Random Noise
Assorted Items...Latest Update 9-OCT-2024
Inverse Functions.
Generally, for a nonlinear transfer function there exists an inverse function which will reverse its effect. I covered this in a page: Inverse Transfer Functions. There are exceptions, for example there is irreversible loss of information during clipping, slew rate limiting, and class-B dead-zones. Apart from the exceptions, if we have two identical nonlinear amplifiers we can put one of them in the feedback loop of an op-amp and generate an inverse function to 'predistort' the signal so that passing it through the second amplifier will return us close to the original undistorted signal. We don't need to go to such lengths, any amplifier with overall negative feedback already generates this sort of predistorted signal at the input of the output stage to at least partly cancel output stage distortion. That is just another way to think about negative feedback, that it generates the inverse function of the output stage nonlinearity at the input of the output stage. To create a perfect inverse would need infinite feedback loop gain, so in practice we never reach zero output distortion.
If the output stage is the primary source of nonlinearity then with heavy feedback applied the relative levels of harmonics of the output signal are almost identical to those of the 'predistorted' signal at the input of the output stage. That is why increasing feedback changes the distortion spectrum, it changes from the spectrum of the original nonlinear function towards the spectrum of the inverse function, but at reduced level.
Listening Tests.
There is very little on this website about subjective effects, personally I was already happy with my sound system 40 years ago, and apart from an occasional backward step I remained happy. What I did write on this subject was about testing methods, and I suggested ways to avoid some common errors. Carrying out accurate and meaningful listening tests is difficult, and a useful first step, often omitted, is to determine whether it is possible to play the same music twice without changing anything. That is more difficult than it appears, if we have not intentionally changed anything how could there be any significant change? I previously mentioned one obvious example, the increase in speaker voice coil temperature after the first play will increase its resistance and reduce the sound level of the second play unless we wait long enough for the temperature to return to its original level. Another example is that if we measure the bass resonance frequency of a speaker before and after playing some music the values will possibly differ, I measured one full range driver changing from 150Hz to 115Hz after a few hours use. Only part of the change is a temperature effect, if we wait an hour for it to cool down the resonance frequency will increase again, but not back to the original value. Another example, after listening the first time we go to the signal source and restart it, then sit down again to listen a second time, but our ears will not be in exactly the same location, and even one or two milimetres difference can change the frequency response and channel phase difference. To avoid that would need your head clamped in position, which I am sure is rarely if ever done. There are more examples, none perhaps making a vast difference, but far greater than for example the effect of using a different brand of resistor, which some claim to hear.
Common Emitter Output Impedance.
I never entirely resolved the question of common-emitter output impedance, but I look out for any useful information. There is a discussion on diyAudio starting at post 10084 about impedance of current sources which looks relevant. There are equations there, which are either wrong or don't apply to zero external emitter resistor, giving R_OUT not affected by RS with R1 = 0, but more interesting a Spice simulation giving a plausible result. My own Spice simulation failed to demonstrate any effect of RS, so maybe some Spice models work better than others, or maybe Spice makes the same 'error' as the equation, and only works well for the current source version. Still puzzled. The simple model I ended up with is really just a variation of the hybrid-pi model, which at least matches the measured results, but it looks like another of those 'wrong but useful' models.
Common Design Errors.
Back to amplifier design: There are a few common problems and errors, and I have tried to cover some of these in the theoretical pages. One important error concerns 'the unity gain frequency' of a feedback loop, the problem being that the unity gain frequency is not fixed, it can vary over a wide range close to clipping or slew-rate limiting, and also depends on the load. There may even be more than one unity gain frequency if the load has dips in impedance at various frequencies. Designing for stability is more difficult than just avoiding too much phase shift at one easily specified unity gain frequency.
Another problem is with 'symmetry' and there is a piece in my 'archive' section about some of the problems and limitations. At best symmetry may cancel some even harmonic distortion, but even in my MJR7 with little or no circuit symmetry the second harmonic at 1kHz is under 0.0001%. Even that low level is almost entirely a result of differences between the p-channel and n-channel power mosfets. The 'complementary' output pair are the only apparent symmetry in the circuit, but are actually the greatest source of distortion.
I have seen a few designs in the past few years with input stages similar to my MC Phono Preamp, with npn and pnp input transistors with separate feedback networks. My circuit immediately connects the collectors of these two transistors, but there are power amplifier designs where they drive separate following stages. I only once saw any mention of accurately matching the feedback networks, and see no evidence that anyone has worked out what happens if there is significant mismatch. My guess is that the operating currents of the following stages will be modulated by the signal, and if this reaches the output stage with nothing to limit the modulation then there could be severe cross-conduction on one half-cycle. In other words high dissipation with risk of failure. With just standard 1% tolerance components and a high feedback loop gain it is just a matter of luck whether such an amplifier works fine or there is enough mismatch to self-destruct. Using a Vbe multiplier to bias the output stage may help prevent excessive cross-conduction, but the driver stage may still be at risk.
Another common design error is to check for stability with capacitance loads of 2uF and maybe 100nF and a few smaller values, and then assume any small value will be ok. I found out why this can miss a stability problem when an early constructor of my MJR7 amplifier connected just a speaker cable, with capacitance 2nF, and found instability, if I remember correctly it oscillated at about 5MHz. The problem was the capacitance resonated with the output inductor at a frequency close to the unity gain frequency, and added enough phase shift to cause the problem. The first idea to solve this was to add 10nF across the output to prevent lower capacitance load. A simulation then revealed that there were a range of inductive loads which would now add similar phase shift near the unity gain frequency, and finally the series 100nF + 1R across the output ensured stability with any reasonable load. Clearly not all amplifier designs have this problem, but testing with a few small values of load capacitance is not guaranteed to reveal this, if I had tested with 1nF and 5nF there would have been no instability, it was just by chance that someone had 2nF cables and found the effect. Other designs may also misbehave with some narrow range of capacitance load but appear stable because they were never tested with the exact value needed for oscillation.
Why Design Amplifiers?
Why design amplifiers? Those who believe all amplifiers sound different have some justification for endlessly searching for what they regard as audible improvements, but those of us who insist that all well designed amplifiers used within their design limits should sound the same (and if two don't sound the same then one or both are not 'well designed') have less of an excuse. Personally, I just enjoy solving technical problems, in the same way some like to solve Sudoku puzzles in their spare time.
If a number of different amplifiers do genuinely all sound different then unless there is some trivial reason such as different output impedances affecting the frequency response, then the obvious explanation is that they have audible distortion, which is my personal definition of a bad design, but some may prefer some added distortion. If so, why would they want to buy expensive amplifiers to add this distortion, why not add it in the pre-amp stage with adjustable controls rather than being stuck with one fixed type and level of distortion? And what happens if the recording engineer also decides that adding 5% second harmonic sounds nice, then a 5% distortion amplifier could add more in phase to give 10% or in opposite phase and cancel to give 0.001%, and there is no option to adjust this. At the very least a signal inversion switch in the preamp could be useful, but for this example neither option is what either the listener or the recording engineer wanted.
Even for those who don't find the added distortion objectionable, there is an additional problem that a nonlinear transfer function doesn't just add distortion, it can also reduce or eliminate wanted components of the signal, something I covered in my page about inverse transfer functions. If an electronic music composer used a square-root transfer function to add harmonics to a sinewave generator, then replaying that through a square-law amplifier could in theory eliminate all those harmonic to leave just a sinewave; not what the composer intended.There are in fact only 4 power amplifier circuit diagrams on this website which ever got built and attached to a speaker to listen to music. One of those is from 1984, just the mosfet amplifier from the Hitachi application notes, with added speaker protection and thermal cutout, and I was happy listening to that for many years. Another is a simple basic circuit I use as a guitar practice amplifier, and the other two are the first (MJR6) and final (MJR7-Mk5) lateral mosfet designs. Most of the other circuits are just ideas, and a few were built and tested to demonstrate that they work as predicted, but were designed to solve some technical problem, not to solve any audible problem, so only measured not auditioned.
Prior to my first mosfet amplifier in 1984 I was using the famous JLH class-A design, with just 4 transistors, and was perfectly content with that. Before the JLH I had a Sinclair Z30, and before that an amplifier board with germanium transistors, possibly a Sinclair Z.12. Before that, around 1965, I had an EL84 single ended valve amplifier I made using parts from an old TV set. That had audible hum, but otherwise not bad.
'Super Feedforward'.
Looking through Audio Power Amplifier Design 6th ed. (Self) I found Fig 4.17, and thought 'that's my MJR9 circuit!' But no, it's the old Sansui 'super feedforward' system, and it was used in the Sansui AU-D22 and others. There is even a patent (USA 4367442 - 1980), but as I said on my MJR9 page, it's just a variation of the Quad 405 from 1976, apart from the addition of a unity gain buffer, which doesn't change the principle of operation in any significant way. The patent is typical obfuscation, there seems some claim that the distortion gain falls at 12dB/oct and therefore the 'prior art' is inadequate, and yet the practical circuit as I said looks just the same in principle as my MJR9. The AU-D22 distortion specification is reasonably good, but nothing special. If there is any really new idea I would claim it for my MJR9 which shows that we can also use shunt compensation instead of the feedback capacitor used in the Quad circuit. The Sansui service manual has a circuit diagram and they also appear to use a feedback capacitor for compensation. Understanding any of these approaches is easiest if we look at the properties of the signal at the input of the output stage. Then it can be explained simply in a few sentences as on my MJR9 page.
Real Output Errors.
Another addition to the list of common amplifier design errors should perhaps be the general assumption that there must be some mysterious form of output error not revealed by the usual measurements. This appears to be a consequence of some listeners being convinced that they can hear clear differences between what conventional testing suggests are close to perfect designs. This has lead, over the years, to a whole list of 'problems', such as TID, PIM, TIM and so on leading to innocent amplifiers being tortured with extreme test signals having little in common with typical music. Already more than 70 years ago amplifiers were being tested using the 'null method' to extract the difference between input and output, and using this method with actual music signals no unexpected errors were revealed. Certainly amplifiers can sound different, and there are some poor designs around, but the most common causes I suggest are things like instability and interference pickup.
My own test of the MJR6 with music driving a speaker reveals just uncancelled music at a very low level with no serious distortion and more or less constant noise level:
If your browser doesn't support the 'audio' tag, instead try clicking this LINK.
The input resistor noise is normally dominant for the MJR6, but that also gets nulled in this particular test, so the noise heard here is from other sources in the amplifier plus noise from the test circuit.Some amplifier manufacturers make a virtue out of having relatively high distortion, the claim being that this in some way enhances the percieved sound quality. Even if there was any validity in this approach it would make far more sense to add the distortion in a pre-amp stage, where it could be made adjustable and have a polarity switch so that for example the second harmonic could be set to add to or subtract from the speaker second harmonic. A few years ago I did actually design what I called a 'valve (tube) amplifier sound effect generator' to add adjustable distortion levels, which would cost less than £5 to build, so a lot cheaper than any of those high distortion power amplifiers. I recall Douglas Self somewhere suggested this sort of adjustable preamp distortion, he called it a 'niceness control'. I may build a more advanced version of my circuit and include it in the 'guitar effects' series, which is one of the few applications where there is some justification for intentional distortion.
The idea that amplifier distortion can cancel some of the speaker distortion is true, but as mentioned earlier on this page what we need for accurate cancellation is an inverse transfer function, which is more difficult than just using a speaker and an amplifier with opposite polarity second harmonic.
I have now added a page with further thoughts about a 'distortion adding' circuit, called ADD H2 DISTORTION.
MJR7 Critic.
On one of the audio forums I found a criticism of my MJR7 amplifier, describing it as a 'dated, non-audiophile design.' What is interesting is that for comparison a link was given to a page of 'state of the art audiophile designs', translated from Japanese. Only the best of these designs, No.14, is close to the distortion measurements of my own MJR7-Mk5, and that amplifier uses 27 assorted bjts, mosfets and jfets, some of which are quite expensive and now possibly unobtainable. The starting point is a claim that 'it is predicted that the smaller the number of stages, the less the deterioration of sound', but even if this was true, it would be difficult to justify a 27 transistor design in preference to my simple 7 transistor circuit.
What may not be obvious to the casual reader is that all the distortion specifications given there are for sufficiently low signal levels and high quiescent currents to ensure class-A operation, unlike my MJR7 tested with only 100mA quiescent current and intentionally specified at signal levels where output devices are switching off. My design demonstrates the effectiveness of high levels of negative feedback in the reduction of crossover distortion in class-AB, but whether those 'audiophile' designs can also achieve this is doubtful.
A more worrying feature of those designs is the lack of a zobel RC or output inductor, leading to doubts about stability into reactive loads. There is also of course no speaker protection under fault conditions. Anyone convinced that these are in some way 'high-end audiophile grade' designs may be thinking of using them to drive expensive speakers, so protection and stability should be serious concerns, and at the very least adding a speaker protection relay and associated circuit seems a good idea. My own experience of using relays has not been encouraging, which is why an output coupling capacitor inside the feedback loop is my preferred solution. I found an example of this idea in a 1956 design, so maybe it is not unreasonable to call it 'dated', but then again, the type of complementary differential input stages used in those 'state of the art' designs were being used at least 40 years ago. To be fair the article is from 1998 so not claiming now to be the latest 'state of the art'. So what is the current (2022) 'state of the art? My own view is that some audio amplifier designs from 40 or more years ago were already better than they needed to be to have no audible deficiencies for normal domestic use, and recent worthwhile improvements are in areas such as efficiency, e.g. class-D. My own MJR7 design was never intended to be more than an example of what can be achieved with a simple circuit and conventional global feedback, but it ended up far better than I had initially planned.
More Cables.
On the Stereophile website I found a page about audio cables, which I should know by now is a topic best avoided. What caught my attention was an article originally from 1985: Electrical Signal Propagation and cable Theory. which I mentioned indirectly in my piece about skin depth in conductors. I made some vague criticism, but there is probably no point writing about a 36 year old article.
Anyway, this sort of thing is mostly pointless; almost the entire effect of a few feet of audio speaker cable can be stated in just four words: 'frequency dependent phase shift'. There are a few assumptions such as the cable being time invariant; e.g. if the separation of the conductors fluctuates significantly then it gets tricky. The test signal suggested in that article stops abruptly and to do this would need to have very high bandwidth. The abrupt stop requires all the frequency components to have certain relative phases, and almost any frequency dependent phase shift, other than a shift proportional to frequency, will change the wave shape and prevent an abrupt stop.
In reality we use band-limited signals and band-limited speakers, not to mention band-limited ears, and as I mentioned in one of my pages any practical speaker has relatively horrendous phase errors. The small effects of what we can assume is a fraction of a degree audio frequency phase error from a speaker cable are relatively trivial and unimportant.I demonstrated the phase shift from a typical cable on my Cable Impedance page, where even at 20kHz the shift was less than one degree. Assuming copper wire the internal inductance resulting from the magnetic field in the skin depth will typically be smaller than the external inductance for any reasonable line, so even less significant. To a good approximation the phase shifts are linear functions of frequency, and equivalent to a time delay typically 125nsec. If anyone wants to check the relative levels of internal and external inductance for a coaxial cable there is a useful formula on page 397 of Jackson's 'Classical Electrodynamics' 3rd Edition.
A more valid test would have been to use the same test signal, but recorded on an audio CD, and detect the speaker output with a microphone, then compare the results with different cables. As far as I know no one has wasted their time doing that experiment, the result is too easy to predict. Maybe I'll do it some time just to prove the point. For a good indication of the sort of thing to expect take a look at the 'square wave' output of a CD recording of a 1kHz square wave about half way down the page of Technics SL-PG390 Mods.
Put simply, band limited signals can not stop (or start) abruptly.
An example of the acoustic output of a speaker with a square wave input appears near the end of the 'Cable Impedance' page linked above.
Simulation Problems.
I am often dismayed at how much simulations are trusted. I never use them for distortion analysis, and generally use linear approximations with voltage controlled current or voltage sources to predict feedback stability or frequency and phase response. The only time I actually used a transistor model it was when investigating output impedance of a common-emitter stage, and the result was completely wrong, showing no effect from changing the source impedance. An IEEE paper on the subject also reached the same conclusion that Spice gets it wrong, so it probably wasn't just my own incompetance. At best it is evidence that some models are poor.
Before taking simulation results seriously a reality check may help avoid errors. For example there was a LTSpice simulation of my MJR7 presented on diyAudio a while ago which gave distortion figures about 50 times higher than I measured. Fortunately someone with sufficient expertise found the problem with the simulation, leading to good agreement, but without a real measurement to compare with there would have been no motivation for tracking down the source of the error.
It doesn't always need to be a measurement we check simulations against, often we can work out an approximation starting from a plausible estimate. The MJR7 has about 80dB feedback loop gain at 1kHz, so if we guess the open-loop distortion to be 1% (-40dB) that tells us the closed loop distortion will be reduced by about 80dB to something like -120dB, agreeing with my measurements. If a simulation gives distortion 50 times higher that would need open-loop distortion 50%, which could only happen if something catastrophic was wrong. Just understanding how a circuit works and the effect of feedback may be sufficient link to reality to tell us something is wrong. Without such checks we can easily be misled by simulation results.
I will continue to trust actual real world measurements, particularly my personal favourite signal nulling method, which is unlikely to miss any mysterious unknown form of distortion, and for some amplifier circuits can even be made to work well with music signals and driving a speaker.
Hafler Test - SWDT.
The nulling test is sometimes referred to as the 'Hafler test' or the 'Straight-Wire Differential Test' (SWDT) from around 1987, but that is a simplified version. It had been found that almost any half decent amplifier could have inaudible distortion when extracted and listened to at its original level provided the nulling included amplitude and phase compensation, but insisting on good nulling without that compensation required a very wide bandwidth low phase shift amplifier, which could then be advertised as the first amplifier designed to pass the SWDT test. Without the rest of the recording and reproduction chain, including our ears, having similar bandwidth and phase there appears to be no real point, and the test only claimed 70dB nulling, so could be passed by an amplifier without needing very low nonlinear distortion. Probably a clever marketing approach, but not widely adopted by other manufacturers as far as I know.
The SWDT test is essentially a lazy version of the signal nulling method I used extensively, which was made popular by Baxandall and Peter Walker at Quad. In this method we trim the nulling circuit to match the gain and phase of the amplifier being tested, which takes time and patience. The SWDT version requires us to design the amplifier to match the response of the test circuit, which leads to a requirement for 1MHz bandwidth amplifiers. Is that ridiculous? My vote is 'yes'.
Peak Intermodulation Distortion.
For a given nonlinear transfer function, (and ignoring real world complexity such as frequency dependence), what is the relationship between the distortion levels of a single sinewave and multiple sinewaves, including intermodulation products? Assuming we have identical peak positive and negative levels for the single sine and the combined multiple sines the distortions also have identical peak levels. Is that obvious? Yes, both signals pass through the same voltages between one peak and the opposite peak, and the error is just a function of the instantaneous voltage, so both signals pass through the voltage level where the peak error occurs and produce the same peak error. Try drawing a nonlinear transfer function, with Vout as a function of Vin for a given range of Vin, and draw the best straight line through it to minimise the peak deviations from the line, and then you already know the peak deviations without needing to know anything about the test signal to be used apart from its peak level. With a different peak level the 'best straight line' may be different, giving different peak errors. (Minimising the peak error doesn't necessarily agree exactly with the usual ways of specifying nonlinear distortion, see Update 2.).
Adding a large number of different frequencies makes no difference provided we keep the peak level constant, we get more intermodulation products, but their combined peak level stays the same, and also using a music signal with the same peak amplitude gives the same peak error as a single sinewave.
So what inspired this comment? Seeing an assertion that intermodulation distortion has higher peak levels for more complex signals. That's only true if you choose not to use equal peak level input signals for comparison.Update 1: looking again at the offending article (I'm not naming names, it's a fairly typical 'audiophile' amplifier designer article). The peak intermodulation distortion is still higher than I would expect, but I see it is extracted by subtracting input and output signals, i.e. my favourite signal nulling method, but what I previously missed is that the highest distortion peaks coincide with the input signal peaks, with nulling adjusted correctly for minimum peak remainder that should not happen, just adjusting the nulling can mostly eliminate the 'distortion peaks', and more closely approach what I called the maximum deviation from the 'best straight line'.
Update 2: To clarify what I meant by the minimisation of the peak error not always agreeing with conventional distortion specifications: If the transfer function is written as a polynomial such as y = ax + bx2 + cx3 +....... then the first term y = ax is conventionally regarded as the linear term, and can be used rather than the 'best straight line', but may not necessarily minimise the peak deviation from the line. Either way we still find the choice of test signal makes no difference to the peak error provided we have the same peak level signal, so the conclusion is the same.
Update 3: Something vaguely related to all this, is that for a given nonlinearity the peak distortion of any signal will be reduced by any level of negative feedback. It is well known that if we start with a square law stage and add negative feedback then higher order harmonics appear at the output and rise to a maximum level for some small level of feedback. The total peak distortion however doesn't increase, it only reduces for any increase in feedback. I think this is also obvious, but if not just look at the plot showing how the different harmonics vary with feedback level for a square-law amplifier, I showed that plot on my Feedback Effects page. The falling level of 2nd harmonic is more than enough by far to counteract the effects on peak level of all the other harmonics even when they increase to their combined maximum. Note: the graph shows distortion on a log scale, convert to a linear scale to make it even more obvious that the falling second harmonic is by far the dominant effect. More generally there are no doubt exceptions, e.g. clipping, dead zones, discontinuities, and so on.
Update 4: I added a page to demonstrate some of this, Square-Law Transfer Function With Feedback. There I used the method of regarding the y = ax linear part of the polynomial as the 'best straight line'. I used a square-law input stage to demonstrate that increasing feedback by increasing the gain in the later stages has the added advantage of reducing signal levels handled by the nonlinear stage, giving far more distortion reduction than we would expect from just the feedback loop gain, and also reducing the higher harmonics to leave almost entirely 2nd harmonic.
Update 5: I just realised the article I was criticising was published over 15 years ago. I was thinking this was good because I never saw the 'error' repeated, so probably everyone ignored it, but then I just saw a similar statement in an audio forum post from 3 years ago: "a nonlinearity causing .001% harmonic distortion causes much more IMD with 20 or 30 frequencies all present at once in actual music." Once this sort of claim is published it can persist indefinitely, even when obviously wrong, and is inevitably followed by some people saying they can hear it.
Just do the maths. Better still do the signal nulling test with real music (and do it correctly to minimise peak residual). Then observe that there is no mysterious amplifier distortion mechanism missed by all conventional distortion testing.Update 6: I found something apparently similar at ASR-Harmonic and Intermodulation Distortion near the end of the first post. This shows that the IMD distortion components are at significantly higher levels than the harmonic distortion. At first that worried me, have I made some mistake? Then I realised what is being compared there is the IMD and harmonic components of distortion for just the two tone signal, not compared to a single sinewave. The two tones are both at level -6dB, so to have the same peak level a single sinewave must be at 0dB, so its harmonic distortion components will be higher, the 2nd harmonic being 6dB higher than for one of the -6dB components, and 3rd and higher harmonics higher still. If we were to combine all the IMD and THD components for the two -6dB tones and work out the peak level, then I am entirely certain we would find exactly the same peak level for the THD of a single 0dB sinewave. I haven't checked the analysis there, it looks to be about right, but the conclusions are a little misleading, for complex signals the individual sinewave levels will be fairly low, so the individual harmonics will also be low, apart from obvious exceptions such as crossover distortion, so the distortion can be primarily IMD rather than THD, but the peak distortion will not be more than for a single tone with identical peak level, so single tone THD can be a perfectly adequate measure of nonlinearity.
How Much Complexity?
Complexity: How much do we need?
I just saw a power amplifier design on diyAudio with no less than 80 transistors per channel. I have no idea whether it is any good or even if it would work at all.
At the opposite extreme are the single-ended class-A mosfet designs with the advantage of being easily understandable but with obvious limitations, being extremely inefficient, relatively high distortion, and in their commercial form often surprisingly expensive.My own interest when designing my mosfet amplifiers was to determine the simplest class-AB circuits with adequately low distortion. The distortion ended up far lower than I had initially aimed for, so my conclusion was that a 7 transistor circuit was about the optimum level of complexity. Before increasing the complexity my first question would be 'what problem are we trying to solve?' I know no good reason to aim for even lower distortion, but other 'improvements' could be lower noise and higher power, neither of which needs great complexity. Just using dual-die mosfets and increasing the supply voltage, plus small heatsinks for the driver transistors, could achieve 100W, and the noise is already low enough for anything other than the highest efficiency horn speakers. With high efficiency speakers we would maybe want lower gain, and then we can reduce the 200k feedback resistor to 100k, that reduces both output noise and gain by 6dB, but some other small adjustments may then be needed, e.g. for optimum stability it may help to increase the 10p in parallel with the feedback resistor to 22pF. Reducing this resistor together with using the dual-die mosfets we would also expect distortion to be reduced further, something like another 10dB. So, even if we wanted to improve the power and noise, and also distortion, it can be done without greater complexity.
Positive Phase Negative Feedback.
I was looking for something in an old copy of Wireless World (May 1973) and found a slightly surprising discussion in the 'Letters to the Editor' page 247. One letter from Mornington-West and Vereker says:
"as has been known for a long time...it doesn't matter how much feedback is applied to reduce distortion, unless it is negative and the phase is correct at all frequencies it will not improve the amplifier's overall performance."
This is followed by a reply from John Linsley Hood, which I expected to correct this, but no, he says:
"the reduction in the phase error of the amplifier chain within the frequency range of interest also reduced the ineffective quadrature component in the feedback loop and allowed more effective distortion cancellation. One might say that negative feedback is indeed an effective way of reducing distortion but only so long as it is negative."
There was more about this in the July issue, there Linsley Hood shows a circuit with phase shift and says adding feedback increased 1kHz distortion. These days we can easily put the diagram in a simulator and see what is happening, when I did this I found a peak in the distortion gain around the 2kHz to 3kHz range where the 1kHz test signal 2nd and 3rd harmonic distortion occurs, so this was actually an example of genuine positive feedback resulting from a combination of added phase shift and low loop gain, causing increased gain for the distortion.Anyway, the mathematical analysis of the effect of phase is fairly simple, I covered it in both my 'Feedback Effects' article and in my 'Amplifier design for Beginners, Part 6', revealing that the phase shift is almost entirely unimportant (but only for high loop gains, at low loop gains you need to worry about stability margins, and may end up with peaks in the response or instability),
To sum up: positive phase feedback is not the same thing as positive feedback, which in addition needs low loop gain. The usual definition is that feedback is negative if adding it reduces the gain, and positive if it increases the gain. With high loop gain positive phase feedback still reduces the gain (and also the distortion), and is then classified as negative feedback.
So where does this sort of misunderstanding originate? The Linsley Hood phrase 'distortion cancellation' may be a clue, if the output distortion was merely being cancelled by the output distortion being inverted and fed back then we may expect accurate phase would be essential, but negative feedback just doesn't work that way, and simplistic explanations about inverted distortion leading to cancellation can be misleading.I have now added a page about Positive Phase Negative Feedback, which includes some of the finer details, for example the step response, which demonstrates that it only works with a single inverting stage plus RC network phase shifts, with two inversions we end up with something like the typical 'bistable' multivibrator, which has only two stable states, so is not much use as an audio amplifier.
rbb' and Cbe Effects.
Regarding the effect of base-spreading resistance rbb' and transistor capacitance Cbe, which together act as a low-pass filter. These are distributed through the base region, and a simple simulation suggests the -3dB frequency will be higher than we would predict for single discrete components with the same values. A detailed account of the effects of distributed resistance and capacitance, also taking into account 'current crowding' is:
P. E. Gray, D. DeWitt, A. R. Boothroyd, J. F. Gibbons. Physical Electronics and Circuit Models of Transistors. Wiley, New York, 1964, Chapter 8.
At the end of that chapter they make the suggestion to build and measure.And why is this important? Because it is easy to underestimate the effect. Data sheets rarely include rbb', and some types have surprisingly high values. Also Cbe specifications are invariably given for reverse bias, which tells us little about the capacitance under typical operating conditions with forward bias, which then includes diffusion capacitance proportional to emitter current. I wrote something about this in my Transistor Amplifier Design for Beginners, Part 4
Killer Sample.
I previously wrote: "Certainly amplifiers can sound different, and there are some poor designs around..." Take a look at the measured performance of a $10,000 single-ended tube amp described by Stereophile as "unerring naturalism, lush, rich, transparent midrange, solid bass, open treble, black background, precise layering of instruments and vocals—and the deepest, punchiest soundstage I've heard". The measurements reveal 10% distortion into 8R at the 30W rated power, and in Fig.11 the intermodulation spectrum for a 19+20kHz input at just 3W power level is one of the worst I can remember seeing. So how can that sort of performance be percieved as a 'transparent mid-range'?
The problem, I suggest, could be the wrong choice of music for the listening tests. The developers of MP3 codecs sometimes use what they refer to as 'killer samples' for listening tests chosen to accentuate known artifacts, one example used the sound of solo castanets to listen for pre-echo.
Google Drive (click the download symbol there) WARNING: It has some high level high frequency sounds near the end, so don't play it loud, you may not hear much but it could fry your speakers, (a literal 'killer sample'), and also distress your children and pets. Headphones are a safer option, but still keep the volume down.
That 19+20kHz intermodulation spectrum suggests something we could use to hear a clear effect. My own hearing stops around 10kHz, so with that signal I would expect to hear silence, as would many over the age of 30, but with typical 87dB/watt speakers that amplifier would add a 1kHz tone at around 70dB sound level, I would need to be almost totally deaf not to hear that.
That however is just a non-musical test signal, but here is an extract from a piece of music called 'Hills of Tartarus', the first link is to a 2-minute sample file:
I selected a few seconds near the end, in the 'add-dist-1' file it is initially undistorted, then the same few seconds with some symmetrical distortion like push-pull tubes plus soft-clipping, then another example, 'add-dist-2', again initially undistorted then repeated with something like single-ended tube distortion.
The first distorted example adds an unpleasant rasping noise, but the second distorted example sounds almost like added bells. The 'bells' are however not present in the original recording, and it's just an accident that the intermodulation distortion sounds like an additional instrument.
To some it may sound better with the added 'bells', but that is not what the composer intended. (I know because I asked him.) The piece is loosely based on the legend of Sisyphus endlessly pushing a boulder up a hill, and there are no reports of him hearing bells near the summit.
This illustrates one of the dangers of relying on listening tests to compare amplifiers, the one with masses of intermodulation products may be perceived as revealing previously unheard instruments and other low level details, when in reality this may be something not present in the recording, it has been added by the amplifier. I admit I do prefer the add-dist-2 sample with the added 'bells', but I wouldn't want all my music to be modified in this way.For both distortion examples the effect is not subtle, we don't need 'golden ears' to know something is seriously different, yet amplifiers adding these levels of distortion are regularly getting rave reviews. Music with such high level high frequencies is not common, but slew rate measurements I mentioned elsewhere suggest full level outputs up to 12kHz are not unknown, so lower frequency intermodulation could still be at easily audible levels.
Evidently some listeners like the sound of some types of distortion, but why spend $10,000 to get that. The distortion in the add-dist-2 sample was added by computer software at no cost. We could then use a much cheaper amplifier with far lower distortion and much higher power, for example the Fosi Audio BT20A Pro class-D, available for less than $100, including tone controls and optional Bluetooth input, and with some good reviews. That's over 100W power, with less than 100th of the distortion, and 100th of the price compared to that tube amp.Update: A limitation of the music sample test is that some tube amplifiers only have really high distortion near their maximum power levels, and my warning to keep the volume down to avoid tweeter damage rather negates the whole point. In the case of single-ended class-A, both tube and solid state, most appear to have high enough distortion to still expect an easily audible effect at moderate levels. That example from a Stereophile test was distorting heavily at only 3W output.
Also of course there is no point listening to the distortion examples if you are actually using one of these high distortion amplifiers. Your added distortion could even cancel some of my own added distortion and give a confusing result.
Everything Free.
As I mentioned somewhere before, nothing on this website is patented by me, and anyone can use anything for any purpose, personal or commercial. One commercial company actually copied my entire M.Sc dissertation in its online advertising literature, but they spelled my name right, so that's ok with me.
So, what is my problem with patents? Partly it is just that so many are such trivial ideas. My most admired designer, Baxandall, didn't patent his eponymous tone controls, yet many millions of them have been incorporated in audio equipment. It was published in Wireless World, Oct 1952.
There is nothing on my website I would claim is anything other than simple and obvious, maybe the exceptions are the second and third version of my class-B feedforward output stage. The first version just subtracts one voltage from another with a standard circuit, it astonishes me that it was never thought of before. The jump to the second version was just one of those leaps in the dark which took just a few seconds to make, but could easily have been missed. The third version was not entirely my own idea, it was just a response to a question I was asked about whether the output stage bias transistor could be included in the feedforward circuit. There was no guarantee that there was a solution, but only a small number of possible circuit arrangements, and it turned out one of them could be made to work.
About patents; Maybe we could set this up as a problem for AI, if it is good enough, to work out all the power amplifier circuit permutations which would work reasonably well, then publish the results and so avoid any future attempts to patent them and prevent their use. How many would there be? Certainly some finite number, I would guess less than a hundred would be significantly different viable power amplifiers.
We could maybe work out all the viable permutations ourselves for a power amplifier with a limited number of transistors. Two or three should be easy enough, and just for amusement I will try to list all the 2 or 3 transistor circuits, at least in their basic form. My initial attempt 2-3 Transistor Amplifier Output Stage Variations so far has just twelve 2-3 transistor output stages, mostly dating from 1956 to 1973, but others may get added.
On that page I say: "Trivial permutations such as common-emitter followed by common-base followed by common-collector are not included, if they were that alone would add up to 27 possible permutations." Being a trivial permutation however seems no barrier to being granted a patent. The series of three emitter followers was actually patented by Locanthi in US patent 3428908. Using that permutation of triples in a complementary output stage class AB amplifier is maybe being claimed as the original idea, but does that mean every application of any transistor triple can be individually patented? Or maybe it was the way the resistors were connected, but there are just three simple options.
There are a few ideas going back to the valve/tube era, for example the 'White cathode follower' patented by Eric White in 1944. That leads to a range of fairly obvious variations based on a single ended class-A output stage with current source load modulated in one way or another by the current through the output stage. One well known example is the Sugden A21 class-A, designed by James Sugden (1967) and built in Yorkshire. There are also a few class-B versions, including the Sinclair IC10 (1968), an integrated circuit power amp (made by Plessey), and I have an old page here with a few variations of my own incorporating feedforward error correction. A significant flaw is that the output power devices are usually the slowest and most nonlinear in the circuit, and the signal is to some extent being passed through these in series rather than in parallel as in most conventional circuits. There are nevertheless reasonably adequate commercial versions, the Sugden example was highly regarded by some, and after more than 50 years is still in production in an updated version.
Lots of information about this sort of circuit, SRPP, SRPP+ etc, can be found at: Tube Cad Journal. As the title suggests this is mostly about tube amps, but the linked page includes a couple of power mosfet examples.
MJR7 Final Comments.
The MJR7 is now just an old DIY design from 2010, but I still feel it is a well balanced design with nothing in need of improvement. Any aspect of performance could be 'improved', but not without either increased cost and complexity (e.g. feedforward as in MJR9), or alternatively with some trade-off making something else worse (e.g. higher feedback for lower distortion but also lower stability). The following adds a few details I may not have mentioned previously. Some of it is motivated by criticisms on various forums, but anyway, some explanation and clarification of design choices may be useful.
When designing my mosfet amplifiers my number one priority was unconditional stability including with capacitive loads up to at least 2uF. And why did I make stability my top priority? Because one of the biggest problems for amplifier designers is that we have no control over what sort of load will get attached. Some commercial designs were found to have stability problems when people started using high capacitance speaker cables. The first version of my own design could become unstable with a 2nF load. Even with extensive testing and simulations this was not picked up until someone happened to use exactly the critical load and reported the problem. Lateral mosfet outputs often have a higher open-loop output impedance than bipolar circuits and so can be more sensitive to reactive loads affecting open-loop gain. For both types the open-loop output impedance is higher if the quiescent current is too low, which is why I specify 100mA as both optimum for temperature stability and also the minimum for good feedback loop stability.
Note: unconditional stability entails more than just not oscillating with various loads, that just requires limited phase shift at the unity gain frequency, but that frequency is not fixed, it varies with different loads, also near clipping, at slew rate limiting and probably during switching on or off, so the phase shift, including that caused by the load, needs to be limited over a wide frequency range and with a wide range of reactive loads. My preferred test for stability is to check for bursts of oscillation when coming out of clipping with a range of capacitive loads, that is evidence that stability is only conditional, with the possibility that some combination of signal and load could trigger continuous oscillation. Testing with every possible signal and load is clearly impractical, so designing for unconditional stability is advisable. As seen for the MJR7 this can be achieved without sacrificing low distortion.
On the 'Latest News' page, dated 18-Mar-2023, I wrote: "Input stage distortion can be far less important than we may expect, with even moderate feedback there are two effects reducing distortion, one is just the feedback loop gain, but also the signal level being handled by the input stage is reduced, and this can be the dominant distortion reduction mechanism." With no feedback the input stage would have to handle the full input signal, maybe 1V, but with 80dB feedback it then only handles 100uV, resulting in far lower distortion.
That is true for amplifiers like my MJR7 with its inverting shunt feedback circuit, but not always for the more common non-inverting series feedback which still has almost the full 1V level at both inverting and non-inverting inputs, and will have some level of common-mode distortion, and other effects such as nonlinear input current. These add distortion outside the feedback loop, and increasing feedback loop gain will not necessarily reduce these, so eventually distortion will level off as we increase feedback, and further increase beyond this point is to some extent wasted. At that point redesign of the input stage is needed for further improvement, or switch to shunt feedback.
Depending on the source impedance shunt feedback may add more noise, but not enough to be a problem at power amp signal levels. With my calculated output noise 40uV and maximum output 15.4V rms the output signal to noise ratio is 112dB, and with an ear held against my 87dB/watt speakers there was no audible hum or noise, confirmed by my resident listening expert. (I don't trust my own hearing for that sort of thing.) I worked out the speaker sensitivity needed to make the noise audible to someone with good hearing at 1 metre from the speaker, and that is 107dB/watt. Such speakers are rare, and a design with lower noise may be preferable in that case, or maybe just listen at a more typical 2 or 3 metres.An easy way to determine whether distortion added outside the feedback loop is making a significant contribution is to start with the open-loop distortion, about 2% for the MJR7, and check that the closed loop distortion is that value reduced by at least the amount of feedback loop gain. The distortion at 10kHz is primarily 2nd harmonic at 20kHz, and loop gain is 66dB (x2000) at 20kHz, so we would expect 0.001% distortion, which is about what we do find, so all is well.
I know one constructor of the MJR7 connected the input direct to a 50k volume control. My advice was that this is fine, both output noise and distortion will fall with a high source impedance. With series feedback amplifiers both will usually increase, and the increases can be surprisingly high. The distortion increase was covered in some detail by Douglas Self in 'Audio Power Amplifier Design' 6th ed. pages 142-150. We have no control over what sort of signal source will get attached to our designs, so designing for the worst case looks like the best approach.Some aspects of the design were given a very low priority, one being the available output level with a given supply voltage. If correctly adjusted for symmetrical clipping with sinewave input the available output swing is +/- 22V measured with a 60V supply. Lateral mosfets have a much higher saturation voltage than bipolars, which inevitably reduces available output, but on the plus side don't suffer from 'secondary breakdown', so higher supply voltage can more safely be used to compensate.
Compare the popular MJL3281A bipolar rated at 200W and 15A to the ECW20N20 dual-die mosfet rated 250W and 16A. At collector voltage 100V the bipolar transistor is derated to 100W because of secondary breakdown, and current is therefore limited to 1A at 100V. The mosfet however maintains its 250W rating up to its 200V maximum drain voltage, and can supply 2.5A at 100V. At 200V the bipolar is further derated to just 40W. With reactive loads output transistors may need to supply high current at high voltage.Any concern about lower output usually fails to take into account the logarithmic nature of loudness perception. The usual quoted figure is a 10dB voltage level increase to sound twice as loud. That requires a power increase from 30W up to 300W. A one or two dB increase is barely noticeable, so if 30W isn't found to be loud enough then 40 or 50W is also likely to be insufficient.
Quantum Magic.
There are a few examples of the abuse of 'quantum theory' in some of the more outlandish audio product promotions. Quantum entanglement is one example, if not correctly understood that could look like a plausible mechanism for some inanimate object interacting with our audio equipment to make some audible difference. However, while particles in different locations can be entangled the initial process of becoming entangled is entirely local. Two particles normally need to be in the same place, or at least close enough e.g. for exchange of spin, before entanglement can occur. Two entangled particles A and B can then move apart, and B could then interact with a third particle C and pass on its entanglement with A, after which B itself must become unentangled, or alternatively just transfer part of the entanglement to a third particle (see the Coffman–Kundu–Wootters inequality), but anything else requiring 'becoming entangled at a distance' is just wrong, as is passing on the entanglement to multiple particles, (See the no-cloning theorem, Wooters, Zurek and Dieks, 1982).
There are one or two interesting variations, e.g. Experimental delayed-choice entanglement swapping, a procedure which can be interpreted as enabling two particles to become entangled without past communication, but this is just about measurements carried out by three observers on two pairs of entangled photons, so not applicable to large scale objects. It may involve a sort of 'backdated' entanglement, but there are some dissenting voices. One easily understandable treatment of a related delayed choice effect is The Delayed Choice Quantum Eraser, Debunked by Sabine Hossenfelder.
To learn about quantum entanglement starting at a very basic level the Susskind Lectures (lectures 77 to 85) are a good place to start, though the video quality is sometimes poor.
Hear What?
My preference for measurement and theory and mistrust of other people's listening tests dates back to around 1980 when my listening experiences were vastly different to reviewer's claims about cartridge sound, causing too much waste of time and money, and I eventually found happiness with my Technics EPC205C-Mk3 cartridge, chosen based on published measurements and technical features. So, I learned the hard way not to pay too much attention to the things other people say they hear. I made an exception for choosing my Mordaunt-Short MS20 speakers, but that was a review based on a blind test by a panel of listeners, which turned out to be more in line with my own impressions.
However, what sounds good to one person may sound terrible to another. As I wrote previously:
"There is evidence that different listeners have different sensitivity, for example some are more sensitive to pitch errors, some more sensitive to pre-echo and so on. An interesting paper reporting an investigation of this variation is Measuring the Characteristics of "Expert" Listeners by Shlien and Soulodre, AES 101st Convention, 1996. Those with the greatest sensitivity to one sort of error were generally much worse for a different type of error, a finding which the authors suggest dismisses the concept of a 'golden ear' listener good at detecting all errors. These findings relate to the evaluation of digital codecs which are known to have real artifacts which can be identified by skilled listeners."I suggest it is inadvisable to just accept what other people say they can hear, it may not be relevant to your own listening experiences. Even if you are prepared to trust their competence and honesty, they may obsess over something of little importance to you while failing to even notice something you will hate, and you could end up wasting a lot of time and money with little or no real benefit, as in my own cartridge trials mentioned earlier.
One of my problems with most cartridges tried was disembodied vocal sibilance, seeming to come from a different location to the rest of the voice, exactly what you would expect from the common falling separation at high frequencies.
My guess is that some reviewers were too old and simply had no hearing at the top of the range. These days my own hearing barely reaches 10kHz, and listening with a cheap 'substitute' stylus on my Technics cartridge it still sounds ok to me, but I can easily believe someone younger could be less impressed. Us old guys need to stop imagining ourselves to be 'skilled listeners', and for audio reviewers an upper age limit around 30 and regular hearing tests could make their reviews more believable. Maybe better to just play safe by assuming them all to be half deaf and delusional.In a 'Letter to the Editor' in Wireless World (Jan 1978 page 45) Baxandall wrote that amplifier designs he was involved in were normally not auditioned as part of the design process, and only listened to after the design was finalised, and yet his then recent design had been voted in first place in a listening comparison of many commercial amplifiers. He said: "Quad too assure me that they adopt the attitude that if you understand what you are doing thoroughly enough there is no need for listening tests during the design and development of amplifiers, and that they do not normally carry out such tests." He also wrote "it does not surprise me to learn, however, that many designers do feel it necessary to resort to listening tests."
That's rather unkind, not everyone can have Baxandall's level of expertise, and some famous name designers with highly popular designs have demonstrated a poor grasp of theory, but fortunately for them even sub-optimum designs can sound good to many.
Signal Nulling With Music Driving Speaker Load.
The signal nulling method of testing amplifiers is sometimes assumed to be too difficult when using a music input and speaker load. The variations in gain and phase caused by the speaker impedance are a problem, but there are at least two ways to overcome this. One is explained in Distortion Testing section 3.4, and an example includes Fig.5.9, 5.10 and 5.11, showing the reactive and nonlinear load used and the results without and with compensation. In effect this compensation is for the effect of the amplifier output impedance, which is generally simpler than trying to compensate for the load impedance.
There is an easier method applicable to inverting 'shunt feedback' amplifiers with high feedback such as my MJR7. A useful feature of my mosfet designs is that there is a built in error extraction function. Being an inverting amplifier the feedback network adds the input signal and the inverted output to give almost total cancellation at the input transistor base, reducing the undistorted component by 80dB at low and mid frequencies, or more with a little trimming, leaving noise and distortion in addition to the low level uncancelled music. I included an example for my old MJR6 design, just a 10 sec extract from 'Year 3000' which was the track found to have the highest slew rate when I was checking CD sources for the maximum levels. That sample was amplified considerably, then further amplified digitally for this version of the MJR6 error signal.
The noise is not the total amplifier noise because the 2uV added by the input resistor is nulled along with the input signal. The total noise at its original level at the amplifier output was still inaudible even with an ear held close to the speaker. The remaining noise in the error signal is amplified enough to be clearly audible, but the uncancelled audio is still undistorted enough to easily follow the lyrics, so even amplified to this level any distortion component is still small.
Conditional Stability.
So what is wrong with conditional stability in a feedback amplifier? A clue is in the name, if there is stability in only a limited range of conditions then we can conclude that there are some other conditions in which the amplifier is unstable. We then need to determine what action will trigger an unstable state. One of my own failed designs appeared to be perfectly stable with all the usual tests, square waves, clipping, capacitive loads and so on, but entirely by accident I found that driving it into clipping and then disconnecting the input resulted in continuous oscillation. So how would I have predicted that? Even if we could test with every possible permutation of source impedance, load impedance, and signal, then we could still miss the trigger condition. Something unforeseen such as unplugging the input at the wrong time, or maybe a burst of high frequency interference could trigger oscillation.
If we want to add another zero or two to the distortion figures it is tempting to resort to higher order compensation, e.g. twin-pole compensation, which can become 3-pole when we add a capacitive load, and I have seen examples with 3 and 4 pole compensation. The resulting conditional stability may not always cause any serious problem with these designs, but there is always some area of doubt and uncertainty, and testing every possible permutation of usage is difficult. Apart from being discouraged by my own experience of the sort of thing that can go wrong, I have found that low distortion can be achieved without taking such risks, so it's not an approach I find attractive.
I mentioned somewhere An-experimental-4-th-order-linear-audio-power-amplfier by GK, which had an idea to detect the approach to clipping to switch to lower order compensation until the danger had passed, and apparently something similar is done for some class-D designs using feedback with high order compensation, so for the known problems there may be solutions, but it's the unknown problems that would worry me more. Adding feedforward as in my MJR9 can reduce distortion without any significant effect on stability, so that looks like a safer approach.I found a comparison (LTSpice) of my MJR7 with a 3-pole bipolar example on diyAudio. At 10kHz my design has around 69dB loop gain, while the 3-pole circuit has 102dB, and yet both have the same closed-loop 10kHz distortion. If we didn't know any better we could calculate the open-loop distortion to be 33dB higher to explain needing that much more feedback to match the MJR7, and with MJR7 open-loop distortion being around 2% we could expect the other design to have 2% + 33dB, which is 89%.
Also, a bipolar output stage will typically have around 20dB less distortion than a latfet output stage, so with 33dB additional feedback we could expect distortion 53dB lower rather than being identical. So what happened to that 53dB advantage?
This appears to be an example of how feedback doesn't always reduces all sources of distortion. The MJR7 is an example where it does. Well, almost all.
Hard Work.
'We do these things not because they are easy, but because they are hard' (JFK).
'If something's hard to do then it's not worth doing' (Homer Simpson).
You can of course buy one of those 700+ page books about how to design audio power amplifiers, and you will learn a lot about circuit design, but does it really need to be such a complex problem? One of the purposes of my mosfet designs was to demonstrate that 'doing it the easy way' can still produce excellent performance.
Lateral mosfet amplifier design generally doesn't need great complexity, with 80dB loop gain easily attainable, at least up to around 5kHz without sacrificing unconditional stability, the input stage is then typically only handling 100uV peak amplitude, and even a single undegenerated bipolar transistor then only adds 0.1% distortion, almost entirely 2nd harmonic, which the 80dB feedback can then reduce to 0.00001%. I recently saw a latfet example with 14 transistors in just the input stage, and total 24, and with distortion specification higher than my MJR6 with only 4 bipolar transistors plus the 2 mosfets.The same unnecessary hard work is common in theoretical analysis, I have just been reading, or at least skimming through, a book about amplifier design, and there were pages with complex 'y-matrix' analysis and root-locus methods, the sort of things I had to learn about in the distant past, but rarely if ever found useful since. That sort of thing may discourage many readers, convincing them that it is a difficult subject they can never hope to understand. Really it isn't. Those complex mathematical methods can be good to know if this sort of thing is your day job, but for more casual enthusiasts just working things out from what are often simple first principles can be easy enough. That is my own approach, to look for the simple easy way to approach a problem. Ok, maybe I'm just lazy.
On second thoughts, 'doing it the easy way' is maybe a good description of class-A amplifier designs. We would expect it should be far easier to design for low distortion if we don't need to worry about crossover distortion. That leads to a strange observation, if we look at a list of currently available amplifiers and put them in order of THD figures, the lowest include many class-AB (e.g. Benchmark AHB2, Topping LA90) and class-D (e.g. Hypex, Purifi), but the highest distortion examples include a surprising number of class-A. Ok, I know THD is just one aspect of performance and there are other considerations, but that is one area where class-A should have a great advantage, which could at least partly compensate for the poor efficiency, and often low power and high cost.
The usual argument is that class-A distortion is mostly low order harmonics, which some listeners like, but as I wrote previously if the recording engineer also decides adding 2nd harmonic distortion improves the sound then adding more in the amplifier may add or subtract depending on relative phase, so giving uncertain results. Adding any required distortion in a separate pre-amp stage with adjustable level and phase, and with a bypass switch I suggest makes more sense.
Phase Margin: How Much is Enough?
I wrote about the MJR7 phase margin being affected by the fT of the input stage PNP transistor, if that is fT=100MHz then unity gain is 3.5MHz with phase margin 18 deg. I said 'that's still good enough' which may seem doubtful, usually a figure of 60 deg or 45deg is recommended. If all we want is to avoid continuous oscillation even a 1deg phase margin is adequate in principle. I did a simulation of a simple unity gain feedback amplifier, with the feedback loop unity gain frequency fixed at 1MHz and looked at the closed-loop gain with different phase margins. With 1deg there was a huge 45dB peak at 1MHz. Not what we want, but it's not necessarily fatal, if the MJR7 had a 45dB peak added at 1MHz that would be reduced by the closed-loop gain falling at 12dB/octave above 60kHz, being around -45dB at 1MHz, so just enough to prevent an actual increase in gain relative to 1kHz. The example I mentioned with 18deg phase margin would in this case have a 14dB peak at 1MHz, again reduced by 45dB by the falling gain, so the resulting gain at 1MHz should be -31dB relative to 1kHz. In practice we would hope there is never any significant input at or above 1MHz, so saying 18deg is 'good enough' seems reasonable. Increasing the MJR7 input emitter resistor from 1R5 to 2R to increase phase margin to 30deg is not essential, but I would still recommend that, or better still use some PNP transistors with minimum fT 200MHz or more. The actual unity gain frequency of the MJR7 is around 4MHz, so any added 'peaks' will be attenuated even more by the falling gain.
Amplifiers not using an output inductor may need far greater phase margin to avoid capacitive loads causing problems, then something like 60deg may be more essential.
Even with an output inductor a small capacitance load, typically 2nF, may resonate with the inductor close to the unity gain frequency and add unwanted phase shift, so that also could require higher phase margin unless steps are taken to avoid that effect. So yes, 45deg or 60deg may in some cases be needed, but 30deg is more than enough for the MJR7. 18deg may also be adequate, but it's not too difficult to find 200MHz PNP transistors or increase the 1R5 resistors to 2R, so the 'risk' is easily avoided.Another reason some advise higher phase margins is a concern about 'transient response', which invariably has nothing to do with band-limited audio transients but involves square wave response. The concerns include overshoot, ringing, settling time and so on. I wrote long ago about my dislike of square wave tests, they usually tell us nothing about audio transients, and are primarily affected by amplitude and phase variations far above the audio range. To see what a real audio transient can look like see the output of a square wave recorded on an audio CD, shown on my Modifying the Technics SL-PG390 page at the end of the 'Measurements' section. That is an almost perfect band-limited square wave, all frequency components up to 21kHz being reproduced with the correct amplitude and phase. If that was passed through an amplifier with a 45dB peak at 1MHz it would look exactly the same. There are various reasons to avoid such a peak, but audio transient response is not one of them.
Update: The 'various reasons' to avoid a very low phase margin include the fact that it is not fixed. Phase shifts inside the feedback loop include the effects of transistor capacitances which vary with voltage and current, e.g. the base-emitter capacitance Cbe includes diffusion capacitance which is proportional to emitter current, and so our 'adequate in principle 1deg margin' is likely to vary at different signal levels, and will also be affected by the load, so could easily dip to zero with resulting oscillation, so in practice we would want to keep a safer distance from disaster. Instead of just specifying a single figure 'phase margin' it would be better to state the 'worst case' phase margin, which is why I was investigating the effects of fT in the input stage PNP transistor.
