What’s all this Black Swan stuff, anyhow?

I’m somewhat of a fan of Nassim Nicholas Taleb’s book, “The Black Swan”. To me at least, the book is about the human tendency to tell ourselves stories about reality, and then substitute the stories for what is really there. This idea should be familiar to any student of Zen. Taleb calls it the narrative fallacy, and explores its messy implications in business and finance.

It struck me today that this is how electronic design proceeds, too. We start by telling ourselves a story about how the proposed circuit will work. The electrons will go down here, some of them will go this way, this part will oscillate at 123 megahertz, and so on. We either make it up in our heads, or orchestrate it on a circuit simulator, but in either case we are dealing with a Platonic approximation to the real circuit.

It follows from this that the lab bench is Taleb’s “Platonic fold”, where our narratives collide with the messy reality of what the prototype circuit actually does. This is the origin of the pearl of wisdom attributed to (the sadly late) Bob Pease or someone similar: that a circuit always works, it just doesn’t always do what you expect. Anyone who has done any practical work with electronics knows the brain-wringing feeling of struggling with a circuit built on wrong assumptions in this way. It simply refuses to do what you want, for no reason that you can see, because your reasoning is based on the same faulty assumptions. The best you can hope is that you have the “Aha moment” and come away with your narratives more firmly grounded in reality.

It also follows that by going into production with a circuit that doesn’t work the way you think, you invite it to start doing things that you didn’t expect when it gets out in the field. This can generate Black Swans in exactly the same way as Taleb’s example of running a hedge fund based on invalid mathematical models.

Usually the results are negative and your company simply goes bust, but once in a while you can benefit, as in Bob Pease’s tale of the Philbrick P2 op-amp. This was a groundbreaking product that contained about $5 worth of components, but delivered enough value-added to the customer that it could be sold for the price of a small car. The P2 made the company, even though (according to Pease) nobody in the company actually understood quite how it worked. But in spite of this they managed to produce it consistently and have it work reliably.

What’s more, if this is true then the world of electronics must have its “Fat Tony” characters, rather than being purely the province of “Dr. Johns” as one might expect. (For those unfamiliar with the book, you might like to mentally substitute Thomas Edison for Fat Tony and Nikola Tesla for Dr. John.) They are probably the same people that George Philbrick called lightning empiricists, after the fashion (though before the time, this being the 1950s) of Taleb’s skeptical empiricists. Indeed, Fat Tony would probably have wholeheartedly approved of the above mentioned P2, if he didn’t actually design it.

Anyway, that’s me on the narrative fallacy in electronic design. Next time I’ll write about the normal distribution and power laws. Taleb has his “Great Intellectual Fraud”, and communications theorists have their AWGN – “Additive White Gaussian Noise”. Until then, what are the odds of Bob Pease and Jim Williams dying the same week? I make it about 1 in 9 million, but sadly it happened, as Pease crashed his 1969 VW Beetle on the way home from Williams’ memorial service. Both were legends of analog electronics, and the impact is hard to overstate: it’s as if Jane Goodall and David Attenborough got trampled by the same elephant.

In a twist that Taleb may have found bitterly amusing, Pease had just self-published a book on safe driving, which didn’t sell.

Douglas Self, Jim Williams, and a sunny Saturday morning

Writing this, I was inspired by an article by Jim Williams called “Max Wien, Bill Hewlett and a rainy Sunday afternoon”, which documents his investigation of the Wien bridge oscillator and how to lower its distortion.

1. I’m a fan of Jim Williams, and his crazy cartoons and application notes with names like “Switching Regulators for Poets”.

2. My prototype Blameless power amp was getting good enough that I needed a really low distortion oscillator to test it. Surprisingly, even my 24-bit home studio gear wasn’t good enough: sigma-delta converters generate a lot of ultrasonic noise that inflates the THD figure. And my Twintrak Pro mainly generates smoke.

3. I could not find a Tektronix SG505 or SG5010 for sale at a reasonable price.

4. Neither could I be bothered building the oscillator section of Bob Cordell’s DIY THD analyzer.

5. A search of my kitchen junk cupboard yielded a RA53 thermistor.

6. A Google search of the part number revealed that it’s the magic ingredient for making a really good Wien bridge oscillator. So, using the RA53 and a NE5532 op-amp, it only took about an hour to make an oscillator that ran off a couple of 9v batteries, and measured about 0.007% THD at 10kHz on my analyser. (The remaining THD is probably a combination of ignoring Williams’ Law, thermal modulation in the thermistor, and the dirty mains in our lab.)

7. So, this morning I tested the Blameless using my new low-distortion oscillator. It was clean enough that I could see the “gm-doubling” distortion described by Self when the amp was biased too hot: the first time this effect has ever been reproduced at Conner Labs. 🙂 Optimal bias seemed to be about 8-9mV per side, though it wasn’t clear whether this was just cancelling the oscillator distortion, and the true minimum might be at a higher idle current.

8. The results were really good. The 10kHz, 100W, 4 ohm THD came out around 0.01%. I used the 80kHz low-pass filter, but from inspection of the residual, it wasn’t filtering much: mostly the 200kHz switching noise that our mains is ridden with. At 10kHz, 2W, it was about 0.007%.

9. I cranked it up to 140W and let it get really hot. This only caused about 1mV change in bias, and checking again at 2W, the THD reading and residual looked pretty much the same. Then I rigged up a fan to cool it down again, and that didn’t make much difference either. Yay for those ThermalTrak transistors, then.

10. Renting an Audio Precision test set costs about £600/month for the entry-level one. So, I decided to call it quits at this point. The Blameless is now complete, and it just needs another channel, DC offset protection, and a box. I shall publish the schematics soon.

11. When Jim Williams was done with his oscillators, he cooked some hot dogs. I am ashamed to admit that I ate a McDonalds.

12. Now I am obsessed with trying to make a digitally controlled version of Cordell’s oscillator. 🙂

Blameless first sound! :D

Today, after much testing with various dummy loads, including the dreaded 4 ohm reactive one (which showed up some parasitics that I managed to get rid of) the Blameless was finally plugged into a speaker.

It werks!
It werks!

Attempts to measure the THD have so far failed. They really just show up the limits of my  THD measuring system, which is currently no good for anything except finding gross faults.

For instance, the reading I previously got of 0.05% at 10kHz and 120W. When I took the amp out of circuit and connected the analyser straight to the oscillator, the THD reading increased to 0.09%.

The THD analyser does show up crossover spikes, though, if the output stage is underbiased. They were pretty much invisible by a bias voltage of 10mV per side (20mV total) which corresponded to 200mA total idle current. I set it to 13, which gives the 26mV total that some experts recommend.

Anyway, it’s working, and experimenter expectancy notwithstanding, not to mention lack of one channel, I swear it sounds better than my old MOSFET amp. Maybe there is something in Douglas Self’s claims of poor crossover distortion from MOSFETs. Once I get the other channel built and the system put together, I will make that low-distortion oscillator and do a THD shootout. Or an ABX test or something. Anyone want to lend me an Audio Precision test set? 🙂

More Blameless progress

The Blameless project is grinding on!


4-layer boards for the output stages were designed in Eagle and ordered from PCB Train. Some samples of the ONSemi NJL4281/4302 transistors with built-in thermal sensing diodes were obtained. The whole lot was fitted to a large heatsink using Sil-Pad A1500 high performance thermal pad stuff.

After testing using a bench power supply, it was connected to a large transformer, rectifier and some capacitors.

The power was turned on and amazingly it failed to explode.

More detailed info to come, but the maximum output is about 120-150W into 4 ohms, the THD about 0.05% or less at 10kHz and 120W (so should be nearer 0.005% at 1kHz) and the short circuit protection, thermal compensation etc. all works as planned.

First THD analyser results!

I’ve finally got the THD analyser hooked up and working! Not very well, though, because I have to use it with my not-too-hi-fi signal generator, on account of the analyser’s own oscillator section being AWOL. My sig gen is DDS-based, so it puts out lots of high-frequency crud and DAC quantization errors, and these overwhelm the amp’s own contribution to the residual. Except if I test at 10kHz and press the analyser’s low-pass filter button, which kind of fixes it…

Anyway, I hooked the Blameless up to an unregulated power supply to pump in plenty of hum and grunge (got to test that ripple rejection too!) and made some THD + Noise measurements.

THD test setupTHD at 50W50W residual

10kHz, 50W into 4 ohms: 0.086%

10kHz, 2W into 4 ohms: 0.037%

(I measured at 10kHz to try and force the amp to generate more noticeable THD levels. And yes I have the hi-pass button pressed: some hum is getting in somewhere…)

I also tried setting the bias pot to minimise THD.  At 50W, this happened at a setting so cold that there was barely any bias at all! I measured a Vq of around 300uV. But at 2W, the minimum occurred at a Vq (across each emitter resistor) of about 14mV.

2W THD, underbiased2W THD, bias just right2W overbiased

I think what’s happening is that at high power and high frequency, an overly cold bias helps to counteract the transistors’ slow turnoff. Too cold bias effectively starts turning them off in advance. This gives a false THD null. 2W seems to be a better power level for setting it.

At both power levels the THD nulls were very broad, and seemed to stay stable when I let the heatsink get burning hot, and then applied a fan to cool it back down.

Still a long way to go in terms of refining the THD measuring setup… but it’s a start!

Blameless short circuit protection

So, now the short-circuit protection is tested.

I used a dual-slope VI limiter as described by Self in his book, except I simulated it in LTSpice and played with the component values to lower the power dissipation a little. Self’s original design allowed the transistors to dissipate nearly their full rated 250W, and I thought that was excessive, since it’s only possible at a case temperature of 25’C, and that will never happen in practice.

I guess his reasoning is that since the amp will only amplify AC signals, then under short-circuit conditions each transistor will conduct with a duty cycle of 50%, so the mean dissipation will only be 125W. But I can imagine situations where that wouldn’t work.I also plan to try the NJL4281/NJL4302 transistors in the future, and these have less SOA than the MJ15024/MJ15025, the devices that Self designed the circuit for.

My new values were supposed to make the circuit limit at about 125W. Anyway, so I made the circuit up and tested it with the method described on Rod Elliot’s site. Namely, I shorted the amp’s output with a 0.1 ohm resistor, and fed 100us pulses at a repetition rate of 10Hz to the input. I did this with the amp running off two regulated supplies, allowing me to vary the rail voltage and note the current for each voltage.

At first, the negative rail had no limiting at all! It started out at 12A and headed skyward from there. It turned out that I put a diode in backwards, and also the gain of the PNP limiter transistor was low, and the VAS current limit was a little high. Once I got that fixed, I plotted out the two sets of results in Excel, and added loadlines for reactive and resistive loads on 40V rails.

Protection locus

So you can see that with one pair of output transistors installed, we can just barely drive a 4 ohm resistive load or an 8 ohm reactive one. To drive a 4 ohm reactive load, we’d need two pairs, which is what I was expecting, and two pairs is what I plan to fit.

Finally as a sanity check I rigged up a reactive load: A big iron cored choke wound with about 80 turns of heavy wire. I put two 4.7 ohm resistors in series with it, and it could drive that easily at any frequency. Go down to one 4.7 ohm resistor, and I found a frequency where the limiter would activate and cause crazy clipping, like in Rod Elliot’s Figure 4 linked above. Again this agrees with what I expected, so we’re good to continue!

Note that before trying this test, I added the catch diodes from the speaker output back to the rails. Otherwise the output devices would be destroyed when the limiter kicked in.

My Blameless is working!

I’m so happy! Ever since I was a humble EE student, I’ve wanted to design my own hi-fi power amp based on Douglas Self’s “Blameless” philosophy. I now proudly present the prototype.

doesn’t look goodbut seems to work well so far

I’ve built power amps from other people’s designs before, but this is the first one I’ve designed, albeit with a lot of help from Self’s “Power Amplifier Design Handbook.” It’s a modular system, with a driver board that can be hooked up to any kind of output stage, to make different kinds of experimental amps.

It’s still not finished: the protection circuitry and THD need testing. But it’s passed the first hurdle, in that it can run with a good DC offset (I measured 16mV), stand +/-60V rails and drive a load without blowing up.

The last three amps that I’ve built were powered by valves (tubes?), and the two before that had MOSFET output stages, so working purely with BJTs was a bit of a culture shock. Self always argued that they were the best amplifying devices, and they certainly seem pretty good. The OnSemi MJ15024/MJ15025 pair of transistors I used in the prototype cost a few dollars each, less than half the price of equivalent MOSFETs, and they make as much Umph as a pair of KT88s. They didn’t want to oscillate or explode, and the whole thing generally just worked first time. Apart from that evening I slipped with the scope probe and took out half a dozen trannies in the driver board.

This is something of a multicultural project. The output trannies were made by Motorola in Mexico, all of the other ones came from Continental Device in India (that’s what you get when you buy Farnell’s “Multicomp” value brand transistors) and the whole mess was assembled by a Scotsman wired on Fairtrade coffee beans.

And yes, Self convinced me to buy a distortion analyzer. So far all it’s told me is that I need to get a better signal generator.

To EQ or not to EQ, that is the Q

If you’re a follower of hi-fi trends, you might have noticed that tone controls don’t seem to be cool any more. High-end amplifiers have become very minimal, with only a volume control and power switch.

Well, there’s high end and high end. Richard Burwen’s system would certainly qualify as high-end by almost any definition, if only because of its 20,000 watts of amplification, 169 speakers, and 34 channels of active crossover and EQ, which Burwen claims to have spent a year adjusting by ear for a flat overall frequency response. In other words, the very opposite of a minimal system.

Moving on to my own hi-fi system, which has 60 watts of amplification, 2 speakers, and no tone controls or EQ whatsoever, and has been plagued by annoying room modes. I’ve tried several different speakers, but the bass on all of them just sounded terrible in there.

Recently, I realised that the fundamental problem is that my living room has the two large opposing walls made of solid brick. These two reflective surfaces allow a standing wave to develop between them, and the result is a highly resonant bass boost of about 9dB at 60Hz. I fed the measurements of the room into an online room mode calculator, and it agrees that I should get terrible bass.

So, what to do about it? The minimal solution would be to damp the resonance by installing bass traps. This would be a major carpentry project, though, and good bass traps have to be physically large, so I would lose space in the room. And, I hate working with rockwool, it makes me itch all over.

So, like Richard Burwen, I decided to install an EQ, and “tune by ear for flat frequency response”. My first attempt was with an Alesis PEQ-450, which is a 10-band digital parametric EQ. It only took about 5 minutes to find the offending frequency and notch it out, and I was amazed by the improvement. I found myself getting out those old hip-hop and drum’n’bass CDs that had just sounded offensive on the system before.

However, I wasn’t too happy with the sound quality of the PEQ-450. Maybe I was imagining it, but I felt that it grunged up the treble somewhat. It was also too big and I had nowhere to install it. I ended up buying two (they’re mono) Presonus EQ3Bs on Ebay, and again, tuned them by ear for best bass. I could have gone digital with a Behringer DEQ2496, but in the end, I decided that the simpler solution would be better.

So now, I find myself in the situation of committing audio sacrilege (tone controls are bad! So EQ must be worse!) in order to get a major improvement in the performance of my audio system. Mmm, sacred cowburger.


The EQ3Bs in place

The system

The system. The graffiti paintings are by my brother, and help to break up standing waves too. 🙂


No, it’s not some sort of futuristic android sex change.

I’ve lived happily with the Crown SXA for about a year now, and by and large, it’s been a pleasure. It sounds great, has more than enough power for me, and now winter is coming, I can warm my feet on it!

My main worry, though, was always the power transformers. Not only are they something like 50 years old, but they were never designed to handle 50Hz power, which is what we have in the UK. So, even with RG Keen’s Vintage Voltage adaptor installed inside the chassis, they hummed really loudly, got really hot, and gave off worrying smells.

My first port of call was Sowter Transformers, a custom winding company in Ipswich. I sent them the dimensions of the original trannies, and got the reply: “We don’t do metric sized transformers”. What gives?! They were made in Indiana in 1960. How can they possibly be metric? But none of Sowter’s standard core sizes were even close.

So I thought, maybe “metric” just means “Not British”. A quick peek in the Hammond catalogue (sorry, catalog!) and sure enough, there were several transformers of the right size. I settled on the 290KX, which is Hammond’s replacement for the Marshall JCM900 guitar amp, and Bluebell Audio in Dundee supplied me with a pair.

After purchasing some end bells from TAD and some M4 threaded rod from “boltmeup”‘s Ebay store, it was time to pull the poor Crown apart!


This took most of the day. The new trannies had lugs sticking out of their bobbins, and needed some trimming to get them through the chassis holes. “It’s just like trimming a toenail”, as Philip from Bluebell told me, but much more expensive if you get it wrong!

New vs. old

After much fiddling, rewiring the rectifier to a bridge, wiring one of the transformers up backwards (thank goodness for the old light bulb limiter trick!) and pulling out the redundant Vintage Voltage unit, she was good to go!


The bad news is, the new trannies still hum a bit. They’re quieter than the old ones, but not silent. They also still run fairly hot. The good news is, they don’t smell!