could you post the schematic of your amplifier if possible?
Some reading....
It is well known that if we start with an amplifier with an open-loop square-law response it will produce only second harmonic distortion, but with overall negative feedback added higher order harmonics will then be produced. This is perfectly true, but almost entirely misleading for several reasons. For a start there are no perfect square-law amplifiers. The closest we can get is probably the field-effect transistor, (fet), but measurements confirm that these already add low levels of high order harmonics even with no feedback. The following graph shows approximately what happens to the harmonics of a typical fet as feedback is applied. The distortion levels at zero and low feedback may differ widely for different fets, but as feedback is increased the results will become more similar to the example shown:
The signal level is chosen to give 10% second harmonic at zero feedback. The harmonics are shown as H2 (second) to H7 (seventh). With zero feedback harmonics up to the 5th are above the -120dB level. Applying a low level of feedback the 6th and 7th harmonics increase a little above -120dB. Increasing feedback further the higher harmonics one by one fall down below the -120dB level until at a little over 80dB feedback we are left with only the fundamental plus second harmonic.
This shows the misleading aspect of the initial assertion that feedback adds high order harmonics. In any single fet amplifier stage the third and higher order harmonics are already there without feedback, become worse with low levels of feedback, but all disappear below -120dB at high levels of feedback. It is only at sufficiently high feedback levels that the 'audible' level distortion is purely second harmonic, and in the present example at 80dB feedback that second harmonic level is at -100dB (0.001%) rather than the -20dB (10%) of the zero feedback amplifier.
This however is not the end of the story. We have only looked at what happens to a single sine-wave input. A music signal includes many frequencies, and even a single note from one musical instrument such as the flute will have a fundamental plus harmonics. If we use a very simple approximation of a musical instrument with just a fundamental plus second harmonic at 20% and third at 10%, and we apply this to a square law amplifier at a level such that the second harmonic distortion of the amplifier is at 5%, then we will find intermodulation products being produced. The second and third harmonic of the input signal will combine to generate a 5th harmonic component. Working out all the added harmonics there will be 4th at 1.2% (-38dB), 5th at 0.2% (-54dB) and 6th at 0.05% (-66dB). These levels are shown in red as h4 to h6 in the graph. Our zero feedback amplifier is now adding even worse higher order harmonics, and would still do so even if a perfect square-law device was used.
There are other problems with a square-law amplifier, such as the addition of a d.c. component at the output varying with signal amplitude. For a typical square-law amplifier with output voltage:
Vo = 100 Vin + 100 Vin2
then using input Vin = A sin(wt) and substituting in the equation for Vo we find:
Vo = 100A sin(wt) - 50A2 cos(2wt) + 50A2.
The first term is no problem, it is the undistorted amplified sine wave. The second term is the second harmonic, which many believe is subjectively unobjectionable. The third term however is a d.c. component proportional to signal amplitude squared. For a constant signal amplitude this would be a constant voltage which could be removed by an output coupling capacitor or transformer, but with a music signal where the amplitude is constantly changing this is an a.c. distortion signal. For the example above an input of 0.2V peak will produce a 2V peak error voltage at the output, the same level as the 10% second harmonic.
The added higher harmonics when using a square-law amplifier is sometimes used as an argument against feedback 'because feedback adds high order harmonics'. This is however an unjustified generalisation, and these added harmonics are not a general property of feedback, it is more accurate to say that it is a property of square-law amplifiers, and some other types. The point is that there are other open-loop transfer functions for which there is no increase in high order harmonics at any level of feedback, and the relative levels of all harmonics remains unchanged as feedback is increased, while all harmonics reduce in proportion to the feedback loop gain.
An example is a class-B design published by Peter Blomley in Wireless World, March 1971. In this design the signal is split into two parts at the zero-crossing point, and the positive half is applied to one highly linear output sub-amplifier while the negative half is applied to another linear output sub-amplifier. The two outputs are then added. Unless the two output sub-amplifiers are exactly matched in gain there will be a change in the slope of the transfer function at the zero-crossing point. If we extract the distortion resulting from this it will look like a rectified sinewave, and this has an infinite series of even order harmonics. The 4th is at 1/5 the level of the 2nd, the 6th is at 1/7 the level of the 4th, and so on. Adding any level of feedback will reduce the difference in level of the two halves of the signal, but the transfer function will still be two linear parts with a slope change at zero crossing, and the distortion will still be the same rectified sinewave at a lower level. All harmonics fall in proportion to the feedback level, and in this case at least there is no increase in high order harmonics at any feedback level.
If some amplifiers with feedback have added high order harmonics and some do not, then is there some simple way to determine which do or don't? One approach is to look at two different ways of specifying distortion. The usual method is to apply a sinewave input and observe the distortion at the output. An alternative is to find out what distortion must be applied at the input to achieve an undistorted sinewave output. In the case of the square-law amplifier the output distortion with an undistorted sinewave input is just the second harmonic, but to get an undistorted sinewave output the input signal must have an infinite series of harmonics, and this infinite series has the same relative levels we will approach at the output when used as a feedback amplifier, as the loop gain is increased towards very high values. For the amplifier with a slope change at zero-crossing the input distortion for an undistorted output has exactly the same relative levels of harmonics as the output distortion for an undistorted input, and high feedback leaves the relative levels unchanged. Looking at this 'input distortion' is a useful clue about what will happen as feedback is increased to high levels. We can conclude that the effect of feedback will be different for different amplifiers, with the square-law at one extreme, and the zero-crossing slope change at the other extreme.
Could you post the schematic of your amplifier if possible?
Some reading....
It is well known that if we start with an amplifier with an open-loop square-law response it will produce only second harmonic distortion, but with overall negative feedback added higher order harmonics will then be produced. This is perfectly true, but almost entirely misleading for several reasons. For a start there are no perfect square-law amplifiers. The closest we can get is probably the field-effect transistor, (fet), but measurements confirm that these already add low levels of high order harmonics even with no feedback. The following graph shows approximately what happens to the harmonics of a typical fet as feedback is applied. The distortion levels at zero and low feedback may differ widely for different fets, but as feedback is increased the results will become more similar to the example shown:
The signal level is chosen to give 10% second harmonic at zero feedback. The harmonics are shown as H2 (second) to H7 (seventh). With zero feedback harmonics up to the 5th are above the -120dB level. Applying a low level of feedback the 6th and 7th harmonics increase a little above -120dB. Increasing feedback further the higher harmonics one by one fall down below the -120dB level until at a little over 80dB feedback we are left with only the fundamental plus second harmonic.
This shows the misleading aspect of the initial assertion that feedback adds high order harmonics. In any single fet amplifier stage the third and higher order harmonics are already there without feedback, become worse with low levels of feedback, but all disappear below -120dB at high levels of feedback. It is only at sufficiently high feedback levels that the 'audible' level distortion is purely second harmonic, and in the present example at 80dB feedback that second harmonic level is at -100dB (0.001%) rather than the -20dB (10%) of the zero feedback amplifier.
This however is not the end of the story. We have only looked at what happens to a single sine-wave input. A music signal includes many frequencies, and even a single note from one musical instrument such as the flute will have a fundamental plus harmonics. If we use a very simple approximation of a musical instrument with just a fundamental plus second harmonic at 20% and third at 10%, and we apply this to a square law amplifier at a level such that the second harmonic distortion of the amplifier is at 5%, then we will find intermodulation products being produced. The second and third harmonic of the input signal will combine to generate a 5th harmonic component. Working out all the added harmonics there will be 4th at 1.2% (-38dB), 5th at 0.2% (-54dB) and 6th at 0.05% (-66dB). These levels are shown in red as h4 to h6 in the graph. Our zero feedback amplifier is now adding even worse higher order harmonics, and would still do so even if a perfect square-law device was used.
There are other problems with a square-law amplifier, such as the addition of a d.c. component at the output varying with signal amplitude. For a typical square-law amplifier with output voltage:
Vo = 100 Vin + 100 Vin2
then using input Vin = A sin(wt) and substituting in the equation for Vo we find:
Vo = 100A sin(wt) - 50A2 cos(2wt) + 50A2.
The first term is no problem, it is the undistorted amplified sine wave. The second term is the second harmonic, which many believe is subjectively unobjectionable. The third term however is a d.c. component proportional to signal amplitude squared. For a constant signal amplitude this would be a constant voltage which could be removed by an output coupling capacitor or transformer, but with a music signal where the amplitude is constantly changing this is an a.c. distortion signal. For the example above an input of 0.2V peak will produce a 2V peak error voltage at the output, the same level as the 10% second harmonic.
The added higher harmonics when using a square-law amplifier is sometimes used as an argument against feedback 'because feedback adds high order harmonics'. This is however an unjustified generalisation, and these added harmonics are not a general property of feedback, it is more accurate to say that it is a property of square-law amplifiers, and some other types. The point is that there are other open-loop transfer functions for which there is no increase in high order harmonics at any level of feedback, and the relative levels of all harmonics remains unchanged as feedback is increased, while all harmonics reduce in proportion to the feedback loop gain.
An example is a class-B design published by Peter Blomley in Wireless World, March 1971. In this design the signal is split into two parts at the zero-crossing point, and the positive half is applied to one highly linear output sub-amplifier while the negative half is applied to another linear output sub-amplifier. The two outputs are then added. Unless the two output sub-amplifiers are exactly matched in gain there will be a change in the slope of the transfer function at the zero-crossing point. If we extract the distortion resulting from this it will look like a rectified sinewave, and this has an infinite series of even order harmonics. The 4th is at 1/5 the level of the 2nd, the 6th is at 1/7 the level of the 4th, and so on. Adding any level of feedback will reduce the difference in level of the two halves of the signal, but the transfer function will still be two linear parts with a slope change at zero crossing, and the distortion will still be the same rectified sinewave at a lower level. All harmonics fall in proportion to the feedback level, and in this case at least there is no increase in high order harmonics at any feedback level.
If some amplifiers with feedback have added high order harmonics and some do not, then is there some simple way to determine which do or don't? One approach is to look at two different ways of specifying distortion. The usual method is to apply a sinewave input and observe the distortion at the output. An alternative is to find out what distortion must be applied at the input to achieve an undistorted sinewave output. In the case of the square-law amplifier the output distortion with an undistorted sinewave input is just the second harmonic, but to get an undistorted sinewave output the input signal must have an infinite series of harmonics, and this infinite series has the same relative levels we will approach at the output when used as a feedback amplifier, as the loop gain is increased towards very high values. For the amplifier with a slope change at zero-crossing the input distortion for an undistorted output has exactly the same relative levels of harmonics as the output distortion for an undistorted input, and high feedback leaves the relative levels unchanged. Looking at this 'input distortion' is a useful clue about what will happen as feedback is increased to high levels. We can conclude that the effect of feedback will be different for different amplifiers, with the square-law at one extreme, and the zero-crossing slope change at the other extreme.
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Really odd, won't happen in real circuit I think. Perhaps Cgd of the mosfet models are way too big. Try using Cordell's model?... But it's still terrible at 10kHz (1.4% @1W). Even more oddly, it actually drops at 100W (0.9%).
But bias at 2nd diff is kind of low, try 20-50mA tail current.
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Jam this seems higher than what I normally get (relying on memory here), I think I normally get around 1% THD or better without feedback (I will check that out though).
From recent memory, measuring ACA and F6, increasing feedback by an additional 6dB to 9dB did not add any increase in higher harmonics (It was purely 2nd and 3rd) at 1W 1kHz.
I have not read everything you have written, I'll go back to reading.
I agree with this aspect.
This is also why I believe, if you want to add colour to the sound it should be applied at only one gain stage in the amp (all other connecting equipment should also be near zero.), the other gain stages should be free of all distortion, as much as possible that is.
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If I eliminate the Miller comp (is it still Miller comp on a differential VAS?) I get a really ugly spike at 10Mhz. (The phase spikes too, so the stability margins remain OK, but it still worries me.)
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If I eliminate the Miller comp (is it still Miller comp on a differential VAS?) I get a really ugly spike at 10Mhz. (The phase spikes too, so the stability margins remain OK, but it still worries me.)
What resistor values did you use at the base of the bipolars when you eliminated the caps?
Try 1kOhm base resistors.
You can obviously use lower values, but start with 1kOhm.
This is very informative.
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Bingo. That works. (I had tried all the way up to 470 with no success.)
Eliminating those caps (Miller or not) gives a huge boost to 10kHz performance....