Latest News

I plan to delete the website later in the year. The free Angelfire version is not always reliable, so as an alternative here is a downloadable zipped folder containing the whole website:
Download zip folder, Renweb-Aug-2023.
It needs to be saved somewhere convenient and unzipped, e.g. by right clicking on the folder and selecting 'Extract all...'. Then double-clicking the index.html file in the unzipped folder will open the home page.
I may update the folder during 2023 if I make significant additions to the website.

I still get occasional questions regarding circuit boards for the MJR7 amplifier, and a few years ago I did make and sell a few, but only about 30, the design has never been highly popular. That is not unexpected, I included a number of 'unfashionable' features such as high global feedback, output capacitor and so on. The website is now only aimed at DIY enthusiasts who can make their own boards. Some have designed their own board layouts, and are happy with the results, but of course all my test results only apply to my own board layout.

WARNING - The lateral mosfets are becoming more difficult to find, and some suppliers are selling fakes. Some examples include cheaper vertical mosfets re-marked as lateral types, and these have a different pin layout with the drain in the middle instead of the source. Both types have an internal rectifier between drain and source which is reverse biased in normal use, but with the fakes these may conduct and at best just blow the fuse.

Missing Links

These are pages which currently only have links from this 'Latest News' page:

Cable Effect On Amplifier Stability.
Random Noise. Assorted thoughts.
Electromagnetism. Collected Comments
Inverting Amplifier - Noise
Guitar Amplifier With 'Flanger/Echo'
Class-B Feedforward Amplifier.
Boxsim Simulation Speaker Design Example.
Distortion Extraction.
A Simple Amplifier Test Method.
Mosfet Amplifier Designs.
Speaker With Conjugate Network.
Transmission Line Speaker Project.
MC Phono Preamp.
Dual-Notch 'Phaser'
Inverse Transfer Functions.
Positive Phase Negative Feedback.
Group Delay, Time Delay, and Phase Shift.
Can Feedback Cancel Time Delays?
Square-Law Transfer Function With Feedback.
Output Capacitor In Feedback Loop.
2-3 Transistor Amplifier Output Stage Variations

The previous item dated 01-Sept got too long for the 'Latest News', so I moved it to the end of the Random Noise page.

Just for amusement I tried to list all the 2 or 3 transistor amplifier output stage circuits, at least in their basic form. My initial attempt 2-3 Transistor Amplifier Output Stage Variations so far has just twelve, mostly dating from 1956 to 1973.

I added a piece about listening tests at the end of my Random Noise page. The developers of MP3 codecs use 'killer samples' chosen to accentuate known artefacts in listening tests, so why not use the same approach to listen for known amplifier distortions? Warning: the music I included as an example contains high level high frequencies which most of us will not hear, but it could damage speakers, so keep the volume down. Those high frequencies can create intermodulation distortion at more easily audible frequencies, which will not be masked by the high frequencies, so it is a more sensitive listening test than just playing some random music.

I added another footnote to my Can Feedback Cancel Time Delays? page, on the subject of recursion, about the idea that error correction travels round and round the feedback loop, which can lead to the idea that there is some sort of 'settling time' for it to reach its full effect. Opinion seems divided on this, my own conclusion is that you can think of it that way if you want, but you need to take into account the ability of a feedback loop to add a negative group delay to mostly cancel the typically few nanosec delay, so that we are left with an insignificant net delay round the feedback loop. In any case the phase shift from compensation capacitors is by far the dominant effect, and that also gets mostly cancelled by a phase advance generated in the feedback loop.

I added an update to my Inverse Transfer Functions page, to further explain something I previously wrote about how negative feedback creates the inverse of the output stage transfer function at its input. It's just another way to think about negative feedback, with the advantage that it explains how the distortion spectrum is changed, starting as the open-loop distortion and changing towards the spectrum of the inverse function as feedback is increased.

My 'recent' amplifier designs (the MJR7-Mk5 dates back to 2010, with just a few minor revisions) use an output coupling capacitor included inside the overall feedback loop. This solves a few problems, but adds one or two others. The most serious of these could be a peak in the signal level prior to the capacitor if we try to extend the low frequency response too far, and this is explained in: Output Capacitor In Feedback Loop.

I wrote previously about how, at least at low frequencies, peak distortion depends only on peak signal level, so it makes no difference what test signal we use, sinewave, music or whatever, if they have identical peak levels then they have identical peak distortion. There is a 'DC Transfer Curve Analysis' option in AIM-Spice, and I assume also in other versions, which can be used to demonstrate this. The distortion plots show peak distortion over the range of input voltage, with no need to specify the test signal being used apart from its peak level. I also asserted that adding any level of feedback reduces peak distortion, even though some individual harmonics may increase. I have added a page: Square-Law Transfer Function With Feedback. The results are as expected, and it was also a reminder that 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. The increased higher order harmonics produced by applying feedback to a square-law amplifier are invariably derived for a fixed input signal level at the input of the square-law device, but if feedback is increased by increasing the gain of following stages inside the feedback loop then the input stage signal level falls and higher harmonics are dramatically reduced to leave almost entirely a low level of second harmonic.
There are of course other sources of distortion apart from the low frequency transfer function, e.g. at very low frequencies there are thermal modulation effects, and at high frequencies the nonlinear transistor capacitances may have a significant effect.

Another new page, Can Feedback Cancel Time Delays?
I mentioned on my Feedback Effects page that negative feedback can create a phase advance sufficient to cancel a small time delay over a limited frequency range, and here is further explanation of how that works.

I added a new page: Group Delay, Time Delay, and Phase Shift.
It was originally motivated by a criticism of my MJR7 amplifier, but sometimes it's better to ignore that sort of thing, and it evolved into something more general.

I added something about the difference between positive feedback and positive phase feedback on my 'random Noise' page. That was motivated by seeing a discussion in Wireless World (Letters to the editor May 1973) between two well known audio designers, my conclusion being that neither had a correct understanding of how negative feedback works. I found support for my version, inevitably in an article by Baxandall, Wireless World, March 1978, page 42, where we find,
"it is sometimes said that feedback is negative if the real component of the feedback voltage.... is in antiphase with Vin and that feedback is positive if the real component is in phase....This however is a popular misconception."
The mathematical analysis is already included in my 'Feedback Effects' page and again in a different version in my Transistor Amplifier Design for beginners, Part 6, but some further explanation is possible, and I have added a page: Positive Phase Negative Feedback.

In a mosfet power amplifier how much current does the driver stage require to drive the mosfet input capacitance? For my 30W example the peak output voltage is 22V into a 7R5 resistive load, but the output stage has less than unity gain, so the driver stage peak output is higher, something like 28V. The input capacitance of the mosfet output stage is something I measured for my original MJR6, and with a 7R5 load it was 200pF. The peak current is determined by the maximum rate of change, dV/dt, of the signal being amplified. My measured maximum slew-rate for CD music was that of a full peak level 10kHz sinewave.
The 200pF has an impedance of 80k at 10kHz so 28V peak sinewave voltage gives peak current 28/80,000 = 350uA.
My MJR7 driver stage can supply 15mA, so quite a big safety margin. A 100W 8R amplifier driving 4R will of course need more drive current, maybe as much as 1.5mA. The only way to argue that more current is needed is to either use vertical mosfets, which can have higher capacitance particularly near clipping, or to insist that you want a full 100W output level up to something like 400kHz. Then you could need over 30mA. I use lateral mosfets, with mostly CD and cassette tape source, and speakers with well behaved impedance, so even if I turned the volume up close to clipping, which I never do, I still need just a few hundred microamps peak drive current.

Update: I checked the current with a simulation, and confirmed the 350uA peak. Increasing the frequency beyond 10kHz the current increases, but is eventually reduced by the 60kHz low-pass response of the amplifier, and the maximum requirement occurs at 150kHz. Then, even with the minimum gm specified for the mosfets and with a 4R load the peak current only reaches 5.6mA, so still well within the capability of the driver stage, and not a problem. (The gm and load are relevant because they determine how far the effect of Cgs is reduced by the 'bootstrap effect'.)

Is low harmonic distortion with a 20kHz input a good indication of amplifier performance? I have added something about that in a footnote in my Amplifier Design for Beginners, Part 6 concluding that it depends on how the low THD-20k is achieved. Improving open-loop linearity at 20kHz is good because it also reduces intermodulation components down in the audible range, but low THD-20k can also be achieved by increased feedback at 40kHz and beyond, which does little or nothing to reduce potentially audible intermodulation, it mostly reduces the already inaudible harmonics at 40kHz plus, while also probably reducing stability margins, so generally not the best approach.

I have now added a new page about modifying the MJR7: MJR7 Modifications.
Most are based on my not entirely reliable simulations, not tried in a real amplifier, so they should be viewed only as suggestions, maybe needing some experimentation for best results. I strongly advise sticking to the original components and layout, these already are known to work well.

I saw an argument on diyAudio about the maximum free-air dissipation for a TO126 transistor, about whether 250mW was ok or not. In my MJR7 the current source transistor runs at 15mA and 30V using a 60V supply, so that is 450mW. Is that safe? The transistor gets fairly hot, but not too hot to touch, so probably around 70deg. I have had 2 amplifier boards used several hours a day for well over 10 years in an unventilated case without any failures, and have not heard of other constructors having any problems. There appears to be no free-air rating on the data sheet, but for the BD140, also TO126, there is a figure of 1.25W for ambient temp 25deg.C. I don't see any reason to worry much about 450mW, but it should do no harm to at least add a small heatsink to the current source (the KSA1381 nearest the top of the circuit diagram), and I already advised using heatsinks if the supply is higher than 60V. I will continue to use my own amplifiers without adding TO126 heatsinks.

I finally added a page about my 'phaser' guitar effect pedal, using a slightly unusual voltage controlled notch filter. It's not a new idea, it was published in Wireless World 'circuit ideas' many years ago, but I added the option of selecting either notches or peaks, so adjustable from a phaser to a wa-wa effect, and a strange dual peak band-pass half way between these options. My construction was a bit messy, needing alterations, with cut tracks and added components, so I have not included a final board layout, just a few photos. It's here: Guitar Effects: Dual-Notch 'Phaser'.

I found an online copy of an article I mentioned relating to signal nulling distortion tests, it is: dynamic testing of audio amplifiers by Frank Jones in Hi-Fi-News Oct-1970, pages 1655 to 1657. It is mostly about the test methods used by Peter Walker at Quad 'for the previous 25 years' so starting back in 1945. The first published example I have seen was by E.R.Wigan: Diagnosis of Distortion in Wireless World June 1953 pp261-266.
My own contribution was my M.Sc dissertation from 1978 available HERE which added not much really new, but achieved greater precision, for example displaying distortion residuals down to 0.0006% in Fig.6.2.
I have now added some test results using this method from an earlier version of the MJR7 near the end of my test page: MJR7-Mk5 Test Results. The Mk5 version has lower distortion, so I never tried the nulling method, assuming it was unlikely to reveal anything useful.

Here again is the result of my nulling test with the old MJR6 using music and driving a speaker
The noise is 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. Maybe sometime I will repeat the test for the latest version MJR7, I know how to do it better, but if even the relatively poor MJR6 has no problems revealed there seems to be little point.

An interesting puzzle: Before my MJR7 I had a mosfet amplifier using the standard circuit from the original Hitachi application notes, and the output at clipping into 8R was 85W using a 94V rail to rail supply. Using exactly the same supply for my MJR7 the peak level was 79W. That's just a 0.3dB reduction. We would perhaps have expected the cascode stage to cause a greater reduction of peak output level, but that doesn't appear to happen. My theory was that when the cascode transistor approaches saturation its current gain drops and so its base current increases, and when that reaches 1mA that removes the bias current through the two LEDs, and so the voltage at the cascode base drops, and so the reduction of clipping level is avoided. I knew the bias voltage could drop, which is why I used only a 1n capacitor across the LEDs to allow fast recovery after clipping. I showed the clipping result at 44V pk-pk with a 60V supply, and even at 100kHz there was no visible problem.

One component value in the guitar octaver circuit has been updated, the 47k control for maximum bass frequency had little effect except at the top of the frequency range, and this will have a wider range of effect if increased to 220k or 500k.

I remember reading one of the Bateman articles about the effect of speaker cables on amplifier stability. I didn't see any reason to worry about that sort of thing, but maybe I need to demonstrate how my MJR7 circuit is affected by cables, and why there is no serious problem. Not all amplifiers are happy with even 'normal' cable and speaker combinations, and some of the more extreme cables may be worse. Anyway my check on the MJR7 and some more general information can be found at Cable Effect On Amplifier Stability.

The 2SC2240BL is now mostly unobtainable, and the 2SC3324BL smd (surface mount) substitute I suggested previously is also discontinued. There is still one equivalent available, the 2SC2713-BL from Toshiba, available from Mouser, RS and others. It is again a very small smd type.

For some projects where I needed just a simple PCB I used an etch resist pen, a now unobtainable Decon Dalo which always gave good results etching with ferric chloride, but my last one is now finished and I needed a replacement. I previously tried the usual 'permanent' marker pens, Sharpie, Staedtler and one sold by CPC described as 'Etch Resistant Pen AR19', but none were very good. Now I found one, the UNI PNA-125, still not as good as the old Dalo pen, but good enough.

I previously wrote about inverse transfer functions, which can reverse the effect of a nonlinear transfer function, but thought I could maybe explain better with an example related to the familiar 'square law' amplifier, so here is a page about Inverse Transfer Functions.

I just checked my hearing range at 20Hz-20kHz, the result being that my hearing stops around 9.5kHz. Fortunately I have a resident 'expert listener' young enough to hear the full range who I can rely on for listening tests. What prompted this was looking at Stereophile's Products of 2021. The first thing I realised is that I probably don't qualify as an audiophile, there are none of the products listed I would be excited to own, or would want to buy even if I was offered a 90% discount, except to resell for a profit, with the possible exception of the KEF speakers, which would fit neatly next to my TV.
Anyway, there is interesting information in the comments section where we learn that the reviewer has hearing limited to 13kHz, and an earlier reviewer reached only 11kHz. That shouldn't be too surprising, old age plus many hours spent listening to high power amplifiers will inevitably have its effect. What this reminded me of is something I wrote about a few years ago on my Assorted Items page about how, many years ago when I could probably hear double my current range, I wasted a lot of time and money searching for a pickup cartridge with good sounding treble, and eventually concluded that many reviewers must be half deaf. Maybe that was literally true, with some of them having half the audio range missing. That experience was one reason why I stopped taking seriously the things people say they can hear and paid more attention to technical considerations and measurements, which led me to happiness with my Technics cartridge. Now I am also happy using a cheap replacement stylus, which for all I know may have the same sort of high frequency problems I could hear long ago.

The flanger effect adds a series of notches in the frequency response which can be modulated so that they scan up and down some frequency range. Using a time delay can give a long series of notches, but if a smaller number of notches, maybe just 2 or 3, is acceptable then there are alternative circuits not needing a time delay. This is often done using a number of voltage controlled all-pass filters to achieve a limited range of equivalent time delay. The result is generally known as a 'phaser' rather than a 'flanger'. That seems to need 4 filters in series to achieve 2 notches, and if we use jfets to control the filters we need 4 fairly well matched. A possibly better alternative is to forget about time delays and just design variable notch filters. I remember an example of a variable notch filter I saw published long ago, which just needs a single jfet for each notch, so for 2 notches we only need to match 2 jfets and use 2 opamps. A simulation confirms that it will work, at least for 2 notches. This certainly no longer qualifies as a 'flanger', and maybe not even a 'phaser', but the effect should be at least similar to a phaser. A complete practical circuit needs little more than a quad op-amp and two matched jfets, plus resistors and capacitors.

I was thinking about two guitar effect projects, one as mentioned below adds distortion, the other is a flanger-chorus-echo with a single simple circuit covering all these options. Searching on Google for ideas about how to do the flanger effect I was dismayed to find my own Guitar Preamp and 'Flanger' appearing near the top of some searches. The problem is that it really is not a genuine flanger, which is why I included the quote marks in the title, but unfortunately Google seems unable to cope with such nuances. The circuit used a single PT2399 time delay which has a minimum delay around 30msec, which is far too long for a flanger, although previous experience with a tape based flanger suggested something like the flange effect was still possible with long delays. Anyway, to keep delays down to the official flanger range we need to use two PT2399s so that the difference in delays can be adjusted down to a low value or even pass through zero if modulated. This then causes another problem, that the final summed output is delayed by about 30 to 40msec, and that is almost certainly enough 'latency' to be annoying for some guitar players. Delay devices with shorter delays do of course exist, but are either expensive or almost unobtainable, apart from some such as the MN3207 available at suspiciously low prices from China, one of which quoted a 2 month delivery time. Another option is to add some level of the undelayed input to the two almost equally delayed outputs, to possibly hide the delay without entirely losing the flange effect. Not entirely convincing, but maybe worth experimenting with.

I added another link above, to ADD H2 DISTORTION. That was a continuation of a piece on the Random Noise page about the claims that some amplifier designs have nice sounding distortion. It's easy enough to design low distortion amplifiers, but if we prioritise other design features such as 'no global feedback', 'wide open-loop bandwidth' and so on, based on the belief that these approaches will avoid some unpleasant distortion mechanism, then in practice many such designs end up with poor or mediocre distortion specifications, hence the claims to produce 'good distortion' rather than the supposedly 'bad distortion' produced at typically -100dB or less by a high feedback low distortion design. The point I made, and which others have previously mentioned, is that rather than compare many expensive amplifiers with a wide variety of audible distortions, it makes more sense to use an adjustable distortion adding stage in the preamp. I designed one example about 20 years ago, and now added another more predictable and versatile example. The earlier design was never meant to be taken seriously, but the latest version has some serious point as an addition to my 'guitar effects' series, one of the few applications where intentionally added distortion can be justified.

The 'octaver' project is finished and it works better than I had expected given the obvious problems. Most commercial analogue versions use a sort of 'tracking hysteresis' in the circuit to extract the fundamental frequency, but I had doubts about the dynamic range, so I used a different approach which turned out to have a good range, and also an additional trick to automatically use a higher division ratio for higher frequency inputs to keep the added bass below an adjustable maximum frequency.
I have only built one, and different samples of the J113 jfets with significantly different characteristics may lead to unexpected problems. I used the Fairchild version, and as mentioned previously different manufacturers may even have drain and gate reversed.

The design is called the MJR-OCT-Mk2.

The next project in my guitar effects series is an 'Octaver' which adds notes one or more octaves below the note played. In its simplest form this just detects the zero-crossing of the input waveform and produces a square wave to apply to a binary divider to divide by 2 and 4 and then add these outputs to the original input via level controls. This has serious problems limiting the effectiveness, but as usual a bad effect may be just what some people want, however something better is certainly possible and there are some relatively advanced versions available.
I started working out a few possible solutions to the obvious problems before looking at a few circuit diagrams to see how others have done it. Some examples look incomprehensible, but there are some common ideas to learn from. Using a purely analogue circuit the problem to extract the fundamental for any possible guitar signal is difficult, and even some of the expensive products advise limited playing techniques to reduce problems, and the use of compression to limit the dynamic range being handled.

My first attempt included a compression circuit, but that failed to work, I eventually decided I must have a faulty jfet so tested a few spares and they also appeared to be faulty. I was already composing an email to the supplier when I thought to check their data sheet. That's when I realised that although the manufacturer is specified as ON-SEMI the data sheet is Fairchild, who are now a part of ON-SEMI. Well ok, that shouldn't matter, surely a J113 is a J113 whoever makes it. But no, comparing an old ON-SEMI data sheet I find the gate and drain connections are reversed compared to the Fairchild data. I had used the ON-SEMI diagram for my layout, so that's why it didn't work. I don't know if On-Semi really did make them reversed or it was just an error on the data sheet. Anyway it now works.

If we divide voltage Vx by infinity we get zero, but if we multiply zero by infinity we don't get Vx. That's why no clever feedback method can ever reduce output distortion to zero. In this case Vx is the distortion signal at the input of the output stage. This has to be derived from a feedback signal, but if there is zero distortion at the output how can we derive Vx from it? Multiply zero by anything you like, you will never get Vx. Output distortion is essential for distortion reduction by negative feedback.

I've fixed the various dead links on this page, and some others, some replaced by new links, others deleted. This is a never ending problem. If all else fails there may still be the Wayback Machine internet archive, with storage of 477 billion web pages. If any of those dead links had been really important that's the place to look.

I asked Profusion:
Regarding the specifications for your range of lateral mosfets: Is the 'Integral protection diode' mentioned just the drain-source diode, protecting against reverse bias, or is there also a gate-source over-voltage protection? The similar Renesas devices include a pair of back to back zeners for that purpose, do yours also? If so what is their maximum current rating?
The reply:
'Yes the Exicon MOSFETs include back to back Zener diodes around 14V but they are not tested in production and therefore no specifications are included on the data sheet. The size would rate them around 1W.'
So, maybe the 12V zeners I included in my amplifier designs are not essential, but including them adds a little extra safety, and at least should do no serious harm.

This 'latest news' page is increasingly lacking in any actual news, it's mostly just comments on whatever I was thinking about lately. Now I have started a new page for that sort of thing, called, rather disparagingly, Random Noise. If there is ever any real news about new projects or new theoretical pages then I will still add a link here on the Latest News page.

All the bits about Corona virus have been moved to a separate page, Corona Days

My board layouts never include neatness or appearance as high priorities, and although some constructors have made better looking versions of the MJR7 power-amp I am uncertain how much these will alter the performance, for better or worse. I saw a new version at diyAudio - post 673 which has the advantage of being close enough to my own layout to have a good chance of being similar in performance, but looking neater. For anyone discouraged by my untidy board design this version may be a better option. I haven't checked it thoroughly, but I don't see any obvious problems.

The version of the Heisenberg Uncertainty Principle I learned as a Physics student was that it is impossible to measure, prepare, or predict both the position and momentum more accurately than specified by the principle. The prepare or predict part is sometimes overlooked. The reason I was reminded of this was reading a paper titled Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle. Being somewhat baffled by this, I looked at some online comments and found one suggesting that Heisenberg's principle must therefore also be doubted. What this is missing is the additional 'prepare and predict' clause. To carry out that sort of listening test it is unavoidable that these signals have actually been generated, and their properties can be confirmed by measurement, e.g. using an oscilloscope.

This is fundamentally different to the quantum mechanical version, where there is no way to directly observe the wave-function of a particle, it just tells us about the probabilities of measurement results. The Fourier Uncertainty principle is of a totally different variety, and the limitation is not absolute in the same sense. It applies in classical theory where everything can in principle be prepared, predicted and measured to any required accuracy, and only applies to the standard deviations of the time and frequency domain distributions. In practice it is the noise level which limits the accuracy, and if the signal was close to the noise level then the standard deviation would have some practical importance, we could not then measure location in time or frequency to much less than that value, but at higher signal levels we can more accurately measure the magnitude and shape of the time and frequency distributions, though we don't need to measure both, the signal level as a function of time of course tells us everything about the signal, we can then calculate the corresponding frequency distribution if we need to know that.
As I understand it the point of the tests was that the result is incompatible with certain models of human hearing, suggesting these are therefore wrong. That may not be sufficient reason to entirely abandon those models provided we take into account their limitations. i.e. all models are wrong, but some are useful.
(Note: the corresponding Heisenberg principle for time and energy (or frequency) is disputed, (example here), something to do with the Stone-von Neumann uniqueness theorem, which I only vaguely understand.)

ON-Semi now list the BC560C as obsolete. A possible substitute, the BC559CTA, is still 'active'.
The obsolete BF862 jfet can be replaced by the 2SK2394-7, and BF245C by J111.

Today I was reading, (really just skimming through, it's 1170 pages long) the latest report (Sept 2019) from the IPCC (Intergovernmental Panel on Climate Change). At one point I had thought of writing something on this topic in my Physics section, but this is a big subject, there are hundreds of research papers listed in that report, and not the sort of thing someone with just a casual interest could expect to write anything useful about. I wrote in my article 'Acceleration and Relativity' about the problems of defining 'sea level' where I said:
"Reality is of course rather more complicated than this idealised analysis. Sea level varies significantly throughout the day due to the gravitational field of the moon, and there are time delays to be expected for large masses of water to move around to change the level, giving different effects in different locations, so even a definition of sea level is problematic."
Chapter 4 of the IPCC report covers the problems in greater depth. One serious difficulty is that the land level is also changing, rising in some locations and falling in others, but since 1992 the use of satellite altimetry has improved accuracy. There are still varying local effects such as tides, rainfall and wind direction, so measuring the global trend requires averaging many locations.

The various pieces about electromagnetic theory on the 'Latest News' page have now been combined in a new page called Electromagnetism. Collected Comments, edited and updated slightly to make it read almost like a single article.

So why do I want to write pages about elementary electromagnetic theory? It was about 50 years ago when I studied the subject in any detail, so I forgot lots of it since then. What worries me is reading things on the internet, and thinking; 'that looks wrong' but not knowing whether it's me or someone else getting it wrong. Some parts I remember well enough and feel confident about, other parts need 'research' looking at multiple sources, and writing things in short articles helps with the relearning process. It's surprising how much disagreement there is even on basic theory. Anything on audio sites about speaker cables needs approaching with caution, but even Feynman's Lectures had many errors, not all of which have been corrected in the online version, so just accepting anything on the internet is a bad idea.

There are already a few pages of em-theory related material, so maybe I will collect them into a separate section. Some need rewriting first. My page about skin depth still doesn't look entirely convincing, but other treatments I found also seem inadequate. The Wikipedia page is rather odd, e.g. it says the field 'forces the conducting electrons to the outside of the conductor' which must be wrong, or at least badly worded, at most it could accelerate conduction electrons more in some locations than others, (perhaps it just meant to refer to 'current'). The density of conduction electrons must be almost uniform throughout a conductor, a difference of even one part per million between two regions would cause huge fields and forces. I gave an example of the magnitude of charge variations in my transmission line page:
"In a 300 ohm transmission line carrying 1 amp the negative conductor has an excess of conduction electrons of the order of 1 part in 1012...."
I need to check that sometime, I think I assumed 300V between the conductors, about 1cm apart, then one part per million excess conduction electrons would imply three hundred million volts across 1cm, which I imagine would have a rather dramatic effect.
The 'circulating eddy currents' in the diagram look a bit misleading too, adding them all together there are almost no actual circulating currents or radial currents, adjacent loops cancel along their common edge, apart from some higher order effects which increase with increasing frequency.

I am working on a piece provisionally titled 'Beginner's Guide to the Vector Potential' The vector potential (A) appeared in the original 'Maxwell's Equations' in addition to the electric (E) and magnetic (B) fields. It isn't really very useful for everyday electronics, and has little relevance to audio design, so it will end up in my Physics section. The vector potential is simple enough, but some understanding of Maxwell's equations and basic vector calculus is probably unavoidable, so maybe I should call it an 'Advanced Idiot's Guide', that being my own level.
Update-1: (31-Jan)
I eventually just called it Maxwell's equations and the Vector Potential and it is now finished, but may get a few updates after further contemplation.

About my MC Phono Preamp design, I mentioned that the first version has a few problems. There is a discussion at DiyAudio about MC preamps, and the Quad version is mentioned with criticism that the input current via the pickup coil can be excessive under fault conditions where the supply voltages are not equal or if they switch on at different times or rates. My own variant I think has some additional protection because of the DC feedback from the op-amp, but is still not completely safe. What may help is an addition to prevent significantly differing supply voltages, and I have added the simplest protection circuit I could think of (apart from just adding an input capacitor). I still have not built and tested this circuit, so anyone wanting to try it may need to solve further problems. Personally, if I had an expensive MC pickup I would use both this protection circuit and an input capacitor, or maybe an entirely different circuit with lots of parallel input jfets.

Apologies for neglecting the website lately. At least I need to fix all the dead links. Maybe now the weather is getting cold it's time to get back to my speaker project. I was trying to choose a good 170mm drive unit, I was looking at two options, one cheap the other expensive, and two of the differences are that the expensive one includes a cast chassis, and also a 'shorting ring' on the pole 'to reduce inductance'. I'm not sure how that works. If I ever understood this sort of thing it was long ago. I found an explanation involving 'Lenz's law' which I don't understand, it looks wrong:

'Lenz's law states that the direction of an induced e.m.f. will be such that if it were to cause a current to flow in a conductor in an external circuit, then that current would generate a field that would oppose the change that created it.'
'The minus sign in Faradayís law of induction is very important. The minus means that the emf creates a current I and magnetic field B that oppose the change in flux ó this is known as Lenzís law'.

I'm sure that minus sign is the result of a sign convention for the positive direction round a loop having first chosen the positive direction through the loop. If we chose the opposite convention then the minus sign would instead appear in another of Maxwell's equations. (That is true for the integral form of the equations, for the differential form there is a similar convention for the definition of the vector product). Also, if the magnetic field changes at a constant rate the emf is constant and the induced current just causes a constant addition to the changing field. 'Opposing the change' doesn't then look like a good description, the rate of change is unaltered. A better wording would perhaps be that it 'adds a field in the opposite direction to the positive rate of change'.
In a speaker with shorting ring there are of course two coils; in effect a transformer with shorted secondary, which is the arrangement often suggested for measuring transformer primary leakage inductance by cancelling the rest of the inductance, so I guess it should work to some extent to reduce speaker coil inductance and associated nonlinearity, as advertised. However, one source claims that some of the lowest distortion drivers available don't have shorting rings, and the 'cheap' Visaton W170S has been tested and found to have reasonably low distortion, apart from a rise at 1.5kHz, so with my intended crossover below 1kHz that may be ok. The Scan Speak 18WU/4741T00 has somewhat lower distortion at high and low frequencies, but at 10 times the price.

There are a few questionable mathematical approaches scattered around the website. My analysis of phase intermodulation split the amplitude modulation of the input and feedback signals, and this leads to some inaccuracy. To see why it is nevertheless a valid method imagine that instead of the input stage nonlinearity causing the amplitude modulation we instead use switched linear attenuation. Then we are just comparing the phase shifts for two different linear states and it is obvious that attenuating the input and feedback signals has the same effect whether done individually or after they are added.
i.e. GA + GB = G (A + B). As I said this excludes some nonlinear effects, but demonstrates what I intended.

An interesting puzzle: Suppose we have two identical full range speaker drivers in two identical rooms. One is current driven by a high impedance signal source. We then apply the voltage appearing across its terminals to the input of a unity gain buffer, which has very high input impedance and close to zero output impedance, and the output of the buffer is applied to the second driver. Both speakers therefore have exactly the same voltage signal across their terminals, even though one is driven from a very high impedance and the other from a very low impedance. The question is will their acoustic outputs also be exactly identical? The immediately obvious answer is 'yes', but it's the sort of problem where if we think about the fine details we could easily have doubts. For example the different impedances give different electrical damping, which will affect the response to reflected acoustic energy. Seeing why this makes no difference is not entirely trivial.

I'm not sure if anyone ever looks at my physics section, but in the piece about transmission lines I mentioned a problem which according to some sources remains unsolved: A uniformly accelerating electron is predicted to radiate electromagnetic energy, but then applying the 'equivalence principle' we would expect a charge held unaccelerated in a gravitational field to also emit radiation, and there is no evidence of that ever happening. I suggested that the solution is that to be equivalent the observer or detector in the gravity version needs to be in free-fall and so is accelerating relative to the charge, and will then observe radiated energy. I thought I was being clever to see that, but it turns out to be well known, e.g. Researchgate.
Anyway, it's still interesting, in the quantum mechanical version a virtual photon in an inertial reference frame can become a real photon for an accelerating observer. This is related to the Unruh Effect and 'Unrhu radiation', which in turn is related to Hawking Radiation from black holes.

I was reading something on diyAudio about the 'Early voltage' (VA) of a transistor, and it included a diagram by Baxandall showing VA as the intercept on the horizontal axis of the Ic/Vce plots for constant base current. In my own explanation at Amplifier Design Part 3 I said: 'Its value can in principle be deduced from plots of collector current as a function of Vce at fixed levels of Vbe'.
So who is correct, is it constant base voltage or constant base current? I did a quick Google search to see which version should be used for the definition of Early voltage and found a discussion at ResearchGate and there seems to be a conclusion that it does make a difference, but I am still uncertain which version is conventionally used in the definition of VA. I have seen each one used by a number of sources, but my limited search suggests the constant current version is more common. Anyway it probably doesn't matter provided we know which version we are using. I mentioned somewhere that the specification of the related parameter hoe may have a ratio of maximum to typical values of 5 or more, so we should probably avoid designing circuits where the value is critical unless we are prepaired to test each individual sample.
This is related to my somewhat confused piece about the effect of source impedance on output impedance for a common emitter stage. There was, and maybe still is, some disagreement about this, my own conclusion was that the output impedance is about doubled for a low impedance source compared to a high impedance source, but various calculations, a published paper and Spice simulations differ considerably.

I added what is probably the final part of my 'amplifier design for beginners' series, this time about noise, but as always just covering the bits of information I remember being useful for my own understanding, so far from complete. There is a link on the home page.

Just got the bill for renewing the website hosting, it's increased about 53% since last year. Do I really need a .com address? The free Angelfire site is updated now, so it would make sense to terminate this site. I have paid for the next year, but that is probably the last renewal. There continue to be annoying pop-up windows on the free site, so I will look for a better free host and just keep two free sites after May 2020.

I have added a few more parts to my 'amplifier design for beginners' series, with links on the home page. I am still not happy that I have struck the right level between oversimplified and excessively detailed. For me, when I was learning about circuit design one of the most helpful sources of ideas was a series in Wireless World starting in June 1971, by A.J.Blundell, 'A New Approach to Transistor Circuit Analysis', and that is the approach I have tried to stick to.
The lack of some basic specifications in data sheets is unhelpful, for example few mention the base-spreading resistance rbb', but there are a few exceptions, the ON Semiconductor data for the BC560C has a plot of rbb', (which it calls rb) as a function of collector current, and even mentions the Vce, test frequency and temperature, which at least tells us these things make a difference.

I wrote on 1-Oct that 'the MJR7 is about the best I can do'. I have been reminded of the sort of specifications being quoted for some expensive commercial designs, one example being able to drive 2kW into 2 ohms and costing more than I paid for my house. Then there are the extreme slew rates and wide bandwidths for those who want full power output up to 1MHz and beyond. I should have defined more clearly what I meant by 'the best'.

Looking back down the page to 23-Dec-2015 I see a reference to an article in Wireless World from 45 years ago which claimed that audio amplifiers should have phase shift less than 6 degrees at 20kHz, and this included preamp stages, so for power amplifiers this should be typically under 2 degrees, necessitating a bandwidth over 500kHz. The obvious error in this proposal has been pointed out, but I included an explanation anyway. I mentioned something similar in my 'Capacitor Distortion' page where I said:

The high frequency response needs far less extension beyond the nominal 20kHz upper limit, most of the phase error from a typical low-pass filter is equivalent to a constant time delay, which will be inaudible and can be ignored. An article by Dr Leach, The Differential Time-Delay Distortion and Phase-Shift Distortion as Measures of Phase Linearity, examined this and concluded that for a less than 5deg phase nonlinearity up to 20kHz a first-order low-pass filter needs to be -3dB at 35kHz or more, while a second-order Bessel filter can be -3dB as low as 25kHz for the same error, though here the gain error may be considered more important. He suggested that higher order Bessel filters add even less error.

So, the overall bandwidth we need can be as little as 25kHz, not 500kHz, provided we understand the difference between linear phase shift and phase nonlinearity. My own MJR7 has a second order low-pass response, giving a phase shift of 24 degres at 20kHz, but the phase shift is almost perfectly linear from 1kHz to 20kHz, equivalent to a constant time delay of 3.3usec. As I have mentioned previously, for accurate amplification of audio transients all we need is a flat frequency response and linear phase shift at audio frequencies, plus low nonlinear distortion. Wide bandwidth or very high slew rate are not needed.

There's a new version of Boxsim available, Boxsim 2.00

My speaker project has not progressed much, I originally wanted to experiment with some sort of transmission line enclosure, but then got distracted by the surprisingly good predictions of a Boxsim simulation. Another distraction was thinking about some sort of bass feedback control, as was done many years ago in a commercial design by Philips using an accelerometer attached to the cone. A calculation assuming +/- 5mm displacement at 50Hz gives peak acceleration about 45g. Searching for published examples, some use the ACH-01 which has a +/- 150g range and its other characteristics look good also. The only downsides are the price, it would cost more than the W170S bass driver I planned to use, and also the mass is maybe a little higher than we would want. The question then is whether it is a better idea to just spend more money on a 'better' driver.

I was reminded of a series of articles in Wireless World many years ago about 'displacement current' in capacitors. Having done a course on classical electromagnetic theory which never mentioned displacement current I was baffled then, and searching through my Physics text books I still found no mention. It appeared that this referred to the dE/dt term in one of Maxwell's equations, but why anyone would want to call this a current I never entirely understood. I thought maybe some quantum mechanical explanation involving vacuum polarisation and relative displacement of virtual electron-positron pairs could be invoked, but the term predates quantum mechanics. Maybe it's just one of those terms invented in the distant past which linger on long after the original motivation has faded. A Google search suggests that the term was invented by Maxwell, who believed it had something to do with stress in the 'aether'. If the capacitor uses a dielectric then there are actual currents because of the displacement of charges, which can be represented by a polarisation vector, but there is still that dE/dt term. The main text book used in my course was Feynman Lectures Vol-2, now available online. The equation first appears in section 1-4 in terms of 'circulation' and 'flux', but it looks wrong, 'the flux of electric current through S' I think should be either 'electric current through S' or 'flux of current density through S'. Curiously the correct equation does appear later in chapter 18, in Table 18.1.

Previously, in August 2017, I wrote a disparaging comment about the concept of 'current feedback amplifiers', and just to clarify that a little, if we use such an amplifier as a RIAA preamp as I did, then the current into the supposedly low impedance inverting input is a source of error, and we want to minimise it by using high feedback loop gain, as I also did. If we allowed that current to be a significant proportion of the current in the feedback network then the closed loop gain is not defined accurately by that network. For a voltage feedback amplifier there is also a source of error, in that case it is the non-zero differential input voltage which we have to minimise for an accurate RIAA response. The current feedback case also has a non-zero differential input voltage. As usual the simple and effective answer is to use lots of negative feedback loop gain. In practice we can usually adjust components in our RIAA network to compensate well enough for the effects of finite loop gain if this is significant.
Of course high feedback doesn't solve every problem, for example nonlinear input impedance and common-mode effects need additional precautions, which is why my MJR7 is inverting with 'virtual earth' input, and the phono preamp has a bootstrapped cascode to avoid or at least reduce such problems.

To be fair I should mention one potentially useful benefit of a CFA compared to a VFA. If we wanted a closed loop gain of 11 for example, then for the VFA we could use a 1k and 10k in the feedback network to achieve this, or equally well use 100R and 1k, it makes no difference, only the ratio of the resistors matters, at least at low frequencies. For the CFA we could use the same 100R and 1k, but if we keep the same ratio but change to 1k and 10k then the feedback loop gain changes, so we have another variable to play around with, which may be useful. In the case of a general purpose op-amp a VFA will usually have internal compensation for stability at unity gain or some other fixed value, and if we wanted to be able to vary this we would need to use a type with external compensation capacitor. For the equivalent CFA varying the feedback network impedance gives us some additional control. For a discrete component design we can optimise the compensation for whatever gain we want, and choose feedback components for low noise, good overload margin, or whatever.

Update: When I said somewhere that the current into the inverting input is inversely proportional to feedback loop gain I should have mentioned that this is true only for a given feedback network, and for a given output level. If we changed the feedback network that could change the loop gain, but then the inverting input current would remain unchanged for a given output.

I have no plans for further work on amplifier design, the problem being that the MJR7 is about the best I can do, and any changes I thought of making to that design will worsen its performance. There is nothing obviously in need of improvement. Endlessly chasing after lower distortion figures seems pointless, but could easily be achieved by adding feedforward as demonstrated in the MJR9. The noise could be reduced by abandoning the inverting design, and I included examples of how this could be done on the MJR11 page. I have added two more diagrams there to try to get closer to the MJR7 including the anti-thump circuit. None of those circuits have been built or even simulated, and unless used with an ultra-high sensitivity horn speaker the MJR7 noise is already low enough, so these 'improvements' are not recommended.

The only further addition I need to make is a list of suitable substitutions for transistor types becoming unobtainable. The lateral mosfets are still available from Profusion in the UK and they seem committed to continued production.
For now suggested substitutes for other types are:
BC550C for 2SC2240BL, or better 2SC3324BL (TO236)
CPH3910, 2SK932, 2SK3557 or 2SK2394 for BF862
J111 for BF245C
The KSC3503 and KSA1381 continue to be widely available, including Farnell in UK.
For any substitutes be careful to check the data sheets for pin connections, there are some variations.

A problem with the Boxsim speaker design listed in the 'missing links' above is that the W170S has a peak in its response at 5kHz which is only reduced to about 12dB below the total speaker response and so may have some audible effect. This could be reduced by adding a 10uH inductor in series with the 100u capacitor in the passive crossover, which gives a notch in the W170S response at 5kHz. That may be worth experimenting with.

A while ago I wrote an analysis of noise in a 'virtual earth' inverting amplifier such as my MJR7, and have now added it to the above list of 'missing links'.

Still working on house renovation, all the urgent stuff is done, so slowing down now. Last week fixed the leaking kitchen roof with bitumen sealant and flashing tape, and securing the loose vent pipe, all I need now is a good rain-storm to test for leaks.

Something just occurred to me regarding the rumble filter circuit, which works by reducing the bass to mono. The problem is that there is reason to believe that this is usually already done as part of the signal processing before reaching the cutting lathe. As I demonstrated, using even two of my first-order circuits in series has an unfortunate channel reversal effect at low frequencies. If it is true that something similar is already applied to the signal, then my single first-order circuit may be the most we can get away with if audible problems are to be avoided. Anyway it sounds ok to me, but did I mention being half deaf? One example of the mono-bass processing is the Neumann EE70 'Elliptical' filter, which uses an alternative first order circuit where the left and right signals pass through resistors and the bass components are blended via an inductor. This should work more or less the same as my version passing the signals through capacitors and then blending the bass via a resistor, which should be cheaper and also reduces offset problems in my phono preamp design.
And why would it be called an 'Elliptical filter' when it is obviously no such thing? The link includes an explanation: 'called an "Elliptic equaliser" by Neumann, because it modified the width of the ellipse on the vectorscope on vinyl lathes.'

I have now set up my audio system in my new 'listening room'. I checked my MJR7 power amplifier to see if it has drifted at all, and found the operating voltage of the mosfet sources is still accurately at close to half the supply voltage. This was checked with speakers attached, disconnecting the speaker made the voltage drift downwards significantly, so I repeat my advice in the Setup and testing page to use either a speaker or a low resistor load when setting the voltage, and check again after the amplifier has warmed up for a final adjustment. Excessive drift caused by temperature changes would suggest either an inadequate heatsink or maybe just poor case ventilation allowing internal heating. Unless the amplifier is often being driven close to clipping a drift of a volt or less is nothing to be concerned about. I once suggested a modification to cancel the temperature effect, but the small drift with my own example persuaded me that this was unnecessary.

A few years ago searching for 'audio amplifier design' on Google listed my old website in 3rd place on the first page, but now it has almost sunk without trace. Even Elliot Sound Products is down to page 4. Few of the current top results look particularly useful for anyone wanting to learn about amplifier design, apart from the Amazon adverts for books.
In one of those books, 'Audio Power Amplifier Design' 6th edition by Douglas Self, he mentions on page 106 that he used a simple 'anti-thump' circuit in one of his older designs with an output capacitor, and the description is similar to my own version. I can make no claim to have thought of it first mostly because it is not really my own idea, it was published somewhere (I forget where) and one of the early constructors of the old MJR6 sent me the circuit as a suggestion for curing the switch-on thump problem. I simplified the original circuit a little, eliminating a transistor, but my version may be more sensitive to capacitor leakage, and needs the 470u capacitor to be a low leakage type. That may be another thing to check occasionally, the voltage across the 10k resistor charging the 470u capacitor should be less than a volt soon after switching on. (It starts at the full supply voltage, so be careful connecting a voltmeter, don't have it set to the 2V range initially.) More than this points to excessive capacitor leakage, either replace with a low leakage type or if a greater switch-on thump is acceptable experiment with reducing the 10k.

The house renovation continues, the kitchen floor is fixed, now replastering some of the walls. All those beginner's guides to plastering on YouTube make it look easy, but it takes some practice to get a good flat surface. Assembling a few flatpack kitchen cabinets is next on the list.

Apologies for having nothing new to add, I am currently distracted by moving house. The 'new' house is starting to look like a long term renovation project. The structure appears to be solid enough, but there are plenty of problems to keep me busy for a while, at least I can do some DIY work myself and keep the cost manageable.

There is a useful feature of my mosfet designs, 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, reducing the undistorted component by 80dB, or even 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 (probably 40dB) but still was almost inaudible using my own computer and headphones. I mentioned a 'normalisation' function (18-July) in the Audiograbber program, so I tried increasing the extract to 70% peak level, but it still seemed quiet. Opening it in 'Audacity' revealed a big DC component, so obviously the original sample had a small DC offset. Adding a high-pass filter effect eliminated this, and now here is a new version of the MJR6 error signal:

This will not work if your browser doesn't support the 'audio' tag, instead try clicking this LINK. The noise is 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 compared to the noise. Doing the amplification digitally is not ideal, any quantisation distortion will also be amplified, the amplification should have been done with the original analogue signal, but even so the result is fairly conclusive. The noise hopefully was enough to add adequate 'dither' and avoid quantisation effects, but as mentioned in the earlier link the noise is not the total amplifier noise because the 2uV added by the input resistor is nulled along with the input signal.

Ideally I would want to include some reference level to give some indication of the levels involved, the noise is not very helpful for this because as mentioned it is not the total amplifier noise. As it stands the extract just demonstrates what the signal sounds like if the 'reduced noise' and distortion are both increased by over 10,000 times relative to the original undistorted input. I think nothing useful would be added by repeating the experiment for the later MJR7, the noise will be about the same but the distortion even lower.

I have been looking at the latest book from Douglas Self, Electronics For Vinyl and was pleased to see my version of the vertical rumble filter included as Fig 12.50. As he says the load impedance needs to be high if we want the most extended low frequency response, but using 2u2 capacitors and 5k6 crossfeed resistor I found less than 0.5dB attenuation of the wanted signal at 10Hz with a 20k load, so not a big problem. I have only looked at the free preview at Google Books so far, but it looks good, and can be recommended for anyone not already familiar with the problems of phono preamp design. Those of us who think we already know it all are still likely to find something new, but may be discouraged by the price. To me the greatest surprise is that it is even possible to write 344 pages about 'Electronics for Vinyl', but it does start at a very basic level, and has a lot about the properties of passive components and opamps. It is suggested that polyester capacitors are unsuitable because they produce as much as 0.002% 3rd harmonic distortion with 10 Vrms applied. There is then an interesting observation that the distortion only triples for a doubling of signal level rather than the expected quadrupling. The main reason I didn't use polyesters in my own preamp is that as far as I know they are unobtainable with 1% tolerance.

A question arose concerning my phono preamp. The thing is that the feedback goes to the source of the input jfet, and there is a resistor, e.g. 100R from that point to earth. The suggestion was that the 100R is in effect in parallel with the source impedance of the jfet, which may be about 50R, and so the feedback ratio should include that. The jfet source impedance is given by 1/gm which can vary significantly between different samples of the jfet, so if that had to be included there could be a noticeable gain difference between the two channels.
The signal fed back includes an undistorted component plus a low level distortion component. For that distortion component the low jfet source impedance is as suggested in parallel with the 100R, and the gain round the feedback loop is significantly affected by the gm of the jfet. For the undistorted component however the gate and source signal voltages are almost exactly equal, the difference being inversely proportional to loop gain, and so with high loop gain the source to gate signal is small and very little signal current is driven into the source. Then the jfet source impedance is in effect high, and closed loop gain is determined almost entirely by the feedback network, as we would normally expect. So, no problem. The jfet gm value still has an effect on the open-loop gain, but far less on the closed-loop gain.

The idea that different components of the signal can see different impedances at the same point in the circuit is just a consequence of multiple signal sources. To take a trivial example suppose we have a 1k resistor and apply Vs to one end and Vs + Vx to the other end (both relative to earth), then the voltage across the resistor is just Vx and the current is Vx/1k. For the Vx component the impedance is 1k, but the Vs component is equal at both ends of the 1k and causes zero current, so in effect it sees infinite resistance. In a feedback amplifier we have the input signal and the signal fed back from the output, so there is room for confusion when talking about input stage impedances.

A quick calculation for the phono preamp. With 1V input at 20kHz there will be close to 1V across the 100R gate to earth resistor (I actually split the 100R into 78R plus 22R in the final circuit, but let's keep it simple). The AC current through the 100R is therefore 10mA. Calculating the AC signal current into the jfet source we get around 10uA, about 1000 times less. With 1V at the source and a current of 10uA the equivalent input impedance into the source is 100k, so in parallel with the 100R resistor the effect is insignificant, just a reduction of 0.1% in the resistance of a 1% tolerance component.

Update: This piece about my phono preamp has some tenuous relevance to a lengthy thread on diyAudio about 'current feedback' amplifiers. That's an argument I believe is always worth avoiding, the alleged distinction between VFA and CFA is something I have never found either interesting or useful. The last time I looked there was an argument involving an input buffer with zero output impedance and zero input signal. Yes, under those circumstances any feedback is entirely current. Under different circumstances it isn't. To take an equally unrealistic example, in this case with an input signal and the feedback network connected, then with an infinite loop gain the AC current into the inverting input is zero, so no current feedback. To stick to a real example, my phono preamp with 1V input at 20kHz has 10mA AC signal in the feedback network and only 10uA into the jfet source, so in that respect not radically different to a conventional VFA. For the phono preamp high loop gain is used for accurate RIAA response, and the single input jfet is chosen for low noise and simplicity.

A useful program I have used a few times is Audiograbber. This has a number of functions, primarily the 'ripping' of audio CDs, so that the tracks can be saved on a computer as wav or mp3 files. One useful additional function is 'normalization' which can adjust the volume of the digital file so that the peak level is some percentage of full-scale. (This is not the same as compression, just a change of volume). The reason why we may want to do this is because of the 'loudness wars' which has led to some recordings going right up to full-scale with no safety margin. This wouldn't matter much except that when converted to analogue in a DAC the result may exceed the 0dB level, an effect known as an 'inter-sample peak'. Some equipment is unable to cope with this and will clip. To put it another way, some badly recorded material played through some badly designed replay equipment may have problems. No surprise there. There are widely varying claims regarding the importance of this effect, but it is easy to check whether there is an audible effect by using the Audiograbber normalization function to reduce the peak level in the digital file. A setting of 90% is probably adequate in practice, taken too far the signal to noise ratio will suffer, but at 90% there is a less than 1dB loss in signal level. There are alternative programs with the normalize function, including foobar2000 and Exact Audio Copy, and some say they are better than Audiograbber, but I never tried these. I just tried comparing a wav file first normalized to 100% then to 90% and then 70%, but it really isn't that easy, unless the track has lots of 100% peaks to start with there may be too few peaks to be a noticeable problem. Also, my current soundcard may have a perfectly adequate overload margin.

Profusion can now supply the Exicon lateral mosfets in selected bands based on the value of Id at Vgs = 0.5V. The lowest (red) band is from 105 to 125mA and the highest (white) from 185 to 205mA. They will not guarantee to supply any requested band, but for a quantity of the same type all will be the same range.
For any of these bands the MJR7 quiescent current can be set to 100mA even with the LED limiting the gate to gate voltage, so this is then certain to not be a problem, and the extra cost of the selected ranges may be worth paying. The unselected range probably includes those rejected as outside the selected ranges, so the chances of getting a high Vgs mosfet may now be higher.

There are still a few pages described as 'work in progress', but that is mostly untrue, I just lost interest or had nothing new to add. These and a few others are incomplete and I hope to update them eventually. One such page is about signal generator design. My conclusion at the point where I stopped was that with sufficiently fine 'tweaking' distortion can be reduced to extremely low levels. Getting easily repeatable low levels from a variable frequency generator is a different matter. One point I intended to investigate but didn't is the optimum jfet characteristics for use as a voltage controlled resistance in the level control. I got as far as mentioning that my choice of the 2N5457 was less ideal than the 2N4091 used by Bob Cordell in a similar but lower distortion circuit. There is probably more to it than just the type, we also have the option of whether to use it at low resistance with close to zero Vgs or at higher impedance with a more negative gate voltage (assuming n-channel). I strongly suspect I got both type and operating resistance wrong, or at least far from optimum. An article from Siliconix, FETs As Voltage-Controlled Resistors says a high Vgs(off) is an advantage for low distortion, so the 2N5457 specified as 0.5 to 6V could be a bad choice.

Updates: There is a very long thread about signal generator design at diyAudio. I don't want to read through the whole thing, but in post 90 Bob Cordell mentions the requirements for jfet selection, and he says high Vgs(off), but also low Rds(on), which may suggest low operating resistance is better. The Siliconix reference, in Table 1, appears to find no advantage in low resistance operation.

In the same thread I also found this link to an article about Amplitude Stability of RC Oscillators which demonstrates that excessively linear amplifiers used in lamp stabilised oscillators can have problems, which reminded me of the unexplained distortion at 100Hz intervals using an LM4562 op-amp in part 3 of my design articles. I'm not entirely convinced, but I really don't care enough to try working through that analysis.
Update 2: I found a similar result described starting here and an explanation in post 6928 that the 100Hz interval components were caused by a nearby DECT base station (cordless phone) which I also have operating within a few feet of where I tested the oscillator. The 55MHz GBW of the LM 4562 may be why this was the only op-amp tested to have this problem.

Also, another recommended jfet is the MMBF4391, or PN4391. These appear to be similar to the more easily available J111.

A Fairchild application note AN-6603 includes distortion plots for various examples. Figs 16-21 show signal levels for fixed levels of distortion as a function of Vgs. Fig.16 for example shows that at 0.5% distortion a 40mV signal level can be used at Vgs = 0 but there is the same distortion at only 6mV at Vgs = -2.5V, so this shows that low Vgs operation is better for low distortion.

I have added a page with my latest guitar amplifier project. I had doubts about whether to include this, it is really the wrong way to make a 'flanger effect', but it is perhaps an interesting example of a PT2399 time delay circuit:
Guitar Preamp and 'Flanger' Using PT2399 Time Delay IC

My old freeserve email address will no longer work from may-2017, the service has had a series of owners, starting as part of a dial-up service run by Dixons and ending up being discontinued by EE. It was never very reliable, I often had problems to log in. Now I am setting up a gmail address.

Apart from that nothing much is new, I have just finished making a guitar amplifier starting with an 'ADS mixer amplifier' I bought on eBay. I removed everything apart from the transformer and bridge rectifier and added a fairly basic lateral mosfet amplifier. There is a row of 7 controls on the front panel, and I want to use 2 for a 'flanger' type effect. Many years ago I experimented with a reel to reel tape recorder using two replay heads connected in series and with a mechanical lever to vary the length of tape between the heads. The result was impressive, but looking at current designs it is invariably stated that the time delay between the two added signals should be just a few msec for this effect. There is an easily available and low cost time delay IC, the PT2399, which looks interesting, but has a minimum delay around 30ms, which may be a problem. My tape effect certainly had a far higher delay and still produced a good result, so some experimentation seems worthwhile. A good source of information is Project 26A on the Elliot Sound Products website, which also says it is unsuitable for use as a flanger. There are a few examples of flangers using this device, but they use a pair for the two signal paths so that the delay difference can be small or pass through zero.

I promised to think about add-on circuits to make the phono preamp suitable for moving-coil pickups. I don't have a MC pickup myself and don't plan to build anything, but I have added a page, MC Phono Preamp with a few not very original ideas on this topic.

I found a page on the TT Electronics Semelab website from Aug 2016 announcing the discontinuation of 'Magnatec' products. The list linked to includes the ALF and BUZ series lateral mosfets and also the 2SC2240BL I still recommend for my MJR7 amplifier. The Farnell UK site also lists the ALF mosfets as 'no longer manufactured'. There are of course alternatives still available, but maybe not for long. I still don't want to resort to vertical mosfets, they add a few problems, but the time may come when that is the only option.

In my phono preamp design pages I mentioned an optional time-constant of 3.18usec, often referred to as the 'Neumann pole' on the grounds that it is sometimes claimed to be included in the pre-emphasis circuits of the Neumann disc cutting lathes. This is widely disputed, and for example here in Neumann's Last Pole is a circuit diagram of the Neumann SE66 recording equaliser, which uses a second-order low-pass filter at 33kHz. The later model SAB-74B is said to have a similar filter at 50kHz. This will have little effect at 20kHz, certainly less than the disputed first-order 3.18usec filter would have, so including this time-constant in the RIAA correction will not be an accurate correction. I mentioned my own preference to leave out the 4th time-constant, and this is now a positive recommendation. In the discrete component circuit the 75pF should be included in the output section, and in the single op-amp circuit the added low-pass filter at the output is included. The simple non-inverting pre-amp has a 4th time-constant whether we want it or not, so the 3.18us value seems to be as good a choice as any, and needs to be calculated anyway so that it can be cancelled by an additional first-order low-pass filter, so we still can't avoid the slightly tricky four time-constant calculation. Fortunately that calculation has been done and published by a few writers, including myself, so provided the 3.18usec 'standard' is adopted there is no need to recalculate everything for every new design.

I found another error in my phono pre-amp layout diagrams, one of the electrolytics was reversed, and now I have corrected this, and marked the component with a red star. The capacitor would certainly be damaged by being reverse biased, so if anyone has used this layout that capacitor needs to be replaced. A worse problem would be if anyone assumed the capacitor to be correct and connected the power supply to bias it correctly, then serious damage to many components would be likely. The correct power supply voltages are shown in the final diagram.

I have also added a circuit diagram showing the voltages at all points in the circuit, which may be helpful for fault-finding.

I downloaded Visaton's free Boxsim program, said to give accurate simulation results including baffle effects. I already have a pair of Visaton FRS8 full-range speakers which could be used with the W170S, maybe crossing over around 400Hz.
I have worked out a few examples using the FRS8 and W170S just to learn how to use the program. The predicted frequency responses are surprisingly good, mostly within +/- 1dB apart from at lower frequencies where we probably don't want a flat response, there being some effect from placement near a wall and floor giving bass boost. That is one part I am not yet entirely sure about, the simulation seems to assume a 6dB loss from low frequency diffraction, but examples from the Visaton website seem to aim for a flatter bass response, maybe assuming intended use well away from walls. Anyway, here is the Boxsim example. I started with a simple passive crossover design, and also included an active crossover version.

I have added my simulation results for speaker current peaks when driven by a voltage pulse, Speaker With Conjugate Network, showing the results both with and without a parallel conjugate network, and the effectiveness of this addition is demonstrated. One slight surprise is that just adding a RC Zobel to prevent the rise in impedance at high frequencies can actually make the peak current requirement higher. Full level rectangular pulses appear not to be a common feature of recorded music, so in practice there is little to be gained by adding a conjugate network, and the inconvenient component values needed are also discouraging.

Earlier on this page I mentioned a piece I wrote about the Peak Current Requirement of Speakers. This was based on reports in recent audio design books, but I had never seen the original paper referred to, Peak Current Requirement of Commercial Loudspeaker Systems.
Now today I have been given a copy, and have been trying to decipher it. There are a few problems, for example describing the test signals as 'bandwidth-limited' could mean anything from a first-order bandpass filter to a 'brickwall' filter, and the input signals shown in the final results look like perfect rectangular waves. Also it is claimed that most commercial amplifiers are designed and tested for only the specified resistive load, which I doubt was ever true, even in 1987.
Anyway, the clever part is the construction of a test signal for a given speaker designed to give the maximum peak current, which represents the 'worst case' signal. These rectangular wave shapes are however just an extreme example of what we will find with any square or rectangular wave input, for a very simple reason. I repeat what I wrote earlier:

'Starting with a square wave voltage applied to a speaker, this consists of a fundamental frequency and a theoretically infinite series of odd harmonics. The resulting current has the same series of harmonics but because the speaker impedance has reactive components there is a frequency dependent phase shift of these harmonics, which changes both the shape of the current wave and its peak level. The square wave harmonics have the relative phases necessary to give the minimum possible peak amplitude, so almost any change from this gives a higher peak level, so the current wave will invariably have higher peak levels than if the speaker was a pure resistance which would have left the phases unchanged. There is no theoretical upper limit, shifting all phases by 90deg would give an infinite peak amplitude, limited in reality by the finite bandwidth and speakers having less than 90deg phase shift.... The effect applies for any rectangular test voltage, in all cases the phases of the frequency components start with the values needed to minimise peak level, so almost any phase shift applied to the current increases its peak level.'

The most serious objection to this sort of theoretical analysis is that it is so much easier just to play some music through the speakers and monitor the peak current requirement. I gave a reference in my previous piece to an example published in Stereophile, which failed to find any unexpected current peaks, and my own tests also found nothing to be concerned about.

Even if there really was a problem we can avoid it without needing to make an amplifier capable of providing 100A peaks. A far easier solution is to design a network to connect in parallel with the speaker to flatten the impedance curve and so reduce the phase shift. This is called a 'conjugate network', and is often encountered in discussions about current-drive speakers. The current peaks into the speaker would be exactly the same with the troublesome rectangular voltage waves, but most of that current will be provided via the parallel network, not from the amplifier. This is perhaps counter-intuitive, adding an impedance in parallel with the speaker we may expect it to take even more current, but think of a tuned circuit with a parallel inductor and capacitor, at resonance the impedance can be very high, so a driving amplifier needs to provide very little current, but the individual currents through the L and C can be far higher, but in almost opposite phase so that they almost cancel. A thread on diyAudio includes on the first page an example of adding a conjugate network. For complex speakers the network may be difficult to work out, but for the present purpose, with voltage-drive, we don't need to be so exact about flattening the impedance, small errors will have little if any effect on the frequency response.

UPDATE: I just tried a simulation for a single pulse and a single drive unit, using a very approximate conjugate network, and found that after the end of the pulse the speaker current peaks at -3A, and at the same time the network current peaks at +1.3A, so there is partial cancellation and the total amplifier current only reaches -1.7A. As expected the amplifier current has almost the same shape as the original voltage pulse, so the total load is behaving more or less as a resistance.

The phono-preamp continues to be the most visited page, which is a little worrying given an almost complete lack of feedback from constructors, with my own construction the only fully tested working example I am aware of. I do know of two constructors who had problems. I wanted to add an alternative simpler circuit which I would be happier to recommend, using a dual opamp and single equalisation networks. Why bother with yet another conventional opamp circuit? Well, the vertical rumble cancelling circuit can still easily be included provided the output load is not much less than 10k. Also, I avoided the calculation for a 4 time-constant feedback network in my previous coverage, but it turned out to not be too difficult. The calculation assumed infinite op-amp gain, but compensating for finite op-amp gain is demonstrated in simulations using small adjustments of the component values. I have added a page Op-amp based Phono Pre-amp..
UPDATE: I have worked out slightly better component values and improved simulation accuracy, and the final circuit is now updated to give a theoretical +/-0.01dB accuracy, but the 'tweaks' involve changes comparable to the 1% component tolerances, so the real accuracy is unlikely to be so good, but still more than good enough.

I mentioned a possible transmission line speaker project, and so far I have been collecting information and ideas, and doing a few experiments to compare absorbent materials. The results are not particularly conclusive, but there is no more I really want to do for now. A practical design may emerge eventually, but for now here is an initial page, Transmission Line Speaker Project.

I suggested earlier on this page that two or more of my first-order rumble filter circuits could be used in series to give higher attenuation at 10Hz. This seemed obvious enough not to need a simulation, but today I tried a simulation of another higher order filter, the Oldfield circuit linked to in my references, Stereo Rumble Filter, and found it worked well, but has a rather unfortunate channel reversal effect over a range of frequencies, with an input to only one channel the output is higher from the other channel. This prompted me to do a simulation of two of my first-order circuits in series, and unfortunately this has a similar problem. I have added an update at the end of the Rumble Filter section on the 'Phono Pre-amp Design Theory' page. The Oldfield circuit has the advantage that the resistor values in the filter can be adjusted to minimise the problem, but working out the optimum values may not be entirely trivial, trial and error may be quicker. The problem appears to be further down the frequency range for my two first-order circuits, under 30Hz, so I would not expect a serious audible effect. Few recordings will have significant levels under 30Hz and any such components will probably be recorded in mono, not on just one channel.

Initial simulations suggest that adjusting resistors to reduce the channel reversal effect in the Oldfield circuit also reduces the 10Hz attenuation, so it may be little or no improvement on my in-series first-order filters. Another idea I checked was that if two of my circuits in series produce this reversal effect maybe more stages will reverse it back again, but it doesn't work that way, adding more stages increases the levels of peaks and dips and also moves them higher up the frequency scale, so using more than two stages is not recommended.

The quiescent current preset adjustment in a power amplifier should always be designed so that if the preset wiper becomes open-circuit the output stage current will fall, not rise. Looking at my MJR7 circuit it is not entirely obvious that it will work like that, the mosfet gate currents are very low, so the only thing discharging the 100n capacitor is the leakage current through the zener gate protection. I think that should be enough to guarantee a fall in quiescent current, but I don't have a figure for drain to gate leakage, I assume it is very small, but to avoid needing to worry about that sort of thing we could add something like 5k6 in parallel with the 100n capacitor. I don't find that worrying enough to take my own amplifier apart to add the resistors, but anyone building the amplifier may want to include this modification.
Incidentally, some mosfet output designs use different value series gate resistors to compensate for higher capacitances in the p-channel device. I used 300R for both, but did try different values when measuring distortion without finding much effect. The 300R limits driver stage dissipation under fault conditions when the zeners conduct, so should not be reduced too far.

There is a new article by Douglas Self, The Devinyliser in Vol.11 of Linear Audio. This is an excellent and thorough treatment of the rumble filter technique where low frequency opposite phase rumble signals are cancelled. My own simple version is included in the article together with higher order circuits giving better cancellation at 10Hz. As I mentioned below on this page (17 Jan 2016) things get tricky if you want more than a 6dB/oct attenuation of out of phase bass. The solution in the Self article is to use an all-pass filter in the subtraction circuit, which is highly effective. One point he may have missed, which I also missed myself until today, is that it is possible to use multiple circuits in series to get higher attenuation, but to match his 2nd order result in Fig.12 would need 4 of my circuits in series to achieve -40dB at 10Hz and -12dB at 32Hz, which needs more capacitors and more op-amps, but on the plus side component tolerances may be less of a problem. (But see update above on 07-May-2016).
(Why, you may ask, would it take four 1st order filters to match a single 2nd order? Partly because Fig.12 is actually 3rd order, which is what you can get if you subtract a 2nd order Butterworth from a 1st order all-pass, and partly because of the more gradual initial slope of the 1st order types.)
Anyway, the article is very good, but unfortunately the Linear Audio page says 'download not available', so it seems to be necessary to buy the entire volume to read it. Someone kindly showed me their copy, so I didn't need to.

I mentioned earlier on this page, 21-Aug-2014, US Patent 8466744 which lists my MJR7 amplifier under 'Other references'. There is now a discussion about this patent on diyAudio which reveals some additional information. A commercial design from Bryston is said to be based on the patent, and a representative of that company says the 'novel methods of maintaining stability' are an important feature. The diagrams are described as 'simplified and representative' so there would be no point trying to build or even simulate the circuit. Anyway, if there is anything genuinely new or useful I don't see it.

I remember a quote, probably from Feynman, concerning the laws of electromagnetism, to the effect that 'there are no known non-trivial solutions to these equations'. The static field of a uniform charged sphere is an example of a trivial solution, and this sort of thing is quite common in physics, hence the well known jokes about 'spherical chickens in a vacuum'. The same thing is certainly true of acoustics, and is why trying to design speakers starting from the laws of sound propagation will only be an approximation. There are apparently some good simulations around which give reliable outcomes, but my own preference is to start with a design allowing adjustment of the important variables so that they can be optimised by variation and measurement. The example I included previously was a distributed port bass reflex, and by blocking some of the ports it was easy to find the best balance between distortion and bass response. I mentioned that I wanted to try some sort of transmission line enclosure, and I have a few ideas how to make adjustments without needing to completely rebuild a conventional enclosure, so that may become my summer project.

I wrote previously that to increase the Q of a speaker we can reduce the box size, which is true, but not a very good idea. I tried a simulation using the Monacor SPH135AD specifications, fs=39Hz, Vas=26l, Qts=0.37. What this shows is that with a 10 litre box the output at 40Hz is down at -11dB, and if we reduce the box size to 5 litres the 40Hz output drops almost to -15dB. An alternative approach is to use a speaker with higher Qts. Keeping a 10 litre box and increasing Qts to 0.8 gives 40Hz at -8.7dB and a boost of 4dB at 80Hz (which we would then correct e.g. using a Linkwitz Transform). If we then increased the box to 20 litres then 40Hz is at -4.6dB. Increasing Qts however can have its own drawbacks, it can be achieved by using a smaller magnet, but that reduces sensitivity, so although output at 40Hz may be better relative to output at 1kHz, if 1kHz output is reduced by using a smaller magnet then actual 40Hz output may not be as good as we hoped. The mh-audio simulation only gives relative levels at different frequencies, not actual sound pressure levels, so some further thought is needed to find the optimum design for high bass sensitivity.

High bass sensitivity allows higher level bass before dissipation becomes a problem if we boost the amplifier gain to achieve whatever bass response we want, but ultimately limited by maximum linear cone displacement Xmax. For the SPH135AD Xmax is specified as +/- 1.75mm, which is not great, but maybe it is good enough if we don't need high sound levels. These speakers have been suggested as substitutes for the KEF B110 in LS3/5A copies, but the B110 has Xmax 6mm. The lower Xmax does however allow an improved sensitivity, specified as 89dB/W.

The 'problems' mentioned previously for the speaker bass boost capacitor can easily be avoided using my MJR7 amplifier. The existing output capacitor of the amplifier could be reduced to something like 1000uF so that it cancels some of the series inductance of the speaker just below resonance. At first this looks pointless because the feedback taken from after the capacitor flattens the frequency response. What it does achieve is to reduce the amplifier output voltage prior to the capacitor in that low frequency range, and so gives a greater overload margin so that we could then boost the low frequency gain using a conventional Linkwitz Transform circuit ahead of the amplifier, but with less danger of amplifier clipping. Designing the speaker for a relatively high Q (e.g. 1.2) could compensate for the attenuation at and above resonance, and the Linkwitz Transform can be designed to match that Q value and give whatever final effective Q we require, typically 0.5 to 0.7. Initial simulations suggest the resulting improvement in overload margin could be more than 3dB, equivalent to doubling amplifier power, but only over a small frequency range. Using this approach we don't need that extra capacitor, and the existing one is lower value and cheaper, and also still included inside the feedback loop to reduce any distortion, and also we can still specify a high damping factor. Anyway, it's an idea to play around with, but probably not really useful, few recordings have very high level low bass, so overload is unlikely to be the most serious problem.

I have been reading more about speaker design, and one idea I was reminded of is to add a series capacitor to the bass speaker, typically 1000uF, to cancel some of the series inductance at frequencies just below resonance. This increases the drive voltage at these frequencies, equivalent in effect to boosting low frequency amplifier gain, but able to produce a higher voltage across the speaker before amplifier clipping. Output at and above resonance is however reduced, but this can be compensated to some extent by designing the speaker for a higher Q, e.g. by using a smaller box. I need to do a few simulations to see if this can be made to work well, I have some doubts, but there is an obvious advantage that the speaker is then protected against damage under fault conditions causing high DC levels. There are probably a few disadvantages, not least the fact that some people will worry about passing the signal through yet another capacitor, and others may worry about their damping factor.

An important point is that some speaker designs do use this technique, and they may have some problems when used with my MJR7 amplifier. I mentioned in my setup and testing page that adjusting the output stage operating voltage has a problem with long time constants if there is not a low resistive load, and it would be a good idea to add a parallel resistor, e.g. 47R 5W, if one of these capacitively coupled speakers is used.

My original notes on crossover filters are 15 pages of rather tedious analysis, so I have extracted a few diagrams and added new descriptions to present the essential information in a much shorter and more easy to follow version, with the title Asymmetric Crossover Filters. This is by no means a complete coverage of the many possible variations or uses of asymmetric crossovers, one example I found recently is that it is possible to use asymmetric filters to compensate to some extent for different acoustic path lengths when bass and treble speakers are mounted on the same flat baffle. An interesting account of this can be found at the Parts Express Forum.

Regarding linear phase filter design using time delays, the invention of this technique is sometimes credited to Lipshitz and Vanderkooy, who described it in their 1983 JAES paper, but they don't make that claim, and their own references include two previous publications describing the time delay method, in 1979 by Tanaka and Iwahara and in 1973 by R.M.Golden. There was also a paper by Ng and Rothenberg, 'A matched delay approach to subtractive linear phase high-pass filtering', published 1982. My own work covered only a small subset of these filters, and I had never read any of the others, so I was pleased to be given a copy of the Lipshitz and Vanderkooy paper today, and I have been trying to decipher their mathematical approach. I see how they did it, matching the time delay element to the low frequency group delay of the low-pass stage. My own method described previously leads directly to the filter responses giving a higher order high-pass. These are covered in the L-V paper but their method of analysis is more general and, to me at least, more difficult, but my results agree with their general formula. It is said that the 5th or higher order low-pass results are 'unstable', which I have no reason to doubt. The 4th order low-pass and resulting 5th order high-pass will work, as I suggested, but the responses are plotted in their fig 7b, and clearly have significant peaks in both high and low-pass, so that saved me from wasting time plotting them myself.

I just noticed a discussion on diyAudio (starting around post 354) about the vinyl rumble filter idea where low frequency out of phase signals are cancelled. My own simple first order Rumble Filter (Part 2) is mentioned later and a few other versions. I listed a few examples at the end of my page, but I never bothered to check these in any detail, assuming that if they were published then they must work well enough. Some have now been investigated by Douglas Self, and it appears the higher order types can have problems, including uneven response and sensitivity to component tolerances. Evidently things get tricky if you want more than a 6dB/oct attenuation of out of phase bass, and fortunately I avoided these difficulties. My circuit with the component values shown only reduces 10Hz vertical rumble by about 10dB, but that is still a noticeable improvement.
Update: post 557 in the diyAudio thread shows one of the problems with higher order filters if you want not just a flat gain but also zero phase error, the unwanted signal can only be reduced at 6dB/oct and even worse has a 2dB peak. This has a known solution, but that involves time delay functions. According to Douglas Self ('The Design of Active Crossovers', section 6.2 page 134-140) using a time delay can give a high-pass with the same slope as the low-pass response. I did some work on that problem long ago when I was a student and my unreliable memory is that there exists one low-pass response of any given order which can be combined with a time delay to give a high-pass of one order higher. I must search for my old notes and check that.
Update 2: Yes, my memory is almost correct, there are low-pass responses for which the corresponding time delayed high-pass is one order higher. I worked that out myself for 2nd and 3rd order low-pass. I have done a Google search and find this is well known, but some say this doesn't work for higher orders (not entirely true, see later). The calculation is easy enough, just start with a first order all-pass (a-s)/(a+s) and subtract a low-pass e.g. 1/(1+bs+s2) and the result can then be made into a third order high-pass by choosing a and b to make all the terms in the numerator zero except the -s3, which makes both a and b equal the square-root of 2. Generally starting with a nth order low-pass we get n equations for n unknowns, which at least for n= 2 or 3 is solvable. If we get a higher order high-pass using the all-pass function then that will also be true for a time delay chosen such that the all-pass and time delay become identical as frequency is reduced towards zero, which is also where the ultimate slope of the high-pass is reached. Maybe I will add a scanned copy of my old work, but it probably adds nothing useful to what has been published elsewhere.
Update 3: I just tried the calculation for a 4th order low-pass and it seems to work fine, 4 equations for 4 variables and easily solved to give a 5th order high-pass. I've just found more of my old notes, and I already did the 4th order calculation then, with the same result. Only the final slope at low frequencies is predicted, actually plotting the complete responses may reveal problems, I only plotted the 2nd order low-pass and corresponding 3rd order high-pass, and using a time delay that had a 0.5dB peak in the high-pass gain about 2 octaves above the crossover frequency. Using a first-order all-pass instead of a time delay avoided the peak.

On my Links page, in the physics section, I recommended the Susskind Lectures available on YouTube, and having nothing better to do I was working my way through some of these. There is one serious problem I found in the Quantum Entanglements Part 1 series (there is no part 2 and what is listed as part 3 appears to be on a different subject, but that isn't the big problem). Having got through the first 4 lectures, about 8 hours, covering some fairly basic theory we arrive at lecture 5 covering Bell's theorem and other more interesting topics, only to find the video quality to have sunk to the level where little of what is written on the board is legible. It isn't just me, the comments on that page make the same complaint. With some difficulty it is possible to reconstruct the missing graphics from what is said, and I would hate to give up after all that, so I will try to continue to the end. Anyway it is probably not such a good recommendation as I thought.
One easy to follow section concerns Bell's Inequality, showing that it is purely classical and extremely trivial, it can be written in one line and the proof is another single line plus a simple diagram with three overlapping circles. The big deal is that it can be violated by quantum mechanics, and this can lead to some interesting conclusions (e.g. the need to abandon 'local realism').

One feature of my amplifier designs I forgot to cover in the design notes is the phase shift. It was suggested in Wireless World August 1973 (An aproach to audio amplifier design) that power amplifiers should have phase shift at 20kHz no more than 6 degrees, including all previous preamp and filter stages, so the power amp alone should be restricted to about 2 degrees, necessitating a bandwidth in excess of 500kHz. The phase shift of the MJR7 reaches 24 degrees at 20kHz, so why is this not a problem?
There is a rather good article on the Audioholics website, Phase Distortion Audibility, which concludes that under typical listening conditions including room reverberation 'phase distortion' is almost entirely inaudible, but under some other conditions a difference can be reliably heard.
Looking at some of the references there is one important point often missed. Suppose we run a listening test with two sinewaves, 1kHz and 10kHz, and shift the relative phase of the 10kHz by 10 degrees, and find under certain conditions, e.g. in an anechoic chamber, that we can hear a difference. The question is whether this is what an amplifier with 10 degrees phase shift at 10kHz actually does. The answer is almost always no. If we look at the two test signals on an oscilloscope then the wave shape will be noticeably different with the different phase shifts. To return the shape to the original without phase shift there are two ways to do this. We could just remove the phase shift at 10kHz, but we could alternatively add phase shift of 1 degree to the 1kHz component, which again restores the wave shape. With 1 degree at 1kHz and 10 degrees at 10kHz we have a 'linear phase shift', i.e. the phase shift is proportional to frequency, and this is equivalent to a constant time delay, in this case 2.78 usec. That has just the same effect as pressing the 'play' button 2.78usec later, or moving your listening position a little under 1mm further from the speaker, and there is no change to the wave shape, and nothing that could be heard. That is more typical of power amplifier phase response, and looking at the simulated phase as a function of frequency for my MJR7 up to 20kHz it is almost perfectly linear, equivalent to a time delay of 3.3usec.

Of course if we go further up the frequency scale the phase will eventually deviate significantly from linearity, and if we used a test signal with frequency components way beyond 20kHz we could observe some obvious effect on the shape. Hopefully we normally listen to band-limited audio signals, and we don't care too much what happens to the phase shift at 100kHz. I wrote on another old and now deleted page that it is unfortunate that there is such widespread use of square wave testing, this can lead to worries about all sorts of 'problems' such as 'ringing' and 'settling-time'. For example I pointed out that ringing is often interpreted as something undesirable being added to the signal when in some cases there is something undesirable (harmonics above the audio frequency range) removed from the signal. Aiming for a 'nice looking' square wave response may be a recipe for changing the wave shapes of band-limited signals, which is what we really need to care about.

To summarise, the one thing we possibly need to avoid is 'deviation from phase linearity' in the audio frequency range. That, together with a flat frequency response, is what determines the accuracy of audio wave shape reproduction.

I mentioned a new idea for improving my distortion extraction circuit. The problem with using the signal nulling method is that to test a non-inverting amplifier we need to invert either the test signal or the amplifier output so that we can subtract them to leave just the added distortion. The inverting stage needs to have distortion well below that of any amplifier we may want to test, and that is difficult. Using a low distortion op-amp is no help because we may want to test such an op-amp, so we want our test circuit to have even lower distortion. One idea I want to try is using feedforward error cancellation in the inverting stage, and I have added a page with a preliminary example, Distortion Extraction.

I mostly used this sort of circuit for measuring low level harmonic distortion, but one useful feature is that tests can be done using music signals. Such tests were done many years ago, first by Quad, then by others, and they found nothing audible when listening to the extracted distortion from well designed amplifiers. That was my own conclusion even for the worst of my recent designs, the original MJR6, but it is difficult doing this sort of test when driving a speaker because of the effect of the frequency dependent impedance, and I had to use a more devious method to get good results in that case. The page where I explained how that was done was deleted some time ago, but I found an old backup copy, and with a few updates is now available as A Simple Amplifier Test Method. The final circuit on that page is the one I used to extract the original MJR6 distortion with music driving a speaker. This method only works for inverting amplifiers with a close to unity-gain output available from the input stage. The MJR6 and MJR7 are this type, but most amplifiers are not, so it is not a widely applicable method.
Here is a ten second example of 'distortion' extracted from the old MJR6 as a wav file (1.69MB). Although amplified considerably this is still at a very low level, and it sounds mostly like noise plus a low level of uncancelled music signal. The track used was the one I found when testing CDs for maximum slew rate, this track had the single highest peak I found after a few hours searching, equivalent to a full level 10kHz sinewave. I had a link somewhere to a Stereophile test of the wider bandwidth DVD-A recordings which only found the equivalent of full level at 12kHz.
Although it is reassuring to find nothing worth worrying about in this sort of test, in practice the standard 19+20kHz intermodulation test is more demanding, far easier to perform, and the results more useful for comparing alternative designs.

Apologies for lapsing into theoretical problems, the website statistics reveal that the vast majority of visitors are mostly interested in the practical projects, but I see no point just adding new projects unless there is some vaguely original idea involved, or something I need for my own use.
What is perhaps notably absent is a high power amplifier example. I have never thought high power levels to be a major design challenge, using 2 or 3 parallel output devices usually reduces open-loop distortion and also allows higher feedback because of the lower output impedance and so reduced effect of reactive loads. Anyway, I never tried my MJR11 circuit, and it could be pushed up to maybe 200W using dual die mosfets, so I may at least try a single channel version sometime. I also need to build a new distortion extraction circuit to measure lower levels, and I have an idea how to do that. These things can take a long time, mostly because of inefficiency.

I have finally given up trying to write a page about the output impedance of common-emitter stages, and how it is affected by signal source impedance. The latest version leads to a simple model (actually just a variation of the hybrid-pi model) giving about the right answers, but still not entirely convincing. I have included the page here for anyone interested, but have to advise against wasting much time trying to follow it, it is all rather confused and confusing. It is worth repeating what I wrote earlier on this topic:
If we just use Zo = 1/hoe we may look at the data sheet for hoe and for the BC560B find its typical value to be 10uS, but we also find a maximum value 60uS. The ratio of maximum to typical is 6, far greater than the ratio of maximum to typical current gain hfe, which is just 1.5. The important thing to learn from this is that it is a bad idea to design circuits where either hoe or hfe are critical, which would require testing and selecting transistors. If we want very high output impedance there are more predictable ways to do that, such as adding a cascode (common base) stage.

The output impedance of a common-base stage is also a function of the source impedance from emitter to earth, but that is relatively trivial to calculate, and a high source impedance gives a high output impedance, though it took me a while to understand why with an infinite source impedance the output impedance is only half of Rcb in the hybrid-pi model. (Hint: the collector and emitter currents are not exactly equal).
Regarding the h-parameters, if we accept the ratio of output impedances for source impedance varied from zero to infinity to be 2 at Ic = 1mA, as suggested by my measurements, then only hfe and hre are independent variables, and given their values we can calculate hie and hoe. If so this would confirm that the 'typical' h-parameters found in data sheets are often not a consistent set, as suggested by one of the references I mentioned. We could also start with hie and hoe and calculate hfe and hre. I mentioned a formula for Zo which gave a negative output resistance for the 'typical' h-parameters of the BC560B, but replacing these with a calculated set gives a reasonable positive Zo, so I guess it is the h-parameter sets which are unreliable rather than the equations or the models. Specified h-parameters should evidently be used with caution.

On this page, 08-Jan-2014, I mentioned a US patent for a 'new' feedforward amplifier, which I suggested was nothing more than the Quad current dumping circuit from 1971, originally used in the Quad 405. I now see that an amplifier is available claimed to be using this feedforward patent. Of course the original patent has long since expired, and maybe I have missed some variation not covered by Quad to justify a new patent, but Quad's clever use of the output inductor as part of the feedforward network appears to have been abandoned, so how this could be an improvement is not clear. An obvious change is the name, from 'current dumping' to 'THX AAA', which may be a good move for the marketing department. Anyway, the new amplifier appears to be reasonably good from the rather limited specifications available, and is probably better than many other commercial designs. There are of course a few good DIY designs with comparable performance. The most impressive specification is for noise, but then looking further the closed-loop gain is unusually low, requiring 10V input rather than 1V in many designs including my own, so this alone gives a 20dB better figure for signal to noise ratio. There is fortunately an alternative switched higher gain level for more typical signal sources.
Incidentally, I mentioned a need for improvement to the Quad circuit to avoid distortion added by the nonlinear input impedance of the output stage loading the error amplifier. One solution I said was published in Wireless World, and I have now found the page, May 1979, page 71 in a 'Letter to the Editor' from Tore Hevreng. My own 'solution' is also mentioned in the 08-Jan 2014 piece.

Update: There are more detailed measurements of the Benchmark amplifier now published by Stereophile. There are some inconsistencies, for example the distortion at 1kHz at 15.4V has very different values in the distortion vs output level and the distortion vs frequency plots. One includes noise, but that should not cause a 4 to 1 increase. Also switching from maximum to minimum gain is said to only change signal to noise by 3dB, which seems 10dB less than we might expect. Anyway, even assuming the worst, the distortion results are excellent, possibly a little better than my MJR7 at high frequencies. Using dual die mosfets to match the power rating should also bring the distortion down to a similar level. Matching the noise would be impossible with my inverting circuit unless I reduced the input impedance to 1k, the input resistor adds 2uV noise. Using the same 2V input reference that gives a maximum possible 120dB signal to noise compared to 128dB measured for the Benchmark.

I mentioned on this page (01-Nov-2013) the difficulty I was having trying to determine how the output impedance of a common-emitter stage depends on the source impedance connected to the input. I found a published formula which gave obviously wrong results, including a negative resistance, and an IEEE paper claimed measured results entirely different. I have now found a piece in an old issue of Wireless World, Jan 1965, page 42, in a reply to a 'Letter to the Editor' from G.P.Hobbs saying that his own measurements gave a ratio of output impedances about 2 or 3 for source impedance varied from zero to infinity, although a calculation gave a ratio of 18. He suggested the problem could be that the 'typical' parameters in a data sheet are each a mean value for a large number of samples, but these values are not necessarily a consistent set. In other words no individual transistor could have exactly all the typical values. Although I don't find that entirely convincing, I have no better explanation, but anyway it is interesting that the confusing results I noticed were known and being discussed as far back as 1965.
Update: The h-parameters are certainly not independent variables, the input impedance hie is proportional to the current gain hfe, and also it is found that samples with higher hfe also have higher hoe and hre, so there is certainly some restriction to what is a consistent set of parameters. For an example see 2N4401 data, Fig11 to Fig14. The parameters are shown for a high gain and low gain sample. (Two curves in each fig. are not explained, on older versions of the data sheet these are shown to be the 2N4400, and again the higher gain version has all other parameters higher.)

The references on the feedforward amplifier page I just added appear to give conflicting advice concerning the best place to attach a temperature sensor to a power transistor. One says the heatsink close to the transistor base is best, another says the top of the transistor case. Both mention measurements being made, so who is right? One possible problem is that it depends on how the measurement is made, if we use a low heat capacity probe we may get one result, but if we use a higher capacity device, for example bolting on a TO-126 sensor transistor, then the low thermal capacity of the plastic case and high thermal resistance from case to junction will have a greater effect. For my own application with output triples there may be no need for a heatsink for the TO-126 transistors, and maybe the best idea is to clamp the two output stage transistors either side of the sensor transistor. Anyway, I need to do my own measurements, and add a warning that the references may not be as helpful as I originally thought.

Another point is that I wrote about bias adjustment for minimum crossover distortion in a conventional amplifier, and was foolish enough to say 'of course the conditions for minimum distortion were known before 1972'. I thought I should probably support that with a reference and started searching, but to my surprise found almost nothing. Eventually I found one example from 1969, a 'Letter to the Editor' from Peter Baxandall about designing quasi-complementary outputs , Wireless World, Sept 1969, page 416, where he writes about an output stage with 0R5 emitter resistors:
"When the output transistor current has risen to about 50mA, the reciprocal of its mutual conductance is about 0.5 ohm and the slope of the pair then reaches about half its final value of 2 A/V. Two pairs of this type (requiring complementary power transistors) would thus have an optimum quiescent current, for minimum crossover distortion, of about 50mA in each power transistor."
The same 0.5 ohm resistors and quiescent current 50mA were used in a design from 1961,'Transistor Audio Amplifier' by R.C.Bowes, Wireless World July 1961 Page 342 but without any explanation of how the correct current was determined, and I am not entirely certain it is still correct for that circuit. At the end of the article the author thanks P.J.Baxandall 'for many helpful discussions', which may be the explanation. That design used OC22 germanium power transistors driven from a transformer. The formula gm=Ic/Vt gives the same result for silicon or germanium, so the conditions for minimum crossover distortion are the same, at least for idealised devices with no additional internal base or emitter resistance.

A few older pages on my old website no longer have links to them, and some are really not worth keeping, but I found one example of a discrete transistor version of my original feedforward output stage amplifier. I may try building it sometime, but for now I have just corrected a few errors and repaired a broken link, and left it as 'work in progress' with the title Class-B Feedforward Amplifier.

The Guitar Pre-amp Mk3 is finished and works quite well. I have added a layout diagram, board design and photo. It needed a few alterations and so looks a little untidy, but apart from that everything works as intended. One important finding was that the J112 jfet in the tremolo circuit may not be an ideal choice. I originally used a surface-mount type PMBFJ112,215 made by NXP and that worked well after adjustment of the 1M preset for best effect. Then I tries a TO-92 case version of the J112 from Fairchild, and only a small effect was possible, and that needed the preset turned down close to the -4.5V supply. The specification for VGS(off) is -1V to -5V, so maybe the Fairchild version is closer to the -5V limit. Maybe the J113 is a better option with its -3V maximum specification. Anyway, I returned to another NXP device and again it works fine. Anyone wanting to try this circuit should maybe obtain both J112 and J113 to try.

I have updated most of the dead links on the website, a few items have vanished entirely and may no longer be available anywhere.

Many old issues of Wireless World are now available online at American Radio History going back to 1913. I started reading the magazine around 1968, but gave up soon after it changed its name to Electronics World in 1996.

I have just read a post on diyAudio mentioning an old advert for the Quad 303 where a number, maybe 20 or 30, were connected in series and the distortion at the final output was still within the specification. I don't remember that ad and can't find it via Google, but Quad did do that sort of thing. Some of the other Quad adverts are shown at pink fish media.

I also checked the calculation I mentioned of capacitor distortion appearing at the amplifier output, based on Bateman's worst case polyester capacitor producing -90dB 3rd harmonic with 4Vrms across it, for a 1V input at 1kHz there is only 6mV across the input capacitor of the MJR7, and making reasonable assumptions about distortion level versus voltage I estimate a contribution to amplifier output distortion around a tenth of a nanovolt. The minimum audible level from my own speakers at the 3kHz 3rd harmonic frequency I found to be 300uV, so the capacitor distortion reaching the output is then theoretically 130dB below audibility.

I still need to build the final version of the guitar preamp, but apart from that I need to do some website maintenance, there are a few dead links scattered around. There are some subjects I could write theoretical articles about, but that seems increasingly pointless, the website statistics show it is the practical designs most visitors look at.
I may still try one of the direct coupled amplifier designs I mentioned earlier, even though as I said then, the only unique feature is the ability to drive DC into the speakers, which we then need to prevent with speaker protection circuits. A direct coupled input also has its dangers, and achieves little more than saving one capacitor. Anyone who seriously believes they can hear differences between capacitor types can of course use something with audiophile approval, but note that the MJR7 distortion measurements include the effect of the cheap polyester type I used, so it doesn't appear to be a problem. I would be surprised if it added more than a few nanovolts third harmonic at 1kHz at the output. (I worked it out somewhere based on measurements by Bateman). My advice remains 'small size and low leakage' and maybe increased value to 4u7.

I have now updated Peak Current Requirement of Speakers to include links to the Google plots in the references at the end of the item. There is also a link to the Stereophile article which describes failed attempts to observe unexpected current peaks with music signals. That page of 'assorted items' was all written a long time ago, and there are a few dead links I need to update sometime.

I think I have made it all look more complex than necessary, the explanation of the current peaks in speakers caused by certain test signals is essentially trivial, at least if we assume linearity, and could be explained in one short paragraph:

Starting with a square wave voltage applied to a speaker, this consists of a fundamental frequency and a theoretically infinite series of odd harmonics. The resulting current has the same series of harmonics but because the speaker impedance has reactive components there is a frequency dependent phase shift of these harmonics, which changes both the shape of the current wave and its peak level. The square wave harmonics have the relative phases necessary to give the minimum possible peak amplitude, so almost any change from this gives a higher peak level, so the current wave will invariably have higher peak levels than if the speaker was a pure resistance which would have left the phases unchanged. There is no theoretical upper limit, shifting all phases by 90deg would give an infinite peak amplitude, limited in reality by the finite bandwidth and speakers having less than 90deg phase shift. This ignores changes in the magnitude of the speaker impedance as a function of frequency, a nominally 8R speaker typically falls to 5R or less at some frequencies, and this also increases the current.

The explanations given by other writers tend to concentrate on a more complex test signal cleverly chosen to maximise the current peaks with certain speakers, and their explanations involve 'back-emf', but what I wanted to demonstrate is that frequency dependent phase shift is a rather easier way to understand the effect, and applies for any rectangular test voltage, in all cases the phases of the frequency components start with the values needed to minimise peak level, so almost any phase changes cause increased peak level.

11-April-2015 (Updated 12 April)
Something I just found out is that you can use Google to plot a Fourier series. To see what I mean copy and paste the next line into the Google search bar and press return:
This is just the first few harmonics of a square wave. Google will plot it for you. Note that the peak amplitude is 1.18.
Try changing the phases in the above series, for example change the sines to cosines, equivalent to shifting them all by 90 degrees:
When this is plotted we find a very different looking wave and the peak amplitude is now 2.39, so increased by a factor of 2. If we had used the whole infinite series of harmonics instead of stopping at the 11th the peak level would have increased to infinity.
The reason I was looking at this was to add something to one of my articles to demonstrate that phase shifts can have a big effect on the peak level of a wave. A typical speaker has a frequency dependent phase difference between voltage and current, which is one reason why if we apply a square wave voltage the peak current can be higher than expected. Of course it works both ways, we could apply a square wave current to a speaker and find unexpected voltage peaks. This is all complicated by the impedance of a typical speaker varying in magnitude as well as phase as a function of frequency. My own speakers fall to 5.5ohms at low frequencies. I will try to find a link to an article I read in Stereophile describing failed attempts to find high current peaks in speakers using music signals. My own tests also failed to find anything to worry about. It appears to be one of those 'theoretical effects' having little practical importance.

Guitar Pre-amp Mk3 is the current version. There may be further changes before I am entirely happy with it, and I have not tried the input stage as shown, I am still using an earlier version, so that is the only part where component values are not necessarily final.

The Mk3 version of the guitar pre-amp is built and tested, and finally it is working more or less as intended. The opto-coupled light dependent resistor (LDR) is probably too fast, one with a slower decay time should remove some slight distortion noticeable at the bass end, so I will get another type to try.
The obvious approach is to add a capacitor after the level detection rectifier stage, but doing this caused serious distortion or instability, whether 2u2 or 1n was tried. Maybe I am just using too much gain round the loop at maximum control setting, but anyway leaving out the capacitor and relying on the slow LDR for loop stability seems to work quite well. The LDR specified for examples on the Elliot Sound Products page has a decay time of 1.5sec which I would have guessed was far too slow, but clearly it has been found to work, so I will try some slower LDRs.

The idea to use a jfet as the gain control in the guitar amplifier sustain function was motivated by the low current requirement, but I have also looked at the possibility of using an opto-coupler with LDR output.

I have a Silonex NSL-32SR3, bought from Farnell (UK), which should work ok at LED current under 1mA. Using this the number of dual op-amps could be reduced to two, though it may then be necessary to leave out the bass control. I need to do some measurements first to find out why the jfet version sounds more distorted than I expected. The latest but not final circuit is shown here as Guitar Pre-amp Mk2.

Much of what I know about physics was learnt from the Feynman Lectures. These are now available free online at:
The Feynman Lectures on Physics
These were written around 1963, so some of the material is out of date, but on the plus side many errors in the original books have now been corrected.

The next stage in the guitar preamp project is nearing a final version. I decided to include a sustain function, this is fairly simple to make, using a level detector to control a jfet used as a variable resistor. Jfets are not very linear in this sort of circuit, but adding half the drain signal to the gate effectively linearises it. Whether we actually want linearity is a different matter, it may sound better with some added 2nd harmonic. I also have included a tremolo circuit, with adjustable frequency and modulation depth. Again there is some uncertainty what will sound best, using a sine, triangle or square wave modulation.

I still want to use a single 9V battery, so this sets limits to what can be done. I need to use 3 dual op-amps, so current drain becomes a bigger problem. There are plenty of lower current types than the OPA2134 used in the first version but there are other specifications we need to worry about such as common-mode input voltage range, which can become a problem at low battery voltage.

I updated the page about cable skin depth to include the points made earlier on this 'latest news' page. One problem has been pointed out to me, that I said the surface field is determined by the instantaneous total current through the cable, which implies faster than light communication, how else can the current at the centre of the wire have any effect at the surface without a time delay. Given the low speed of electromagnetic energy inside the conductor the delay could be expected to be significant. I added a few words to try to explain that also, but I need to think more about that. More generally one of Maxwell's equations gives this 'instantaneous' effect, this relates the line integral of the magnetic field round a loop to the total current through the loop. The integral round a loop is equal to the sum of the integrals round two smaller loops or the sum for any number of smaller loops we choose to divide the original loop into. For any two adjoining loops the common boundary is counted twice in opposite directions in adding the integrals, so these all cancel and only the single outer loop counts, and includes the effects of all the inner areas. I also need to add something about the other term in the Maxwell equation which is the rate of change of the electric field, which is sometimes confusingly referred to as 'displacement current'. If the current at some depth in the wire changes then there must be a changing electric field, so this term needs to be included if we want to understand more completely how the surface field is related to a changing internal current.

I mentioned one of my recent projects was a guitar preamp, and I have added a page showing how this is progressing. So far it is very basic, just an experiment to see what characteristics are most useful. The idea to include asymmetric clipping was not found to add anything very dramatic, and has been abandoned for now.

I have been trying to understand US Patent 8466744 which lists my MJR7 amplifier under 'Other references'. The circuit shown as Fig.20 appears to be based on my old MJR6 circuit with just a conventional differential input stage added, and some component values changed. The claimed distortion figures, -167dB at 1kHz and -137dB at 20kHz I am almost certain are impossible for this circuit, unless I am missing something important, or unless stability is highly conditional, and anyway it appears the distortion figures are only simulation results.

I have now transferred the MJR9 feedforward amplifier page to the new website, and have rewritten it to include information about how it works and a simulation result, originally on other pages.

I have been asked whether my phono preamp circuit can be easily modified to work with moving coil cartridges. The 100R gate input resistor could be omitted, but the source resistor still adds too much noise. Just reducing the source resistor to something like 10R may reduce the noise far enough for all but the lowest output cartridges, but there are then other problems. The DC output voltage stability is not great to start with, and reducing the resistor will make that worse. The capacitor coupling to the next stage makes the DC level less important, but we would not want it to drift much more than a volt. Maybe a bigger problem is the drop in loop gain and consequent reduction in RIAA equalisation accuracy. The 68p compensation capacitor can be reduced to 10p, which should help a little. A further problem is that with the 10R source resistor the BF862 could have drain current up to 20mA, and this is greater than the minimum Idss of 12mA for the BF245C cascode fet. A different type with higher minimum Idss may be needed. Keeping the original source resistor and adding the 10R with a 2200uF series capacitor from source to earth could avoid some of the problems, but then some people will worry about having electrolytics in the signal path. With the 10R source resistor the 22R in the feedback network needs to be increased to 91R. Keeping the jfet current low however will reduce gm and increase its voltage noise, so that also needs to be considered.
My answer then is yes, the circuit can be modified for use with moving coils, but it is far from ideal for that purpose, and I think it would probably be better to add another gain stage at the input or use a transformer.

I try to suggest alternative transistor types for my designs, but some of those I have mentioned so far are listed as 'obsolete' and likely to become unobtainable.
There are still a few types widely available which could work well enough in the MJR7 amplifier, the input stage can use npn type BC337-40, which has the advantage of a fairly low rbb' (30R), or the BC550C which may have a higher current gain. (High rbb' types such as the MPSA18 are probably not good for loop stability), and the BC560C pnp can be replaced by any similar high gain high fT type such as the BC557C. Gain over 500 and fT over 200MHz are the main requirements for the pnp, and those made by ON-Semi sometimes have higher specified fT than others, e.g. from Fairchild. The BC560C is preferable if still available, the noise contribution will be slightly lower, and current gain is usually over 550 at 5mA.
The KSC3503D and KSA1381E are still available from Mouser (US).

The guitar pre-amp I mentioned earlier has been built and tested, and is working well, but maybe can be improved. The adjustable asymmetric clipping turned out to have less audible effect than expected compared to symmetric clipping, although it is confirmed to be working as intended by checking with an oscilloscope. A simple tone control appears to be more useful in practice, and I have added an adjustable low-pass filter at the output, which also works as a volume control if the output feeds a low impedance such as headphones. I may add the circuit diagram here when I arrive at a final version.

Audio design would have far less point without the creation of music by musicians and composers, and we can all benefit from the encouragement of new talent. I mentioned that my son is learning to play the electric guitar, but he is also a composer of synthesised electronic music. Some of his work can be found at Bandcamp. It isn't the sort of music I usually listen to, so it's hard for me to judge, but I quite like the second track. Have a listen and see what you think. I have to confess I do sometimes make suggestions, such as 'more dynamic range', 'less repetition', or 'what it really needs is some tubular bells.'
The tracks at Bandcamp can also be downloaded in various formats for a fee, but you can contribute as much or little as you like, anything from zero upwards. Bandcamp keep 15% and pass the rest on to the artists.

Searching for 'audio amplifier design' via Google today had my own website in third place on the first page. The only problem is that it is my old site on Angelfire, which has annoying pop-up advertising, my new website is somewhere on page 5.
In second place was the wikipedia page about audio power amplifiers which looks about 40 years out of date, including uncritical reference to the work of Otala on 'TIM' (with no mention of earlier publication by Daugherty and Greiner). It has been pointed out often enough that what matters is the magnitude of the overshoot (in volts) not the percentage relative to its final level.
I was pleased to see at the top of the list was the Rod Elliott website. It has lots of useful information for anyone interested in amplifier design. My own website is intentionally limited to topics I think are not covered very well elsewhere, and slightly unconventional designs, so more useful as 'further reading'.
Anyway, I am tempted to delete the new website, or maybe replace it with something completely different, and leave the old 'free' website as a possibly more permanent record.

I mentioned that I have not built anything for a long while, but I do have a project or two. My son is learning to play the electric guitar, so I wanted to make a suitable pre-amp with a few 'effects'. Reading about guitar amps is something of a revelation, the usual hi-fi aim of low distortion becomes relatively unimportant, with the amplifier intended to contribute to the final sound. The pickup output is higher than I expected, and so is the recommended load impedance of over 500k. A unity gain input buffer with a jfet input op-amp such as the OPA2134 looks like a good place to start, plus a second stage op-amp providing frequency response equalisation and adjustable clipping. Apparently germanium diode clippers are favoured by some, and I have a few OA5 to try. Maybe optional asymmetric clipping to add some even order harmonics is good also.

I left one problem unsolved regarding my phono preamp. I originally included 100k offset adjustment preset pots for the output stage op-amps, but found these difficult to adjust. For my own use that was of no importance, my main preamp has capacitors feeding the volume control, but for anyone needing low DC at the phono preamp output I should suggest a solution. The cause of the problem is the interaction between channels via the 5k6 resistor (R10) forming part of the 'rumble filter'. The procedure I followed of just trying to set one control and then the other is not guaranteed to work. A better idea is to short one op-amp inverting input to earth and then adjust the other channel preset for zero DC output. Then remove the short and set that channel also. That way both op-amps have their inverting inputs set close to zero, and the outputs are also both close to zero. I tried this, and could easily get both outputs down to 0.2mV or less, compared to typically 2mV without the adjustments.

Looking again at the animated plot at Some Skin Effect Notes the points on the plots at the left hand side oscillating between +1 and -1 represent the field levels at the surface and outside the conductor, and that field may travel close to light-speed carrying energy to the load at the end of the cable, while the internal variations travel into the wire at much lower speed, e.g. 3m/sec for a 60Hz signal. I suggested it can easily be understood from the animated plot why the delayed and reversed direction currents at different levels in the wire are not a problem.
The total current can be found by integrating the current density through a cross-section, and the time delays and current reversals may seem to complicate this, but one of Maxwell's equations, for the curl of the magnetic field H, tells us that the line integral of H round the circumference of the wire is proportional to the instantaneous total current along the wire, so the value of H at the surface tells us that the total current including delays and reversals is proportional to the surface current with just the 45 degree phase difference between J and H at the surface mentioned previously. The animation assumes a wire of large diameter compared to the skin depth, which is rarely the case in audio frequency applications, so the less delayed current near the left side of the plot is all we are concerned about and the resulting phase shift may be far less than 45 deg.

There are other ways of looking at this. The 60Hz example has a time period of 16.7msec, enough time for the internal field to travel 50mm into the wire, if it was thick enough. Using a more typical 1mm diameter wire the 'slow' internal field will reach the centre after 167usec, at which time the surface 60Hz wave has only changed phase by 3.6 degrees. At higher frequencies the refractive index is lower and the internal field travels faster, so it gets to the centre of the wire quicker, but the phase of the surface wave has changed more. Anyway the internal field is not some highly delayed version of the signal, it is just phase shifted a little, with higher phase shift at higher frequency. The internal energy storage with phase shift increasing with frequency is equivalent to just an internal inductance, in effect in series with the external inductance, though not a simple fixed inductance, its value changes with frequency. The reducing skin depth at high frequencies means the internal energy starts to drop when the skin depth becomes comparable to the radius of the wire, so the internal inductance falls.

A possibly important question is whether the added phase shift is a linear function of frequency so that there is a constant time delay. An interesting link covering this question is Effects of wire diameter and spacing where Fig 14 shows that group delay is virtually flat up to 25kHz for 1mm dia wires, but is not so flat for 2mm or greater, but even then the change in delay at 25kHz is mostly under 50nsec, so fairly harmless. The results shown there are for a 3m length of cable driving a 8R load.

I may eventually transfer these pieces about skin depth to the relevant page, but I will try to improve the explanations a little, I am not sure I explained it clearly. I maybe need to explain why the internal inductance is in effect in series with the external inductance, otherwise we could imagine the internal and external fields are two separate signals travelling along the cable. We could say the internal field is caused by the external field, but there are perhaps equally good reasons to say the external field is caused by the electrons in the wire, so maybe causality arguments are not helpful. Either way the two signals are linked and must travel along the cable at the same speed. The electrons in the wire need not travel along at the speed of the external field, it is only changes in electron density which match the speed of the field.
Also to be explained is how the field travelling into the metal is related to the field travelling along the wire, I wrote something about that in the transmission line page, which could also be improved, that was originally an unpublished 'letter to the editor' about an article in Wireless World many years ago, so it is probably trying to answer questions no longer being asked by anyone.
I maybe need to mention that exact solutions of this sort of problem are often extremely difficult, and explanations of the sort I sometimes attempt are usually over-simplistic and only close to the truth under a limited range of conditions, so it may in practice be easier to just measure what happens under the conditions of interest.

Looking back through this page I see I have not actually made anything since October 2012. Part of the reason is that I have my own audio system as good as I need it to be. My hearing has deteriorated to the point where I am unlikely to hear any further improvement, and the only worthwhile changes left are the speakers and listening room, which I hope to improve soon. Much of my listening is done using headphones (Sennheiser HD238) via my computer soundcard, which my measurements confirm is far better than my CD players.

I wrote a piece some time ago about conduction in metals, but realise some of that is at least simplified if not actually wrong. The part about skin depth certainly needs improving. It is based on the explanation in Feynman's Lectures Vol.2 which involves the refractive index of the metal. I learnt all that over 40 years ago and never thought much more about it since. There is an explanation in Wikepedia in terms of circulating eddy currents cancelling the current at the centre of a wire, but I think that is not the best way to understand it.
I only recently learnt that the skin depth is just the wavelength of the signal divided by 2 pi. The relevant wavelength is inside the conductor, and for example in copper at 60Hz the skin depth is 8mm and the wavelength is just 5cm. The wavelength in a vacuum is 5000km, and the ratio of wavelengths tells us the refractive index of copper at 60Hz is around 100 million. The velocity of the electromagnetic field into the interior of the conductor is therefore a surprisingly slow 3m/sec. One result of this is that the surface current can change polarity while the current further below the surface is still in the original direction. In other words the current can at times be in different directions at different depths. A good animated plot can be found at Some Skin Effect Notes (But there are errors in some of the equations.) Note that the magnetic field H lags the current density J by 45 degrees at the surface. Note also that the animation looks the same for a wide range of frequencies because of the fixed ratio between skin depth and wavelength, and because the horizontal axis is in multiples of skin depth rather than actual distance.
It may be tempting to think this must cause problems in audio cables, if part of the current is determined by what happened maybe as much as a msec earlier would that not 'smear transients'? I think that was actually suggested in a published article some years ago. The reason why it is not a problem I am sure has been explained somewhere. I think it should be easy to explain by reference to the animated plot, but I'm a slow thinker, so I'll get back to that in a while.
That reminds me of a story about a professor telling some theory to his students and saying 'I'm sure this is obvious, just give me a minute to work out why'. Then after 3 hours deep in thought, and long after all his students had left, he announced 'Yes! I was right, it really is obvious!'

The phono pre-amp pages continue to be the most popular. This is closely followed by my CD player modification page, which is perhaps unfortunate because the conclusion was that none of the 'improvements' tried actually made any measurable difference.
I have added another rumble filter design to the references at the end of the Phono Pre-amp Design Theory page. This version is from Dimitri Danyuk, and is a second order version which includes a high-pass filter which can reduce horizontal rumble effects in addition to the cancellation of vertical rumble. The two channel filter could be adjusted by a single variable resistor, which at first I thought was not possible, but I now see it really can work.

On this page a while back I said "For a given speaker almost any cable will add some frequency dependent amplitude and phase variations". There are two types of distortion, linear and non-linear. The non-linear variety adds new frequencies such as intermodulation products, and can be detected with the usual distortion measuring equipment, and if it can be detected at all for a copper cable it is invariably found to be down near the limits of measurement (For example see Cable distortion and dielectric biasing debunked by Bruno Putzeys.)
Various mechanisms have been proposed for cable nonlinearity, ranging from unlikely 'micro-diodes' to known effects such as magnetoresistance. My own view is that there is no point looking for or inventing different explanations unless some reliable measurements can provide data sufficient to distinguish between them. Even for the known effects it is difficult to find any convincing calculations of the distortion levels to be expected in typical copper speaker cables.
Linear distortion adds no new frequencies, so each frequency component can only be changed in level or phase, so frequency dependent amplitude and phase variations are the only effect possible.
Some years ago I wrote a piece in my physics section, Cable Impedance, showing how even the worst possible example, with a current step driving a lossless open ended line, which produces a continuously repeated upward step output having no resemblance to the single input step, is just the same effect as a single capacitor for band-limited audio signals. I recently noticed that AIM-Spice includes a lossless transmission line model, so I have extended that page to include a few more examples, together with amplitude and phase plots to show that nothing bad happens within the audio range.
Maybe sometime I will extend the article further to include resistive losses and properties of dielectrics, but I am fairly sure nothing important would be revealed. I will continue to use my cheap zip-cable, but of course anyone using speakers with extreme low impedance dips or amplifiers with stability problems may need to select cables more carefully.

The idea for the MJR11 power amplifier started from the phono-preamp input stage. The simulations to investigate stability revealed that the 2nd stage transistor is more critical than I expected, a type with low base-spreading resistance rbb' gives a better stability margin. I suggested a BC560C would be good enough for the preamp, and checking again shows the stability margin is just adequate, but substituting a BC327-40 with rbb' 30R is a big improvement. My own preamp uses the 2SA1085E with even lower rbb', but these are unobtainable from most reputable sources. Few data sheets specify rbb', and some Spice models appear to be unreliable, so some care is needed when specifying alternative types not actually tried.

I mentioned a design for a higher power direct coupled amplifier, and although this may never get made here is a preliminary example of the sort of thing I was thinking of, called the MJR11-Mk1. So far it has a few problems which need sorting out, but I like the general idea.

Looking at the website statistics the most popular page is my phono pre-amp design. That is certainly far more complex than is really necessary, but none of the components are expensive, so I just made it as good as I could without going to ridiculous extremes. I should maybe add an optional input stage for moving coil cartridges. There are plenty of published examples of MC input stages, but if I think of anything different I will include it sometime.

Thinking about new projects for the future, power amplifiers are not high on the list, the excellent results from the MJR7 would be difficult to improve on. One option would be a direct coupled higher power version. Dual or triple mosfets will have lower open-loop output impedance, which will reduce the effect of reactive loads, and so allow higher feedback, and should also have lower open-loop distortion. Achieving low distortion with higher power amplifiers is therefore less of a challenge, but lower distortion with a single pair of mosfets is also easy enough using feedforward as in the MJR9.
Just using dual die mosfets in the MJR7 and increasing the supply voltage should be enough to push the power output well beyond 100W. I have seen amplifier modules claiming power rating up to 200W with just single lateral mosfets, which may be ok with resistive loads, but reactive speaker loads with impedance dips in the audio range are a different matter. I usually assume a minimum impedance of 3R but a few speakers fall even lower.
I am not enthusiastic about direct coupling, it just adds more problems. Its only unique achievement is the ability to drive DC into the speakers, which we then need to prevent with speaker protection circuits. The avoidance of amplitude and phase errors at low frequencies can also be a feature of direct coupling, but my usual approach when using capacitor coupling is to set the -3dB frequency to about a tenth that of the speakers so that additional amplitude and phase errors are relatively insignificant.

The entry for 14 June 2013 mentioned "The original plan when I set up this new website was to add some products for sale, maybe a few different kits, some hard to find transistor types and so on." That is still a possibility, but past experience suggests my existing designs are unlikely to attract many buyers, so maybe the 'higher power direct coupled amplifier' could be worth working on, I have a basic idea using a single jfet input something like the phono preamp input but with servo control. That would also need to include reliable speaker protection, I would hate to be blamed for destroying anyone's speakers.
If I wanted to be cynical I could always produce some 'exciting new concept' in speaker cables and sell them at an astronomical price. Such products continue to be available, with impressively imaginative advertising, so there must be plenty of potential buyers around. My own speaker cables are an unknown brand, they look like fairly cheap 'zip-cord', which came with the speakers when I bought them secondhand, and I never found any reason to change them. I accept that for a given speaker almost any cable will add some frequency dependent amplitude and phase variations which in extreme cases could be audible, but anything beyond that I suspect is 'marketing'. Some of the more expensive cables probably are 'extreme cases' and really do sound different, or in some cases cause instability in badly designed amplifiers. (My original MJR7 was an example of this, but fortunately one of the early constructors discovered the problem and kindly told me about it, so a hasty modification was needed, which is why I now use a RC Zobel in the 'wrong' place, which turned out to be the right place.)

One more point regarding the 6th edition of 'Audio Power Amplifier Design', on page 333, and in Fig.13.5(b) shunt compensation is criticised on the grounds that for the example given a shunt capacitance of 44nF is needed, together with 155mA from the VAS to drive it. This appears to be another example where what may be true for some BJT amplifiers with moderate feedback is not necessarily true for mosfet designs with high feedback, my own MJR7 being an example needing only 100pF driven by a stage running at 5mA. Shunt compensation may be less problematic for what is in effect a two stage circuit.

One possible advantage to shunt compensation is that it is minimum phase, unlike the Miller compensation in which there is feedforward through the capacitor adding more phase lag. This is often dismissed on the grounds that the effect only becomes significant far beyond typical loop unity gain frequencies. This is usually true, but only for a stage with high gm, which is not necessarily true close to clipping where the gm of the VAS falls. For Miller compensation the phase shift may therefore increase near clipping, but for shunt compensation if the impedance at the VAS output falls near clipping, as it does in my MJR7 circuit, then phase shift added by the capacitor is reduced, and stability margins get better instead of worse.

I have never tried comparing the clipping behaviour with reactive loads for the two compensation methods, so I don't know for certain how important it is in practice. The feedforward problem was mentioned by Baxandall in his 1978 Wireless world series (part 3), but only his remark in part 4 about shunt compensation being 'in all respects sub-optimum' seems to be remembered, even though he pointed out that just adding a series resistor could solve the most serious problem.

I have been looking at a US patent for a 'new' feedforward amplifier, No.8,004,355. Maybe I am missing something obvious, but this looks identical to the Quad current dumping circuit from 1971, apart from a few changes to the bridge components which appear to lose one advantage of the Quad circuit, that the output inductor needed for stability into capacitive loads is part of the distortion nulling circuit. My own MJR8 and MJR9 from 2007 were also based on the Quad idea, as explained on the MJR8 page. The original Quad patent has long ago expired.
The only real problem with the Quad circuit is that the nonlinear input impedance of the output stage loads the driver stage, and any resulting distortion is not nulled by the feedforward. There are a few solutions, including one published in the letters pages of Wireless World, and also one of my own untried ideas (Output Stage Variations, 2006) where the output stage drive is taken from a driver stage supply line rather than from its output. The distortion figures for the Quad 405 were nothing special, and my own experiments with feedforward were mostly discouraging, it was easier to achieve low distortion using conventional negative feedback. The point of the Quad circuit was to achieve adequately low distortion without any adjustments or accurate control of quiescent current, which has considerable advantage for a mass-produced commercial product.

I have been looking at the latest (6th) edition of 'Audio Power Amplifier Design Handbook' by Douglas Self. Some sections can be read for free on Google Books
There are inevitably some points I disagree with, but otherwise it looks good. The book concentrates almost entirely on BJT amplifiers, so some of the conclusions are not necessarily applicable to mosfet designs. Here are a few points worth mentioning:

On Zobel Networks he writes about the usual RC Zobel that it is 'always fitted on the inside (i.e. upstream) of the output inductor.' Also the resistor value he says 'approximates to the expected load, and is usually between 4R7 and 10R'. In my MJR7 I used a 1R resistor plus 100nF capacitor, and added the RC after the inductor. At very high frequencies the resulting load is still mostly resistive, about 2R5 total. I explained somewhere why I put the RC after the inductor, it concerns stability with capacitive loads around 2nF which resonate with the inductor close to the unity gain frequency. It may be that BJT output stages are affected less by such problems than those using mosfets because of their usually lower open-loop output impedance.

In Fig 14.11 the 'optimal coil shape' for the output inductor shows that my own coil design is hopelessly inefficient, it should have higher area and shorter length. What I didn't find mentioned there is another factor which is that increasing the area increases the pickup of interference from varying magnetic fields, although the problem of pickup from external fields is mentioned in the section on 'Coil Placement Issues'. Higher area gives higher pickup, but the lower number of turns for the same inductance reduces pickup. My calculation suggests the 'optimal' coil is worse by a factor of 1.7, but this is probably not very accurate.

On page 108 it is stated that there are only two cures for output capacitor distortion, both involving expensive capacitor types. This is puzzling because a third method is mentioned later, where the capacitor is included at least partly inside the feedback loop. This approach was probably first used in a famous design published in 1956 by H.C.Lin., the circuit of which appears in chapter 30, Fig.30.5, followed a few pages later by an example by Hardcastle and Lane in Fig.30.8. It seems unlikely that those designers were worried about reducing capacitor distortion, but inclusion in the feedback loop can be highly effective for that purpose.

I mentioned a while ago that I was working on a 'beginner's guide' about amplifier design. That never got finished, and the only section I did finish is really not very good. I think the problem is that I never studied electronics at an elementary level, except as part of a physics course, so I have no good ideas where to begin or what to include. Starting from Feynman's Lectures Vol.2 is probably not good advice. Even so, I have added a page called Transistor Amplifier Design for Beginners which just covers a few details I remember having difficulty with many years ago. Beginners now inevitably have a different starting point, there is almost unlimited information available on the internet, compared to when I started learning, at which time Wireless World was almost the only easily available source.
I also wrote a page about the common-emitter output impedance, trying to explain how it depends on the source impedance. I finally realised I don't fully understand that topic, and I need to do further investigation before either adding the page or admitting defeat.

I have rebuilt my old Angelfire website so that it includes most of the material on the new website, but continues to include some of the older pages which were never transferred in an Archive page. One of the pages listed is the MJR9 feedforward mosfet power amplifier. Unfortunately there is a limit of 20Mb on the 'free' site, so something had to be left out, and that was the 'Constructor's Page'. (Update June 2014, I have added a reduced version of the Constructor's page to the Angelfire site, leaving out measurements, which mostly only applied to earlier versions). As far as I can see the free websites have no time limit, I just found an even older website I made over 12 years ago which I never update, but still it continues to exist, and I like the idea that my website at least could go on into the indefinite future.

The common-emitter output impedance Zo is actually a more difficult problem than I thought, unless of course we just take it to be 1/hoe and look up the h-parameters in the data sheet. Many data sheets fail to include even that, but if we do get the value there is still the question of how the output impedance is affected by the source impedance Zs. I have only a vague idea about this, so I started with a Spice simulation, which showed no effect from Zs. Spice models are not necessarily reliable, so I searched for a formula, and found one in 'Small Signal BJT Amplifiers' (now a dead link). The formula there is Zo = 1 / (hoe - (hfe.hre / (Rs + hie))) . Taking the h-parameter typical values from an old BC560B data sheet I got Zo = 100k for a very high Rs, and for zero Rs I got Zo = - 59k. Yes, a negative resistance. Trying again with a more recent data sheet for the 2SC4117 gave more reasonable results 400k and 2.8M with high and low Rs respectively. To make matters worse I found an IEEE paper Output resistance of the common-emitter amplifier which states that the ratio of Zo values for high and low source resistance is 1.5, and shows measurement results which appear to support this. Worse still, the higher Zo is for higher Rs, the opposite of the formula, and not what I would expect. The article does agree with my own observation that Spice simulations can fail to show any effect from Zs.
If we just use Zo = 1/hoe we may look at the data sheet for hoe and for the BC560B find its typical value to be 10uS, but we also find a maximum value 60uS. The ratio of maximum to typical is 6, far greater than the ratio of maximum to typical current gain hfe, which is just 1.5. The important thing to learn from this is that it is a bad idea to design circuits where either hoe or hfe are critical, which would require testing and selecting transistors. If we want very high output impedance there are more predictable ways to do that, such as adding a cascode (common base) stage.

I promised a long time ago to add some pages for beginners, and I have been trying to write a page called 'Transistor Amplifier Design for Beginners'. The trouble is that to make it easily understandable it would need to be simplified to the point where it is at least misleading, and in some ways just wrong. I don't know how to explain the output impedance of common-emitter stages in a simple way. Just drawing equivalent circuits such as the 'common-emitter hybrid pi-equivalent' gives no real understanding of what is happening or why. For example how can there be a resistor between collector and emitter when there is no direct connection between them, all current from collector to emitter must pass through the base region. I will carry on trying to get it right, but may have to change the title to 'Amplifier Design for Advanced Beginners'.

My search for good low noise transistors continues. The really hard to find types are those combining high current gain with low rbb', and so possibly having low current noise and voltage noise. The 2SC2547E I originally used is one of the best, with high gain and rbb' sometimes claimed to be around 2R. The 2SC2240BL is about 40R. The only good and available example I found so far is the 2SC3324BL, rbb' less than 20R, which is a surface mount type looking very similar to the 2SC2240BL.

I was looking at the RS website, and noticed that the 2SC2240BL is now listed as 'discontinued', and apart from a few of uncertain origin avilable via eBay at well above the old RS price these now appear to be unobtainable. I still have some for my own future use, but I am looking for alternatives. The high gain MPSA18 are also listed as discontinued. Farnell may have them available soon, but only with a 2000 minimum order. They have a far higher rbb', around 800R, than the 2SC types I originally used, so no good for low impedance circuits such as mm-preamps, but for the MJR7 with over 10k series input resistance that is the least of our worries, and the high current gain is far more important. The high rbb' will however have other effects including adding phase shift round the feedback loop, so the MPSA18 may be a problem. There seem to be endless variations on the BC550C, (rbb' = 160R at 0.5mA) which may be good enough, but genuinely low noise types are becoming rare. Both input stage transistors need high current gain for best results, 500 or more is good, and if using alternative types or if they could be fakes the current gain should be checked. Even some very cheap multimeters have a current gain measuring function. I will try to do some tests on some of the more easily available types to see if any can be recommended for the MJR7. Past experience suggests there can be considerable difference between the same type from different manufacturers.

I have added a page of links to interesting websites, including a few related to audio and electronics plus some other topics, from physics to food and drink.

The original plan when I set up this new website was to add some products for sale, maybe a few different kits, some hard to find transistor types and so on. I was expecting to 'retire' a few years early, so I would have lots of free time, and for financial reasons needed to be at least nominally self-employed. That may happen sooner or later anyway, but for now everything is held up by problems selling my apartment, the local housing market is slow or stopped. At some point I may copy the new website content onto the free Angelfire site so that there is some chance of it continuing to exist indefinitely.
Apart from that, no news. It's summer and I rarely do much electronics when the weather is good.

I have probably already written more than enough about amplifier design in general, and far too much about slew rate, but I was playing around with a simple simulation and found some interesting results which I had previously suspected but never checked, so just one more article, then I promise to never mention slew rate again. The point, if there is one, is to compare the relative importance of slew-rate and gain-bandwidth for the accurate amplification of transients. I already knew the answer, but I was still surprised at how little difference a higher slew-rate limit makes.
As soon as we introduce a band-limited input signal these considerations become entirely unimportant, and the accurate amplification of audio frequency transients is determined by the phase linearity in the audio range, which is why I showed the phase response from 1kHz to 20kHz for my MJR7 design, but rarely mention its slew rate limit. The article also shows that the low-pass filter used in the MJR7 is practically the only effect on step or square wave inputs. Anyway, here is Slew Rate Part 2.

I still have a page of 'untried and abandoned' designs on the old website, and having accumulated a few more I have included two of these here on a new page Mosfet Designs.. As before, although they may be of some interest and could possibly be made to work well enough with further development, these have been rejected for good reasons, and are not recommended in their present form. A few more examples may be added eventually.

I had a few enquiries whether I was going to make boards available for the phono pre-amp, and I did consider this possibility, but I have no great enthusiasm for making boards, and there are anyway board makers willing to make small quantities at a low cost from gif files similar to those I give, for example this one found on diyAudio. I think I would probably want to charge more if I made them myself.

There is another reason to be reluctant to sell boards or kits, which is that I only made one pre-amp for my own use, and I have no feedback from anyone trying the circuit. Anyone with sufficient test equipment and the knowledge to track down and solve problems will probably be able to make their own boards anyway, so I don't want to encourage less experienced constructors to make this circuit until I am more certain of its repeatable performance. It took until the Mk3 version of the MJR7 before I had enough feedback from constructors to persuade me that it had developed into a reliable and repeatable product, and I made a few boards. Even then I didn't promote it to any great extent, and suggested it was not suitable as a beginner's project.

Well, I still have no bright ideas for another electronics project. I have been working on an addition for my physics section, but that also is maybe going nowhere. I just found a musical link mentioning both the Higgs boson and Miley Cyrus, I'm not sure how they are connected, it's Higgs Boson Blues by Nick Cave. The sound quality is not great. It somehow reminded me of the Britney Spears' Guide to Semiconductor Physics which is actually a serious physics site. Also, I have been listening to 'Anywhere I Lay My Head', which is Scarlett Johansson singing Tom Waits songs, made even more remarkable by the appearance of David Bowie as a backing singer on some tracks, including Fannin Street.

Components for the MJR7 continues to be a problem, the vertical mosfets are still widely available, but very expensive in some parts of the world, with an inevitable consequence that fakes are also being sold.

My website provider makes available many statistics, for example the number of pages downloaded for different countries, and the most popular files. The top country as expected is USA, followed by UK and France, but with occasional surprises, at one time I was popular in Finland. The top links to my site include a few of the audio forums including, audiokarma and diyaudio. The top file is currently the phono pre-amp page, but there is also some interest in the distortion testing files. The pdf document listed there was written 35 years ago, when I was a student and a relative beginner, so there are some things I would now do differently, but I don't think there is anything seriously wrong in that original version. The unity gain inverting amplifier used for some measurements could easily be improved, but was good enough for most applications back then.

I have been taking a break from electronics for a while. The signal generator designs I was experimenting with work well enough, but nothing exceptional, and I may try one further idea some time. My other great interest is physics, but I have too limited mathematical ability to make any worthwhile contribution to that subject, and just struggle to understand some of the current theories. This week I was reading about black hole 'information loss', and the firewall theory.

I have decided on a few practical circuits for my signal generator project. They are just interesting ideas I want to try rather than anything likely to have exceptional performance. For anyone wanting to find some better designs a good place to look is a diyAudio discussion, Low-distortion Audio-range Oscillator, now up to 83 pages and with lots of useful links. My own first effort using a twin-T oscillator was somewhat discouraging, but did show that the simple light bulb method of level stabilisation can still achieve low 3rd harmonic distortion, better than -120dB. The control loop adjustment was far too critical however.

I am starting work on my signal generator project, but it may be some time before I have anything to report. I have moved an earlier section from this page to a new Signal Generator Design, Part 2 page. So far it just includes a few design ideas, not anything final. I need to order a few parts for some initial experiments. My design aims include low cost and simplicity, not necessarily the ultimate low distortion, I will be happy with anything under -120dB. There are plenty of excellent published designs, including some with distortion under -140dB. Some of the best use Silonex optocouplers, such as the Silonex NSL-32SR3, available from Farnell (UK), so I will also order one of those to try.
(I checked the Silonex data sheet, and found that although based in Montreal they also have an address on Princes Street, Ulverston, in the English Lake District. I was there just a few weeks ago with my family, walking down Princes Street from the train station. Ulverston is most famous as the birthplace of Stan Laurel. I didn't notice Silonex, but we did find the statues of Laurel and Hardy outside the Coronation Hall theatre.)

There has been occasional disbelief that such a simple power amplifier circuit as the MJR7 could have very low distortion figures, and maybe my unconventional distortion measuring technique using signal nulling is partly to blame, so I am pleased to have been given a link to a page of measurements by Forr of the latest Mk5 version using more conventional test methods, and I have added a link at the end of my 'test results' page. The tests include inductive and capacitive loads, revealing that there is no serious effect on distortion levels. I was surprised to see the test with a 16.8uF load, I never tried more than 4.4uF and had expected instability with higher values. Checking a simulation I find that the feedback loop phase shift does then go well past 180 deg. but the loop still has gain far enough above unity to remain at least conditionally stable.
Other tests include supply rejection, which again I am pleased to find are in agreement with my own observations. Many thanks to Forr for some impressive work.

I have added a few updates and new sections.

There are various design notes already scattered among the various MJR7 pages, but I have collected a lot of this onto one page, MJR7-Mk5 Design Notes which summarises the design features and its advantages.

I added a few diagrams to the end of the Capacitor Distortion page. They really add nothing new, but may help dispel unnecessary concern about choice of input coupling capacitors. My recommendation was, and remains, to use a low leakage type with small physical size to minimise interference pickup.

I continue to add and rewrite sections on the Assorted Items page. I use that page for more doubtful items with in some cases too much personal opinion, and 'facts' I am less certain about.

The only project I have been thinking about recently is a design for a low distortion signal generator. The one I use at present has about 0.007% distortion at 20kHz, and I made it around 1982. Even back then there were plenty of better designs around, the best I was aware of was published as 'Spot-frequency distortion meter', by John Linsley Hood, Wireless World, July 1979, pp.62-66, with distortion 0.00015% at 1kHz. This used the R24 glass encapsulated low power NTC thermistor for level stabilisation, and these are practically unobtainable now. An important specification is the 'dissipation factor' which is 0.02mW/deg.C for the R24. Available types such as the Epcos G540 series are 0.4mW/deg.C and so need to be operated at much higher power dissipation. Anyway, I never tried thermistor control so I probably don't understand all the problems and design requirements. My own design used a jfet for level control and switched ranges covering 10Hz to 100kHz, sinewave and squarewave. A more or less similar circuit was published by Bob Cordell in 1981, which I unfortunately had not seen, otherwise I would have realised my choice of op-amp and jfet was far from the best even then. I have added a page with some initial ideas.

I have updated and rewritten a few pages. One addition is to the MJR7 Constructor's Page immediately after my own version near the end of the page is a very impressive version of the Mk5 using a double-sided board and a highly original layout. My own design looks a little untidy in comparison, but the single-sided board should be easier to make for less experience constructors.

I have added a page showing my efforts to improve my Technics CD player, 'Technics SL-PG390 Mods'. None of the changes I tried produced any obvious measurable improvement, but at least my experiences may be a useful guide to what not to do. I was anyway already happy with the sound quality, so I will give up on any further attempts at improvement for now and just enjoy the music.

I originally found that the 1kHz at -60dB test track spectrum had higher components at the 50Hz supply frequency and its harmonics than before the modifications, so I thought I had made this worse, but what I forgot to check is the effect of reversing the two pin power connector, and having now checked this I find that it does make a difference to the measurement, and connected one way it gives results almost identical to that before the mods, so it may be that I had the connector reversed between the two measurements, so I am happy to believe my efforts really did no harm. The 100Hz component, which may come from the full-wave rectified supply rather than from the transformer field is actually reduced, so maybe the improved supply smoothing did have some benefit. Moving the output section further away from the transformer would almost certainly reduce the 50Hz and 150Hz components.

I now have a Technics SL-PG390 CD player to experiment with. Initial tests show that it is already quite good, but maybe it could benefit from an op-amp upgrade and some attention to supply regulation, and maybe replacement of the muting transistors with a relay. When I have tried a few modifications I will add a page to report my results.

I have also finished my own final version of the MJR7-Mk5 power amplifier, which I am now using in place of an older mosfet power amplifier I made over 30 years ago. I have added a few photos of my own version to the end of the 'Constructor's Page'. This uses a recycled case from the old amplifier, so it looks a little untidy, but works fine.

I have finished the phono-preamp, and it is in a separate screening box and connected to my 'new' pre-amp, which as mentioned earlier is built in an old Cambridge ATAC3 case. I kept the original tone controls apart from replacing the op-amp, there is a bypass switch to disable them but I can hear very little difference when the controls are in the flat position. I tried my old Technics EPC205C-Mk3 cartridge with my Pro-Ject 1 Xpression turntable, expecting the worn stylus to sound bad, but it actually sounds remarkably clear. I previously only used that cartridge with a Thorens TD125 and it may be that slightly different alignment means that a different area of the stylus is now contacting the records, but whatever the explanation it does sound good to me. The Technics cartridge is a low output type, about 0.5 mV/cm/sec, but even so the noise level from the pre-amp is low enough, far below typical record surface noise, so I have no plan to try the active input resistance idea to reduce noise further. The 'rumble filter' appears to be effective, listening on headphones where lack of acoustic cancellation could make rumble a problem I still found it reasonably unobtrusive.

I was thinking of upgrading some of my other signal sources. These are a Marantz CD273SE cd player, a Nakamichi CR-2E cassette recorder and a Denon TU-260L FM tuner. Listening and comparing these the one standing out as most in need of improvement is the Marantz cd player. I also have a Panasonic SL-CT700 portable cd player, and much prefer its sound. Looking for some technical information it appears that the Panasonic uses a MASH multi-stage noise shaping single-bit D/A converter as used in many Technics players. I had just assumed that this was a low cost inferior alternative to the more expensive multi-bit converters as used in the Marantz, but I see even some 'top of the range' players also use single bit technology. It is perhaps natural to assume that 16 bits must be better than 1 bit, but clearly it is not so simple. One point I guess may be important is that single-bit is inherently highly linear, but a 16 bit converter needs accurately trimmed components to achieve the same linearity. In a 25 year old player could it be that some of those 'accurate' components have drifted far enough to cause noticeable effects? Anyway, I will search eBay for one of the later Technics models to compare to the Marantz. There are then various well known 'improvements' to experiment with, for example replacing the output muting transistors with a relay.

I have made one, probably final, change to the phono-preamp, which is to omit the 100k preset offset adjustments for the op-amps. For some unknown reason they had to be set close to one track end to get close to zero output, but removing them entirely there was only about 1mV output. I should maybe investigate this further, one problem I can see is that there could be some interaction via the 5k6 in the 'rumble cancellation' circuit, but anyway I don't need extremely low output dc level so I have now removed the 100k presets from the circuit diagram. I have left them in the layout diagrams, but they should be considered optional, and not recommended. I have replaced the 220R presets with fixed resistors on my own board after first finding the settings for low dc output from the input amplifier section. The presets need to be removed from the board after adjustment before measuring their values, otherwise there may be errors. Parallel pairs of resistors were used to get close to the measured preset values. I doubt whether there would be any significant improvement from replacing the presets, so this also can be regarded as optional.

The phono pre-amp is completed and preliminary testing shows that it is working well, with no signs of instability. My usual distortion measuring methods using test signal nulling are not easily applicable, but distortion testing is not really essential, the distortion will be primarily second and third harmonic, and the high feedback loop gains will ensure it is at a very low level. The RIAA accuracy, as I mentioned earlier, will depend mostly on component accuracy, so testing my own version only shows how accurate my components are, so I just did a check on the relative gains at 100Hz, 1kHz and 10kHz to be sure there are no serious errors. What is easily checked is input overload level, and the peak inputs before clipping are about 800mV at 20kHz, 200mV at 1kHz and 50mV at 100Hz, all of which are very good. Assuming a cartridge with typical output 1mV/cm/sec and referring to the Shure plot of maximum observed recorded velocities the peak input voltages likely to be encountered at the three frequencies are about 55mV, 40mV and 5mV respectively, so there is a good safety margin, particularly with my own low output cartridge. I used a 20k gain setting resistor, and in practice this should ensure sufficient overload margins even for high output cartridges.
The 100k op-amp offset adjustment presets needed to be adjusted close to the track end, which is slightly worrying, but maybe normal. The input stage presets were set for zero outputs from the two input stages, and then measured as 153R and 163R, so I will replace these with fixed resistors. There is really not much more I want to do other than connect it to an amplifier and have a listen. I have added a few photos, and there is a board layout page to help anyone wanting to try this design.

I am in the process of replacing my old pre-amp using a case from an old Cambridge ATAC3, which is similar to the A1, which can often be found for sale 'faulty' on eBay, which is how I got mine. The power amplifier was rather poor, using TO92 case devices driving the power output transistors, and when these turn to smoke they can take a whole chain of other components with them. I am only using the case, the input switching and the volume control, which is the dual-concentric type, which avoids a separate balance control. To avoid the input sockets I have soldered all the input cables direct to the input board. The original transformer was a little noisy so I replaced it with a smaller and lower voltage type, and added the +/-15V regulator shown on the phono-amp page. I will also add a headphone amplifier at some stage, not necessarily the fet circuits I already included on the website which were intended as self-contained amplifiers with active volume controls.

Future plans include updating my FM tuner, this is a Denon TU-260L, again bought 'faulty' on eBay, which just needed a slight adjustment to the detector stage inductor. This has a reasonable VHF tuner (it works well for my own reception conditions anyway) but a rather ordinary filter, detector and stereo decoder. I have some good linear phase 10.7 MHz filters which I used in an old DIY design which worked well apart from a not so good VHF tuner, which used what were then the latest dual-gate mosfets but for unknown reasons, probably instability, had low gain and high noise. A transplant operation could combine the best of both designs. Then again there are some very good old tuners, if I remember correctly Technics and Yamaha were particularly good back in the 1980s, so renovating one of those could be a good option.

I have no plans for power amplifier designs, the MJR7-Mk5 is, I believe, about the best I can do with a single pair of lateral mosfets at 100mA apart from the option of adding feedforward, which I included on the old website as the MJR9 just to show what is possible rather than because it has any serious point. The earlier feedforward output stage published in Electronics World as 'Class-B in a New Class' is maybe worth returning to some day, I have added a few new comments at the start of that page to explain more about how this works.

I have changed the phono pre-amp circuit a little. The first version had some problems including probably a big switch-on thump. The circuit has been simplified, and now the preset pot is used as first stage load. Replacing with a fixed resistor, after adjusting for zero output voltage from the input stage and measuring the value, is possibly a good idea.

I have what may be the final circuit for my RIAA phono pre-amp, and have added it as Phono Pre-amp Circuit. It includes the warning that none of the circuits shown have been built and tested, they are just theoretical designs. I have most of the components, and have started working out a board layout, so all being well it will eventually be built. Beyond stability and overload margins there is probably nothing worth measuring, the RIAA accuracy will depend almost entirely on component tolerances, so if I made an inverse RIAA filter that would have the same level of errors as the pre-amp, and so testing for an overall flat response will not be helpful. This is one example where a simulation result is good enough, an actual measured result would just show how accurate or inaccurate my particular set of components were.

About 15 years ago I checked a few published RIAA phono pre-amp designs for accuracy, and found that only 2 out of 7 had anywhere near the correct equalisation component values. That was possibly an unrepresentative sample, but recently I checked a published 'inverse RIAA' network I wanted to use for testing purposes and again found an error. I also saw a very expensive pre-amp tested by Stereophile with surprising frequency response errors, so this seems to be a recurring problem. The correct equations for one common equalisation network were published in Wireless World in 1969, and with modern simulation techniques it is easy to check for errors.

I need a pre-amp for my own use, and at first I intended to just copy a simple op-amp based circuit, but then I decided to try something more unusual. The ideas I wanted to try are nothing new, they were known at least 35 years ago, but these things get forgotten, rediscovered a few times, and even renamed, so they may not be familiar to everyone. For this reason plus the continuing equalisation errors I thought it worthwhile to add a design theory article. It ended up as 8 parts, a consequence of having a long winter holiday with nothing much else to do. Eventually I will try building and testing a real circuit, but for now it is just Phono Pre-amp Design Theory.

I really want to start adding some new material soon. I am working on an article covering various aspects of RIAA phono pre-amp design. I need a new pre-amp for my own use, so this should eventually lead to a practical design. As always I want to try something slightly unusual rather than just copy one of the many published designs.

I have almost finished rewriting and transferring to the new website. The original plan was to delete the old Angelfire site, but there is still a lot of old information which may be of interest, so I may eventually just give it a new home page with links to those pages not on the new site.
Another consideration is that searching for 'audio amplifier design' on Google lists the Angelfire site at the top of the 1st page, but the new site is just about nowhere. It seems unavoidable to keep both sites for now.

I have been experimenting with Audio DiffMaker, a program which analyses pairs of audio signals and extracts the difference. In Part 2 of my capacitor distortion article I included the 'error' introduced by two different 2u2 input coupling capacitors as a sound file, and said that to me there appeared to be very little difference. Using DiffMaker I compared the two signals, and was surprised to find that the difference signal produced is quite large, so I am not entirely convinced that the result is correct. The measurements of the peak frequency spectrum suggest that the difference is not in frequency response, and the signals don't sound vastly different, so I can only guess that it is the different phase shifts which is responsible, as expected from my simulations of the effect of D/A in Part 1. As I said before, extracting the difference is of limited help, it tells us only that a difference exists, not which is better. The simulations suggested that the 'poorer' capacitor with D/A actually reduced phase errors and transient errors. Listening to the extracted capacitor voltages I think should be the most revealing test if there really are important sonic differences.
Adding resistive losses to a capacitor can reduce the resulting phase shifts compared to an ideal purely reactive component, but in input coupling applications any phase shift is in principle an unwanted effect. Anyway, the reduced error from a 10u type compared to 2u2 suggests that the capacitance value is by far the most important parameter for input coupling.

I started to investigate further, but installing DiffMaker had the unfortunate effect of preventing my spectrum analyser program OscilloMeter from starting. I had to uninstall DiffMaker and reinstall OscilloMeter. I have not looked further into this other than repeating the installation to check that it was not just coincidence.

I have updated the home page, there are now links to articles about distortion measurement and speaker design.

I am continuing to update some older pieces and then transfer them to the new website. Re-reading old material there are always bits I think need improving or clarifying. The output stage protection article has been added and also the original 'feedforward class-B output stage'. That design continues to attract some interest, and it is probably the only really clever and original idea I ever had, so although I think the later mosfet amplifiers are better I don't like to be too discouraging. I have one small improvement I never tried, so maybe someday I will try another variation using a more ordinary circuit with LTP input stage and direct coupled output.

I have added a Capacitor Distortion Part 2 page. The plan was to extract the error added by various input coupling capacitors, but with any of the test signals tried there appeared to be no signifficant difference betwen a polyester and a polypropylene both with value 2u2. A more sensitive test could subtract the two effects to reveal any difference, but trying a 10u non-polar electrolytic gave a big reduction in the signal related voltage across the capacitor, which is what we really want to reduce. My only conclusion was that increasing the capacitor value is far more beneficial than any small difference between dielectrics, unless something unusually bad such as a high-k ceramic is used.

I don't have any immediate plans for either construction projects or articles, but I had a collection of short pieces which never became articles, so I have strung a few together in a 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 some of that wrong.

On a totally different subject, I still have a physics section, with an article about relativity including application to rotating reference frames. I was reminded of this on hearing the announcement from CERN about their apparently faster than light neutrinos. The speed measurement needed accurate distance and time measurements. To measure the time between emission and detection 730km away clocks at those two points must first be accurately synchronised. There are at least two 'correct' ways to do this (and an infinite number of incorrect ways), one is global and the other local as explained at the above rotating frames link. The two methods do not match up exactly, for example locally synchronising a series of clocks round the perimeter of a rotating disc will require a discontinuity at some point. A global method could involve transporting clocks symmetrically outwards from the centre to the perimeter, which avoids the discontinuity, and will match up with clocks synchronised in a non-rotating frame, but gives local errors because the effect of the Coriolis force makes adjacent clocks experience different gravitational potentials during transport from the centre so that they run at different rates. The use of the GPS satellites for timing suggests global synchronisation was used, but then there is a mention of checking with some sort of portable timing device, which I would assume was only valid for local synchronisation, so it is not clear to me how this was done. Anyway, I am sure these sort of things were accounted for, and even if not the resulting error should be far less than the 60nsec discrepancy found. Actual faster than light travel would be far more interesting, it is allowed in current theories for virtual particles, but for real particles it would in principle allow transmission of messages backwards through time, with consequent problems for causality. If a faster than light particle is travelling forward in time in one reference frame then there exist other reference frames in which it travels backwards in time.

I have been trying alternatives to the 2SA1209 and 2SC2911, which are becoming more difficult to buy. The 2SA1381 and 2SC3503 should be good substitutes, and I have bought some of the Fairchild versions, the KSA1381E and KSC3503D. The E gain range is 100 - 200 and the D range is 60 - 120. The higher gain types are no advantage for the cascode stage so the NPN type can be D range. I found that these are in a fully insulated version of the TO-126 case, so there is no visible metal back plate, so the thick lines on my layout diagram used to indicate the 'metal back' should be understood to refer to the plain back surface, with the printing on the front.
I have substituted these types in my own prototype, and so far have found no problems, so after a few more checks these could become the recommended types.

I think there may be a problem with my email service at present, I have had a few emails saying I haven't been heard from for a while, even though I had sent messages recently, so if anyone is having problems getting in touch I apologise. I have replied to all the emails I have received, but clearly some of my replies have gone astray. Checking spam filter settings may be a good idea for anyone having problems.

It's summer holiday time and there will be a short delay before either website is updated. I planned to add some affiliate advertising to the new site to make it self-financing, that is why there were initially large unused spaces at the sides of pages, but now that is abandoned and only the full page version appears now. I also had a plan to write a few articles aimed more at beginners. There were a few problems I remember having difficulty with myself many years ago when first taking an interest in circuit design, so maybe covering that limited range of topics would be more useful than duplicating information already available on many other sites.

I wrote a section about slew rate a while ago, but I decided to replace it with a new article, Slew Rate, to make it a little clearer and include a few diagrams. This is just standard theory, but there are a few points not always covered. I mentioned the effect of increasing input stage current for a conventional degenerated differential input stage, this increases slew rate limit and also reduces distortion at lower levels. I originally guessed that doubling the current would reduce distortion only by a factor of 2, but after more thought revised this to 4, and then did a calculation for one example and got a factor of 7.78, which makes me think this is a more complex question than I first thought. This is relevant to the article on input stage distortion where I compared a few different circuits and concluded that the CFP was the best. I mentioned there that different signal levels would change the relative distortion levels of the different circuits, but I should have mentioned that the stage current would also affect results. There seems no point going through endless variations of input stages and their operating conditions to compare distortion, there are always other conflicting factors of importance such as noise and offset currents.

The limited availability of the transistors specified for the MJR7 could be a problem, so I have been looking at alternatives. The lateral mosfets are available from a number of sources still, and there are a few alternative lateral types which are almost identical to the Renesas types, made by Exicon and Semelab.

The small signal transistors for the MJR7 are a problem. I have plenty of 2SC2240BL and BC560C, but Farnell don't seem to have anything obvious to substitute for the 2SA1209 or 2SC2911. In USA Mouser have the KSA1381E in large quantities at a low price, and these are rated 300V which may be some advantage. (I mentioned in my 'Common-Mode Distortion' page that high voltage transistors could be expected to suffer less from base-width modulation. That was little more than a guess, and searching on Google failed to find confirmation, but I have now seen one comparison of VAS transistors (Groner) where high voltage rating was found to correlate fairly well with low distortion). T5 has higher power dissipation than the others and something in the original TO126 case will be more reliable, maybe with a small heatsink if using much more than a 60V supply.