Work In Progress
I had a collection of short pieces which never became articles, so I have strung a few together in this page of 'Assorted Items'. Some are not very good, or at least too much personal opinion, and one is about DSP which I really know very little about, so maybe I got that all wrong. Anyway, my usual aim to present reliable information has been relaxed a little for some of the items on this page.
My hearing has steadily deteriorated with age, so I am definitely not the best person to make pronouncements on sound quality. Even when I was much younger and could hear up to 20kHz rather than the present 12kHz, I could rarely hear any of the many improbable effects claimed to be so obvious by many others. Turntable mats were one of the few notable exceptions, I was surprised to hear a clear effect when trying different types. The one I liked best was one I cut out from a piece of felt bought from a local craft shop. I had a Thorens TD125 turntable back then, with a Hadcock unipivot arm.
My greatest problem was trying to find a pickup cartridge with good sounding treble. All those I tried sounded different, but all produced the same 'spitting sibilance' on vocals. Trying different pre-amp circuits and load impedances seemed to help very little if at all. Reviews which mentioned the 'smooth treble' proved to be unhelpful, and walking round a local Hi-Fi Exhibition and listening to the exhibits, they all seemed to have the same problem to some degree. Some people seemed to be happy with this sound. I found it more obvious when listening on headphones, and one effect of poor high frequency channel separation is that vocal sibilance can become disembodied, appearing to come from a different location than the rest of the voice. To me the best sounding of the cartridges I tried back then was a cheap Audio-Technica (AT6S?) with spherical stylus, which had tolerable treble but also sounded a little distorted and muffled.
It was many years later I saw a review in 'Hi-Fi Choice' for the Technics EPC205C-Mk3. The high rating given in that review was not the deciding factor, I had seen plenty of good reviews for previous disappointing purchases. What attracted my attention was the flat frequency response, well maintained channel separation to beyond 20kHz, plus a claim to have the lowest ever tip mass for a mm-cartridge, and also an unusually low inductance, making sensitivity to load impedance less of an issue. When I eventually bought the Technics cartridge the resulting sound was an astonishing revelation, it was vastly better than anything I had previously heard from my records, and even some discs which I had assumed were seriously bad recordings were now perfectly listenable. I still have a turntable, now a Pro-Ject 1 Xpression, but a replacement stylus for the Technics cartridge is practically unobtainable, apart from a few very expensive re-tipping services.
There are some cheap replacements not made by Technics and not identical, but possibly better than nothing, including an example from Stylus Plus, currently available at £16. I thought this would just be a waste of money, but then I found one of these on eBay for even less so decided to give it a try. The sound is certainly not in the same league as the original stylus, but nowhere near as bad as I expected. It still sounds better than any of my other mm cartridges.
For comparison the next photo is my Technics cartridge next to a more typical example, the Ortofon VMS20E MkII, showing the difference in size of stylus and cantilever.
My first CD player was a Marantz CD273SE, and it is still working well. Some of the first CDs I listened to were disappointing, with what seemed like a very harsh sound, but others I thought sounded near to perfect. Listening on the Marantz, or on a portable Panasonic player or on the very cheap dvd drive on my computer makes very little difference, the bad CDs still sound bad and the good ones still sound good, so it seems recording quality is far more variable than playback equipment differences. The computer uses an EMU-1820m soundcard, and initial checks with a test CD show the computer player to be close to perfect. I have always liked the Panasonic player sound more than the Marantz, although I am uncertain whether this is a real or imagined difference, and now, April 2012, I have bought a Technics SL-PG390 (£16 on eBay), which uses the same single bit technology as the Panasonic portable, and tests show it to be already quite good. Attempts at improvement made little measurable difference, but I was already happy with the sound, and my modifications appear not to have done any harm at least, either audible or measurable.
One thing I found to make the best recordings sound worse is to convert them to MP3 (128K LAME 3.97). At higher or variable bitrates any deterioration seems far less obvious. I have many tracks available only as MP3s, and can easily believe a non-lossy format could sound better, but still enjoy listening to them. Encoders continue to be improved, LAME is up to version 3.99.5, and an interesting discussion about this can be found on Hydrogen Audio.
I use Sennheiser PX100 headphones (not the Mk2, I have tried them but prefer the originals) for much of my listening, and these have the sort of clear and relaxed 'laid back' sound I prefer. Many years ago I had some Yamaha HP1 headphones which had the same sort of sound, and I just saw a pair for sale on eBay with bidding well over £300. I remember them sounding good, but not that good, maybe no better than the PX100s.
My Mourdaunt-Short MS-20 speakers have a very similar sound to the PX100s, apart from a lack of low bass, provided the front wood/fabric grilles are removed, which reduces a treble peak, and having used these for many years I am still happy with the sound. There was a later version with a reflex port and a different tweeter made after the company was bought by the owners of Goodmans, but I never heard much about that version, so maybe it was nothing special. My version has the name in the bottom right corner of the front panel. They were highly rated, 'at the upper end of the 'good' category', in at least one 'blind' comparative test involving many other models, some far more expensive (the original 'Hi-Fi Choice', from around 1985 when it was published as a series of A5 size books, and still used blind testing), and another test (Hi-Fi News Jan 1983) compared them to the Quad ESL-63 electrostatics and found only minor deficiencies. They would of course not be much good for those who want extreme sound levels or floor-shaking deep bass, but for those with more delicate sensibility they are worth considering. Of course there is less incentive to buy something 'almost as good as a Quad ESL', if the real thing is within our price range, but having always been somewhat impoverished my interest is in trying to achieve good results at low cost.
My MS-20s were secondhand when I bought them, but the only problem I have found with them after many years use is that the bass driver cones tend to sag a little, and the coil starts to catch on the magnet poles. This is not a terminal condition, all you need do is remove the 4 screws holding the bass drive unit and rotate it through 180 degrees and replace the screws, then gravity pulls the cone in the opposite direction, that has always solved the problem in my experience. I have had to do this maybe twice in ten years.
A quick experiment reveals that a peak level of 2V at my speakers is the level at which other members of the family start complaining, and the lowest level audible at 1metre is 300uV rms at 3kHz, giving a level range of 74dB. My 'low power' 30W amplifier has another 20dB available, so with wider dynamic range material than the track I used for the experiment I could in principle reach a 94dB range, which neatly fits into the nominal 96dB available from CD recordings.
The other equipment I am using at present includes a Nakamichi CR-2E cassette deck and a Sansui TU-S33L tuner, both of which I am mostly happy with. The Sansui tuner is from 1982, and works well for my local reception conditions and my favourite stations. It was a surprise to open the case and see the level of complexity. I bought it on eBay for £6 as a temporary substitute for my Denon tuner while I do an upgrade, but it has such a clear sound, and looks good too, so I may stick with it. I also have a Technics RS-B305 cassette deck, which has less obvious distortion than the Nakamichi, but I like both about equally.
Speakers further up the price scale may produce higher sound levels and more extended bass, but apart from this I have rarely been impressed. Some examples made me want to plug my ears. Actually, when I first heard the MS-20 speakers at a local hi-fi dealer I thought they sounded dreadful, but I soon recognised that this was the poor signal source being used. So why would anyone in the business of selling speakers use such poor input? (Unless they were hoping to sell me something more expensive). If it sounded bad to me surely it should sound bad to them also? This could relate to the problem I mentioned earlier where I thought many pickup cartridges had unpleasant treble, but some listeners seemed to find it acceptable. 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. From this we could conclude that what sounds good to one person may sound terrible to another. These findings relate to the evaluation of digital codecs which are known to have real artifacts which can be identified by skilled listeners.
This may not be quite so relevant to the sort of 'subjectivist' listening tests where virtually everything is claimed to be audible, no matter how improbable, and double-blind testing is usually avoided.
As it happens, the reviews I have found most useful were those with blind listening tests conducted by a panel of listeners rather than the opinions of one or two individuals. Some of the early Hi-Fi Choice books were good in this respect, with large numbers of products over a wide price range included in the same test. This led to some cheap items being preferred to some far more expensive products.
As for amplifiers, I always use my own designs, so I make no comment on listening impressions of commercial designs. For any design the only thing coming out of an amplifier in normal use should be the voltage between the output terminals, and if at a certain instant there is 1V at the output it makes absolutely no difference what sort of circuit produced it. A volt is a volt, there is no such thing as a 'high-end' volt or a low-fi volt or a zero-feedback volt. If the output voltage is right there is no way to improve on that. The direct comparison 'nulling' method of comparing the output and input signal voltages is my own favourite method of checking for errors in the output voltage. Used with a music signal and driving a speaker any real audible effect should be easily identifiable by this method. My tests using this method show that for my own recent amplifier designs there is nothing identifiable to suggest that the amplifier could cause any audible degradation of the signal. Similar test results were being achieved by Quad more than 30 years ago, so my amplifiers are nothing special in this respect. The first published example I have found of the test signal nulling technique was in Wireless World 1953, by E.R.Wigan, and appears to have been used by Peter Walker of Quad as far back as 1945. My own work on this method in 1978 (shown here) achieved signal nulling well in excess of 100dB, allowing distortion at 0.0006% to be extracted and viewed on an oscilloscope with no obvious test signal breakthrough, shown as Fig.6.2.
Slew Rate or Half-Power Bandwidth?
When slew rate first became a popular concern among audio designers there was already a widely used specification which usually tells us almost exactly the same information, but in a more useful form for comparing amplifiers. That specification is 'half-power bandwidth' and is the frequency at which the maximum output power into a specified load falls by half compared to the 1kHz figure. For example a 100watt amplifier may be able to drive an 8R load at 50watts only up to a maximum frequency of 100kHz, no matter how far we increase the input, then 100kHz is the half-power bandwidth. This can be made more precise, for example by specifying the maximum output as the level at which distortion rises to 1%, but this is not necessarily more accurate or meaningful, the distortion will be reduced to some extent by various sources of high frequency attenuation which will differ between amplifier designs. The low to medium frequency power specification is also conventionally the 1% distortion level, but I doubt whether many designers actually measure distortion to arrive at this figure, my own approach is to look at the sinewave output on a 'scope and increase the input level until the onset of clipping becomes just visible, which is close enough to the 1% level for most purposes. The 1% distortion at the half power frequency will in most cases be a result of slew-rate limiting, which may be less obvious on a 'scope, but there is no point objecting that half power bandwidth is more difficult to measure than the slew rate limit because one can easily be derived from the other, so we can just measure whichever is more convenient. It may be a good idea to measure both to check that it is only the slew rate limit determining the half-power bandwidth, it could include some other effect such as cross-conduction in the output stage pulling the supply voltage down.
The advantage of the bandwidth figure is that we can more easily use it to compare different amplifiers with different power ratings. If we require a 100W amplifier to produce its full power at 20kHz it will need a much higher slew rate than a 10W amplifier needs to produce its specified power at the same frequency, so we need to calculate the equivalent figure for different power ratings. The half-power figure gives a simpler comparison with no need to adjust for power rating.
There can be some danger in measuring high power output at very high frequencies, for example the resistors in the output Zobel network may not have adequate power rating for such a test, and there may be other problems such as cross-conduction in the output stage. The dangers can be reduced to some extent by using a toneburst signal. I only tested my MJR7 up to 100kHz because that is the upper limit of my signal generator, and there was no obvious reduction in maximum output or any other problem at that frequency.
I have been reading 'The Scientist and Engineer's Guide to Digital Signal Processing' by Steven W. Smith, which is available for free download. It starts at a very elementary level, but eventually gets round to windowed-sinc filters, z-transforms and so on. Some more advanced topics such as limit cycles seem to be missing, but it seems like a good starting point for a relative beginner in this field like myself.
One of the problems I have been puzzled about is 'pre-ringing' in low-pass digital filters. What confused me most was the way many descriptions of this phenomenon also describe it as 'pre-echo'. Pre-echo is a widespread and familiar problem, it occurs for example as a result of print-through in magnetic tape recordings, and also in MP3 encoding. An interesting page of information about the MP3 problem is at Tests for Pre-Echo using Castanets. (Dead link). This includes ABX test results suggesting that all the encoders tested had audible effects which in most cases could be identified in 16 out of 16 tests, while measurement results also show clear effects. This is from 2001, so some encoders have been improved since then.
So how can a 22kHz low-pass filter used in an A/D or D/A converter and having flat amplitude and phase response cause pre-echo as is sometimes stated? The answer, as far as I understand it, is that it doesn't, but it can add pre-ringing to transients, which is not the same thing. An echo of a sound is generally defined as the sound itself delayed or advanced in time. Ringing is rather less easily defined, and what looks like 'ringing' may actually be an accurate result of removing high order harmonics. There is good reason to be cautious about the avoidance of ringing. An ideal low-pass filter which simply removes everything above fo and has no effect on anything below that frequency will pass a band-limited audio signal perfectly if it has no frequency components at or above fo. A square wave however will have its high harmonics removed, and will appear to have overshoot and continuous ringing. No matter how high we make fo the overshoot will remain, this is called the 'Gibbs phenomenon'. So how can we get filtered square waves with flat tops and no overshoot? This can be achieved with analogue filters called 'minimum phase', which actually add non-linear phase shifts, and therefore distort the wave shape even for signals already limited to the audio frequency range.
The point of all this is that attempts to achieve a particular visual appearance when using a signal which could never be a part of a normal recorded audio signal can actually distort the waveshapes of real audio signals. In the case of 22kHz digital low-pass 'brickwall' filters with linear phase response in the audio frequency range the impulse response has both pre and post-ringing, but again the unit impulse is not a normal audio signal. There is still reason for concern however, because the response to an audio transient is determined by its convolution with the impulse response, and so it seems unavoidable that normal recorded transients will also have some degree of pre-ringing.
What we need to consider is whether a few cycles of low level pre-ringing around 22kHz is likely to be audible. Those of us of more advanced age, with in my case practically no hearing above 12kHz, probably have no need to worry. Even those who can still hear something at 22kHz I guess need it to be fairly loud. Various methods to avoid pre-ringing have been developed, and although successful in achieving this they generally replace one problem with another. For example if a less sharp cut-off filter is used components above 22kHz may be inadequately attenuated leading to aliasing distortion products in the audio band. Use of digital versions of the analogue 'minimum phase' filters will also add phase distortion to audio band signals. My own guess is that for most if not all people the 22kHz pre-ringing is likely to be the lesser of several evils.
An unfortunate by-product of all this is as I mentioned the widespread mis-naming of the effect as 'pre-echo'. This may lead some listeners to believe they hear a pre-echo from their digital filters when some other cause is responsible. One writer described hearing a 'wooshing' sound prior to a drum beat when using a linear phase filter, which if it is real seems unlikely to be a filter effect. Older recordings originally on magnetic tape may still have real audible pre and post echo, but in this case the time dalay or advance will be long enough to make the origin of the effect obvious. Apparently some older digital filters had significant ripple in the pass-band and a real echo effect associated with this, but more recent designs have reduced these effects to extremely low levels.
There are many different ways to conduct listening tests, but the most convincing are those which can separate real from imagined effects. There are of course reasons other than imagination why listening test results can be wrong. Unfortunately arguments about 'subjectivism' tend to degenerate into accusations that those on one side are liars or fools, while those on the other side are deaf. Maybe these accusations are sometimes true, but without reliable testing methods how would we know? Reliability however is unlikely to be easily agreed, those who 'know what they can hear' naturally will regard failure to confirm this knowledge as evidence that the test method is in some way faulty, while for positive results those who think these audibility claims are nonsense will blame experimental error, and again maybe sometimes these assertions are true.
Personally I prefer an alternative approach, having devoted some time to error extraction testing I know that signals below a certain level when reproduced alone are inaudible, for example anything below 300uV at my speaker terminals is below audibility at 1m distance for even a test subject with far better hearing than mine. The lowest audible level I found is for frequencies around 3kHz as expected. Anyone claiming to hear effects below this level as part of a music signal is in effect claiming that these effects become identifiable in the presence of music played at their normal listening level. This implies some sort of reverse masking effect. Testing for such an effect is easily done by keeping the 'distortion' signal separate from the undistorted music signal, including using a separate amplifier and speaker. The distortion signal can then be played alone and switched on and off to confirm that there are no audible clues such as background noise or switching clicks. It is then a relatively simple matter to determine whether any test subjects are able to repeatably identify whether the distortion signal is on or off when accompanied by much higher level music.
Surprisingly there has been one test reported where inaudible signals apparently did become audible when another signal was also played, but that was for a highly artificial situation with signals close together in frequency applied to separate ears and beats heard (Groen, 1964, Acta Oto-Laryngol. 57 p224-230). This appears never to have been confirmed by other researchers. A paper published in 1995 was entitled 'Failure to hear binaural beats below threshold' (J. Acoust. Soc. Am. Volume 97, Issue 1, pp. 701-703, 1995), and as the title suggests the researchers failed to replicate these findings, and no difference was found between detectability of the beats and the audibility of the weaker sinewave.
I mentioned ABX double blind tests in the previous piece. Negative results from a single test, even if the listener is known to have good hearing, prove nothing other than that the listener at that time and under those particular circumstances was unable to reliably identify a difference. That tells us very little about whether an effect can ever be audible to anyone, at most it is evidence that extreme pronouncements, e.g. that anyone who can't hear it must be deaf, are gross exaggerations. If many listeners known to have good hearing fail to identify a difference we may deduce at least that it is fairly difficult to hear. If possible it helps to repeat the tests with the difference increased to the point where it becomes obvious and then decreased in steps until it is no longer distinguishable, this provides some practice and also demonstrates what effect is being investigated to help the listeners concentrate on the right thing. An example was featured on a BBC TV program about a professional violinist, to demonstrate that she could identify small distortions in violin music far better than the other listeners tested.Positive results, unless repeatable by different listeners with different equipment, are also of limited value, making a test blind or double blind is no guarantee that what is being changed is only the effect we intended to test for. Experimental error is always a possibility. An example I have mentioned somewhere is that if we play a piece of music and then change some component such as the speaker cable and listen again, then for the second audition the speaker voice coils start at a higher temperature because of power dissipation during the first audition. The increased temperature causes increased voice coil resistance which reduces output sound level, which may affect listening impressions. Repeating the test several times in different order can help reveal this sort of problem.
Even repeatable positive results are not necessarily correct if the same incorrect procedure is used. Another example I read about is an experiment comparing a 10kHz sinewave with a 10kHz squarewave. The only difference should be harmonics at and above 30kHz, which appear to be inaudible when produced alone. The experimenter explained that to ensure the 10kHz components were at the same level the peak voltages at the speaker input were set in a ratio 1.273 for the two test signals. The calculation appears to be correct, but one important source of error is being overlooked, and again this is thermal compression. The square wave with its additional harmonics causes a significantly higher dissipation in the speaker voice coil, which increases its temperature more and therefore increases its resistance and so reduces its output. To achieve the usual requirement of 0.1dB level matching additional adjustment may be needed. A better way to carry out this experiment would be to use two separate drive units, one with a continuous 10kHz sinewave and the other with only the harmonics needed to produce something as close as practicable to a square wave. This second signal could then be checked with the sinewave absent to ensure there is nothing audible such as background noise or switching clicks. If it is inaudible when heard alone but its presence becomes identifiable with the sinewave switched on, then this would appear to confirm a real audible effect. Maybe someone has tried this approach, which could be applied to many high frequency or sub-threshold effects, but I have so far found no examples.
It may be that a 30kHz component of a square wave really has some audible effect, but unless all alternative explanations, no matter how improbable, have been identified and excluded by further experiments then the conclusions must be considered unproven. I have suggested one explanation for this example, but there may be several more, for example intermodulation in the ear could produce a 20kHz component as the difference between the 10kHz and 30kHz components. A possible test for this would be to repeat the experiment at a range of square wave frequencies, e.g. from 7kHz up to 15kHz to find the upper limit for a positive identification of the harmonics. If 10kHz is close to the upper limit then an intermodulation effect becomes more probable. If it continues far beyond 10kHz then audible components within the conventional audio band are discounted.
Open-Loop Distortion. How low does it need to be?
This may seem like a strange question, for a feedback amplifier it is only the closed-loop distortion which ever appears at the output. What prompted this piece was having seen numerous statements to the effect that starting with a highly nonlinear open-loop response and 'straightening it out' with lots of feedback was a really bad approach. Having designed an amplifier, the MJR6, with more than 10% open-loop distortion and 66dB feedback at 20kHz I feel I should comment on this.
This idea that high open-loop distortion is a problem is often associated with a series of articles by Peter Baxandall in Wireless World in 1978, but possibly began even earlier with an article I mentioned on another page:
"In 1961 M.G.Scroggie published what at first sight appears to be an analysis of almost exactly the same circuit arrangement used by Peter Baxandall. This was reprinted and updated in Wireless World, Oct 1978, p.47-50, the author writing under the name 'Cathode Ray'. A square law device has overall feedback applied, but with 40dB feedback there is now over 7% third harmonic, 3% 4th, and so on."
These figures are far worse than Baxandall's results, but they are based on about 8dB higher open-loop distortion, yet the Baxandall figures with 40dB feedback are far better, e.g. 3rd harmonic is about 60dB lower, so what is really going on?
The factor which is frequently overlooked is that the Scroggie article is really about clipping, and the signal level used was such that the open-loop gain actually fell to zero at one point on the wave. The '40dB feedback' only applied to zero input voltage, and was higher for one polarity, and lower for the opposite polarity, eventually falling to zero. This is not therefore a failure of feedback to reduce distortion, it is really a failure to apply any feedback at all at some output level. The feedback loop gain actually varies from zero to over 40dB with this signal.
My MJR6 has over 10% open-loop distortion measured at 6V output, well below clipping. Over this peak to peak output voltage range the feedback loop gain probably varies from about 65dB to 67dB, so there is still high feedback over the entire output wave. The result is extremely low closed-loop distortion, with third harmonic 0.006% at 20kHz. At 1kHz loop gain is around 80dB and closed-loop third harmonic is -120dB (0.0001%).
A common idea is that open-loop distortion is not really eliminated by feedback, it is merely transformed into another form, for example the dreaded 'high order harmonics'. As I have mentioned on my page about Feedback Effects, there are transfer functions for which the addition of feedback makes no difference to the relative levels of the harmonics, and the square-law example used by Baxandall is just an extreme example where harmonics not originally present are produced when feedback is added. Even then using high levels of feedback the harmonics will fall in level as the order increases.
To summarise, a given percentage open-loop distortion such as 10% can involve incremental gain variations which reduce feedback to zero, e.g at clipping, or at zero-crossing with an unbiased class-B output stage, and in this case trying to 'straighten out' the transfer function with feedback is doomed to failure because when the open-loop gain is zero there can be no feedback. The MJR6 has none of the problems associated with high feedback or high open-loop distortion, and is an excellent counter-example. High feedback in this case really does 'straighten out' a relatively mediocre open loop response. With the addition of one more transistor to improve the open-loop linearity the MJR7 has even lower closed-loop distortion, but really the MJR6 was already excellent.
A while ago I bought Bob Cordell's excellent book 'Designing Audio Power Amplifiers', which gives examples of two pole compensation (TPC) and transitional Miller compensation (TMC) on pages 178 and 182, and I tried a simulation to compare these methods. The results are not exactly what I expected, at very high frequencies I thought the two capacitors in series would need to have the same value for the two circuits to have matching loop gain, so finding that the TPC version needed far lower capacitance than expected was puzzling. I don't see anything wrong with the simulations, so maybe it is correct, but I have never seen this mentioned anywhere, so I can easily believe I made a mistake somewhere. Using 20k in the feedback network in one circuit and 2k in the other may explain some or all of this difference. What may seem odd is that I have connected R3 (2k) to the nominally 1V 'output' rather than the actual output at node 5, which may look wrong , but connecting the other way the observed 'loop gain' no longer is second order, and attenuation starts at a far lower frequency. The connection shown gives the 'right answer' for the loop gain, but it takes a little thought to see why.
Initially, using AIM-Spice, I got a series of error messages, possibly because the dc gain was infinite, and I had to add 100k resistors to earth from both input and output of the VAS to get something like the TPC plots in the book. The TPC capacitors were then reduced to 25p, and a 0.035pF added between input and output of the VAS to match the peaks in the responses. Only small differences remain between gain and phase, showing that output stage distortion reduction will then be about the same for both methods. An optimum design of a real amplifier may of course lead to different conclusions, but these simplified circuits suggest that the only significant difference is the smaller capacitors in the TPC which will require less current from the input stage, and so could be an advantage.
Here is the simulation using AIM-Spice:
(In the first diagram for clarity I have left out the 100k resistors from input and output of the VAS to earth and the 0.035pF capacitor.) The gm signs look wrong, but that is how the voltage controlled current sources work, the current is into the output terminal not out. The 1V is the output of the output stage, and the gain and phase shift round the feedback loops are found by observing V5 (TMC) and V7 (TPC). There are of course other feedback loops, but it is these loops round the output stage which determine its distortion reduction. Both TPC and TMC are simulated together as a single diagram so that the results can be seen together on the same graph for direct comparison.
TMC-TPC-Compare. VIN 6 0 AC 1 R1 1 0 1k R2 1 6 19k R3 3 6 2k R4 2 0 100k R5 4 0 100k R6 11 0 1k R7 11 6 19k R8 9 0 20k R9 8 0 100k R10 10 0 100k C1 2 3 36p C2 3 4 150p C5 8 10 0.035p C3 8 9 25p C4 9 10 25p E1 5 0 4 0 0.96 E2 7 0 8 0 0.96 G1 2 0 1 0 -0.002 G2 4 0 2 0 0.04 G3 10 0 11 0 -0.002 G4 8 0 10 0 0.04
The red traces are TMC and green traces are TPC. At the top is the gain, and below is phase, or to be more precise, excess phase beyond the 180deg resulting from the inversion in the feedback loop.
The small differences could probably be reduced further by a few small adjustments. It appears there is no great advantage in either version, but both have the same dangerously high phase lag in excess of -170deg over a similar wide frequency range.
For comparison here is a recent result for the MJR7-Mk5 feedback loop phase response, first with 7R5 load:
The phase lag reaches only -110deg, which may seem excessively cautious, but now look what happens when we add a 2uF load:
The phase now dips a further 60deg to reach -170deg around 100kHz. With different capacitor values the maximum phase lag will be at different frequencies. Imagine now what will happen to the TPC and TMC examples in a real amplifier with a capacitive load. The same 60deg increase in phase lag would take the total far beyond -180deg and stability is then conditional, requiring that loop gain must not fall too far, as it will normally do near clipping, near slew rate limiting, and during switch-on or off. The effect of capacitive loads will not be the same for all amplifiers and so the effect may be better or worse than this example. It depends on several factors including open-loop output impedance and the value of the output inductor and its damping resistor.
It is possible to achieve excellent distortion figures without resorting to conditional stability, and if ultra-low figures are really thought to be important then my MJR9 is an example of how this can be achieved using feedforward, which has no adverse effect on stability. One version had the second harmonic of 10kHz at or below -130dB (0.00003%).
A common example used to illustrate the effect of dielectic absorption is to charge a capacitor by connecting it to a constant voltage source for a few minutes, then discharge it by connecting a small value resistor across its terminals just long enough for the voltage to fall close to zero. Then, having removed the resistor the voltage is monitored by a high impedance voltmeter, and is found to slowly drift back up to a significant fraction of the original voltage. If the original charging period had been as short as the discharge period then the upward drift would not happen, or at least nowhere near to the same extent. From this we could conclude that the capacitor is in some way reluctant to accept a full charge, and then continues to store it long after it appears to be discharged, only releasing it at a later time. This entire behaviour can be produced using ideal capacitors with no dielectric absorption by simply adding a second capacitor with a large value series resistor in parallel with the main capacitor, as in the next diagram:
The parallel RC values are not necessarily correct for any typical capacitor, for example the values for a 1u mylar type are given by Bob Pease as 0.006u plus 1000M, and his more accurate equivalent includes several more parallel RC combinations. A single RC is however sufficient to explain the basic behaviour of a capacitor with dielectric absorption.
Suppose both capacitors are initially discharged to zero volts. Moving the switch to C (Charge) a high current will flow through the 1R resistor and the 1u will charge with a time-constant of 1usec, and it will be close to the full 10V after 1msec. The 0.1u capacitor however has by then barely started to charge because the 10M resistor only allows an initial charging current of 1uA, and after 1msec it will only have reached 10mV. If we instead leave the switch at C for a few minutes then the 0.1u will also become charged close to the full 10V. If we then move the switch to the discharge position, D, for just 1msec, then the 1u will discharge back close to zero in that time via the second 1R resistor, but the 0.1u will barely change at all in that time, it will fall by only 10mV, down to 9.99V. With the switch now open we have a 0.1u capacitor charged to almost 10V connected to a 1u capacitor at 0V via a 10M resistor, and current will flow back into the 1u, slowly increasing its voltage and reducing the 0.1u voltage, until both capacitors are at the same level, about 900mV.
That is about all there is to dielectric absorption, at least if all we need is to understand the practical effect in electronic circuits. There is not actually a separate resistor and capacitor inside a capacitor with DA, this is just a useful way to simulate the effect, and also it appears that capacitors with high levels of DA often, but not always, have higher nonlinearity than capacitors with low DA, which suggests that the actual mechanisms within the dielectric material may in some cases include nonlinear effects. For most capacitors the nonlinearity is very small, there are only a few types such as high-K ceramics which add unusually high distortion.
Capacitors used in amplifier circuits can be divided into two groups, those used for signal coupling purposes, which should have very little signal voltage across them, and those used for filtering and frequency compensation, which may have much higher signal voltage across them, and therefore can with some advantage be chosen as types such as polypropylene with low DA and very low distortion even at high voltages. For coupling applications DA is less of a problem, and the only significant effect appears to be a reduction in unwanted phase shift compared to ideal pure reactive components.
From a practical point of view this is all very convenient, because filtering and frequency compensation capacitors are usually of relatively low value, and polypropylene types are then both cheap and of small physical size, which helps avoid interference pickup. Input coupling capacitors are often of several uF, and then polypropylene types are both large and expensive, but fortunately unnecessary, and smaller and cheaper types such as polyester can work as well, if not better. In one of my own tests a large polypropylene picked up 12dB more interference across the audio band compared to a small polyester. This I suggest is more important than whether the third harmonic distortion added at 20Hz is at -140dB or -160dB.
I have seen occasional claims that coupling capacitors with DA add some sort of delayed signal, rather like reverberation. This would involve the capacitor somehow recording the input signal and playing it back with a time delay, which would be a remarkable achievement for a simple capacitor. There appears to be no direct evidence other than the things some people say they can hear. DA certainly has an effect, but in reality it is little more than storing an exponentially decaying long term average of the applied voltage. For sinewave signals the effect is to reduce low frequency phase errors, while for pulse inputs the decay at the end of the pulse is present whether the capacitor has DA or not, and may again be reduced by the presence of DA, as suggested by simulations on my Capacitor Distortion page.
There are some applications such as 'follow and hold' circuits where DA is a serious source of errors, but this is because then the voltage is required to follow the signal accurately and hold that voltage when disconnected from the signal source. The problem is that a very short time-constant is needed to 'follow' the voltage, and the long internal time constants then continue to charge or discharge the capacitor and cause voltage errors during the 'hold' period. In input coupling applications long time-constants are good, we want the voltage across the capacitor to remain constant, any change is added to or subtracted from the input signal and is therefore undesirable. That is why we want to use a fairly high value capacitor feeding a high input resistance so that the voltage across the capacitor can only change very slowly, and consequently errors are added only at very low frequencies.
Peak Current Requirement of Speakers
There is a widely quoted claim that the peak current requirement of a typical speaker is far higher than we would expect from its minimum measured impedance. Some experimenters have done real tests with music and speakers and found that current peaks are unexceptional compared to the voltage peaks, but even so it is interesting to try to explain why the theoretical prediction is either wrong or at least irrelevant to music signals. The explanations I have seen for the current peaks mention the effect of 'back-EMF', but this is already accounted for by the inductive component of the impedance. Assuming linearity, for any individual frequency the current is determined entirely by the impedance at that frequency, and any more complex signal can be analysed as a sum of different frequencies, and the individual currents added, taking into account their phase angles in the usual way. So if each frequency has the current expected from the speaker impedance plot, where do those predicted high current peaks come from?
To see the problem from a different direction, consider a periodic signal voltage, so this involves just a fundamental frequency plus its harmonics. Keeping the amplitude of each harmonic constant but adjusting their relative phase we could ensure all frequency components are at their maximum positive voltage at the same time, and then the total signal would have its maximum possible peak at that instant. When applied to a speaker the frequency dependent reactive impedance ensures that the frequency components of the current are shifted around in relative phase, and are not then all at their maximum at the same time, so the current never reaches its maximum possible peak level. We could, instead, adjust our test signal so that it is the frequency components of the current which are all at their maximum at the same time, then we will get the maximum possible peak current for this set of frequency components, but no longer have the phases we needed to get the maximum voltage peak. We can then observe a ratio of peak current to peak voltage which if we assumed them to be directly related might suggest that the speaker impedance is far lower than our conventional minimum impedance specification.
Real music signals however include many different frequencies, some being harmonics and others unrelated, which will invariably combine to give peaks in both speaker voltage and current, but at different times unless the speaker is a pure resistance, and it is these we need to compare because in practical use the amplifier gain will, or should, be kept low enough to avoid clipping of the voltage peaks, and then hopefully this will also keep the current peaks adequately low. Using a test signal designed to have high current peaks without high voltage peaks allows us to turn up the volume further before voltage clipping compared to a signal with the same frequency components but with voltage peaks, and so gives a false impression, not applicable to a typical music signal. It would of course be possible to include a section of this test signal close to the voltage clipping level in an otherwise normal piece of music, but to do so would be perverse to say the least, and it is hard to believe any music lover would find the result enjoyable, irrespective of whether or not their amplifier could supply the current demand.
A simplified calculation: Including harmonics up to the 29th, the peak amplitude of a square wave can be increased by a factor of 2.97 just by adjusting the relative phase of the harmonics. An example in Ref.1 has a load with sections of a 28V square wave applied, which if we take the average impedance as 8R would suggest a peak current of around 3.5 amps. An adjustment of the harmonic phases to maximise the peak current level then gives a peak current 2.97 times higher, i.e. 10.4 amps, near enough to the 10 amp peak shown to occur. The calculation method is not entirely correct, we should use the actual impedances at each of the harmonics rather than a very approximate average, but is good enough to suggest that the phase shifts of the harmonics of the current are able to account the observed current peaks. The factor of 2.97 is not a maximum for all functions, it applies only to a continuous square wave including only harmonics up to the 29th. If we included all harmonics up to infinity we could in theory get infinite peaks of zero duration. See reference 5 for more details.
It is easy enough for an individual to check the maximum current they need, just by adding a small value resistor, e.g. 0.1 ohms, in series with the speaker and looking at the peak voltage across the resistor using an oscilloscope. With my own MS-20 speakers playing typical commercial cd recordings at the highest level I would normally use the peak current was around 500mA. With less efficient and lower impedance speakers, a bigger listening room, or music with very high peak to average ratio, and for those who like their music loud, levels well above this figure may be needed, but even my 'low power' MJR7 amplifier has at least a 23dB margin relative to the 500mA level. There may be commercial reasons for amplifier manufacturers to suggest that hundreds of watts and extremely high currents are needed even for typical domestic use, but instead of just accepting this I recommend checking the real level needed for any given application.
REFERENCES5. Google can plot a fourier series, here are the results for a square wave up to the 19th harmonic: square wave
1. Designing Audio Power Amplifiers, by Bob Cordell, (McGraw-Hill 2011) p373-375. The diagrams on page 374 include the voltage and current waveforms, with high current peaks but no similarly high voltage peaks. It is not clear whether this is part of a periodic function or just a single sequence lasting 50 msec but either way the signal has been specifically designed to give this disparity between voltage and current peaks.
2. Self On Audio, 2nd Edition, by Douglas Self includes a similar treatment on page 402. The idea appears to have orriginated with a paper by Otala and Huttunen, but I have yet to find a link to an accessible online copy. They mention peak currents up to 6.6 times those expected for a 8 ohm resistor for a commercially available speaker, using a complex signal cleverly contrived to maximise the effect. Probably in addition to the phase shifting effect I mentioned the speaker minimum resistance is lower than the nominal 8R, as is the case for most speakers. I measured the resistance of my own speakers as 5.5 ohms but clearly some are even lower, which is why we often specify amplifier power into 4R. The mention of 'stored energy' again, as I understand it, seems to be accounted for by the effects of the reactive components of the impedance, at least as long as the speaker remains reasonably linear. At sufficiently high levels nonlinear effects such as inductor saturation can have rather more dramatic effects.
3. How Speakers Torture Amplifiers. This piece from Stereophile, 2007, mentions two examples of experimental checks which failed to find any unexpectedly high current demands, but I will look out for more detailed coverage.
4. A Technical Guide to High Current Capability Amplification.This appears to be primarily a promotion of the Harman Kardon high current range of amplifiers from around 1980, but is an example of what can happen if some of these 'theoretical' ideas are taken too seriously. An output current requirement of 100 amps is claimed, along with mention of 'momentary impedance nulls'. I guess they must be using some new definition of impedance to arrive at that idea. Most of the rest of that piece also deserves criticism, but I will resist the temptation.
Here is what happens if we shift each frequency component by 90deg, which is easy to do just by changing all the sines into cosines. 90deg phase shifted square wave
It can be seen that the wave shapes are very different and the peak level far higher for the phase shifted version, increased from 1.17 to 2.69. If we had included all harmonics up to infinity the series for the peak amplitude is divergent, i.e. the peak is infinite, but also of zero duration. This demonstrates that phase shifts alone are able to increase current levels by any factor limited only by our upper frequency limit. Fortunately speakers invariably have impedance phase angles well under 90deg and we use band-limited music signals which are highly unlikely to include the sort of voltage waves needed to maximise the current peaks.
I wanted to buy some new headphones, but have problems finding reliable comparisons. Of course if it was possible to try a few of the short-listed items even for a few minutes this would at least narrow the search, even accepting the 'burn in' idea, but the models available for audition at local stores tend to be the fashionable and expensive variety, and those I tried proved seriously unlikeable to me, not even close to my old PX100s. Subjective asessments are sometimes difficult to take seriously, and separating the good from the bad can be a problem.
There are a few sites showing frequency response graphs, for example HeadRoom where 4 models can be selected and displayed on the same graph for comparison. There is some difficulty making meaningful response measurements because of interaction with the measuring equipment, and looking at other sources the results can vary considerably. What we can still do is compare results based on our personal likes and dislikes, so for example some models have extended bass response, some have heavily boosted bass, and some have worryingly high peaks at around 7 to 10kHz which suggests exaggerated vocal sibilance, one of my personal hates.
Apart from my PX100s I recently have heard the Sennheiser PX360, which I don't like much, if at all, the PX100-II which I don't prefer to the original version, and the JVC HA-S400 which seem very good apart from what I thought was a slightly hollow effect. These use carbon nanotubes in the diaphragms. I could probably get used to the sound over time, or maybe they really do 'burn in' as some say. Possibly I have become accustomed to open headphones and these closed types have a less familiar sound.
On the subject of 'burn in' I found that after many years use my PX100s developed what sounds like a response peak around 1kHz, and I had to use the equalizer on Foobar to cut the output about 6dB at 880Hz and 1.2kHz to get a good result. Then I bought new ear pads, and found the problem had vanished, I no longer needed the equaliser. Eventually the unpleasant sound returned, and once more I have the equalisation in use. It could be that the new foam ear pads allow sound energy to escape past the ears and this damps a resonance. When the foam becomes compressed after lengthy use it becomes a tighter seal, and there is less damping. Maybe, it's just a guess. Actually I think I prefer the worn earpads plus equalisation to the new earpads without equalisation, but it's very close.
I have some Sennheiser HD238s, which the HeadRoom graphs suggest are not too far removed from the HD600 frequency balance, but I bought these on eBay as 'faulty' hoping it was just a cable problem, only to find both drivers open-circuit. If one driver fails why would anyone carry on using them until the other driver also failed? I suspect some misguided attempt at 'burn in' using excessive drive voltage. Drivers can be bought for some models, but apparently not for these, however it appears many Sennheiser models use either identical or very similar drivers, even when there is a considerable price difference. The drivers in the PX100s look identical from the front, but I don't want to wreck them just to see if they work well in the HD238s, so I have bought some damaged PX100-II on eBay for experimentation.
Now I have taken apart both PX100-II and HD238s, and as I expected the drivers look identical. The front plate cutouts also look identical, as can be seen in the photos. The top two are the PX100-II and the others are the HD238.
The drivers are securely glued into the HD238s, so some damage was done to get them out, but fortunately the PX100-II has just two small blobs of glue so the good drivers came out without damage, and after fitting them in the HD238s they still worked fine.
I now have working HD238s and have listened for an hour or two, and I am starting to like the sound. There is almost no chance of any further 'burn in' if that happens at all, I am sure the drivers were already well used, but I may get more accustomed to the sound eventually. Whether they sound better than my original PX100s I am so far undecided, but they are certainly different, with brighter more extended treble, and maybe slightly excessive sibilance.