Author Archives: admin

33 Negative Resistance Part 3

33 Negative Resistance Part 3 in which I realize that we need to distinguish between the negative resistance of a component and the resistance of a circuit. Maybe the solution to the tetrode oscillator problem was easier then it first looked. I also expose (but do not solve) a mistake I have made.

Last time I showed that the tetrode negative resistance oscillator, that would not work from a 90 volt supply with a dropping resistor, would work ok with a low impedance 45 volt supply. See earlier posts.

Later I realized that it had not been quite correct to say that the oscillator would not work with a 90 volt supply and a dropping resistor. In fact the originator of the circuit had been quite wrong when he complained that it would not work. It would work all right, it just would not start! This can be shown by starting it with a low impedance supply and letting it continue to run with the dropping resistor.

Cubic_osc_arse_kick_circuitThis is what I call my “Kick in the Arse” circuit. It starts off with the switch closed. This provides a low impedance 45 volt supply to establish 45 volts on the 2u cap C2. The oscillator starts. Then the switch opens, and the oscillator continues to operate perfectly well with what amounts to the original circuit!

In fact it would have been much more easy than this to provide the required “starting kick”. Consider this circuit:
Of course, there would have had to be a power switch, or probably two power switches, as it would have been necessary to heat the cathode before applying the starting kick. Again, (in simulation) the oscillator starts and runs.

We might wonder if the simulation model is too “ideal”. A real 90 volt battery would have some series resistance. It might also have properties that dictate that it is not good practice to create large transient currents by placing a microfarad directly across it. I have tried placing a resistor in series with the supply. This resistance can be as high as 1k and the oscillator will still start. You can regard this 1k as modelling the battery intrinsic series resistance, or as an imposed surge current limiting resistor, or you can share the 1k amongst these concepts. It all depends on your line of thinking.

To further drive home the distinction between the negative resistance of a component and of the circuit as a whole, I set out to check the power supply input characteristics of this circuit. First, I tested my oscillator circuit model, and determined that it would start and run with a supply voltage range that exceeds 25 to 50 volts.

Then I set up a model to see how the supply current varied with supply voltage over this range.

The current source and the capacitor C2 provide a voltage ramp. The voltage controlled voltage source E1 follows that voltage and provides current that will not interfere with the current in C2. The resistor R1 has been included to allow C2 to present the lowest impedance shunt path for the oscillator signal. This enabled us to plot the output current of E1 with minimal high frequency ripple.

Let us limbo dance under the barrier to high frequencies presented by the capacitor.

I have relabelled the x axis to show the variable supply voltage, instead of the time, which was the true independent variable in the simulation. The red line is the curve generated by the simulation. The “spike” at the left side, is, I believe an artefact of my start-up transient. Indeed, although I cannot slow down the whole sweep very much, as the simulator is generating data for every cycle of the oscillator, and attempts to run the sweep very slowly lead to the generation of files that are too large for LTspice to handle, I can do a slowed down simulation of just the first couple of milliseconds of the sweep. If I reduce the sweep rate, the height of that initial current spike is also reduced.

The green line is a tangent that I have added by hand to determine the dynamic resistance of the oscillator as a load on the supply. The blue line is the load line for a 90 volt, 20k supply. It is evident that the operating point is completely stable. Note that the operating point is not at exactly 45 volts, but about 43 volts. That is not skin off anybody’s nose.

The ‘split capacitor circuit that I showed above, (repeated here to save you looking back)

exhibited a characteristic for the first 100 μs like this:

The brown trace is the tetrode anode, and the blue trace is the junction of the two 2u capacitors. It occurred to me that if we run that blue plot for a longer time, we should see it sink to about 43 volts, the stable “operating point” that we determined with the load line above. I did the simulation, and this is what I got:
Split capacitor quiescent point

You can see that the quiescent point for the junction of the two 2u capacitors is about 45.5 volts. I cannot see how this can be different from the operating point we found with the load line (above). Can you?

32 Negative Resistance Part 2

Dear reader,
If you were interested in my first posting on negative Resistance, then I must apologize for such a long delay before I return to the subject. Pressure of other things.

In the first posting, I resorted to an old trick of offering a packet of Smarties as a prize for the best answer to a question that had been put to the readers of Wireless World in April in 1939. I suppose that date puts things in perspective and makes my delay of a few weeks in returning to this look pretty minor.

You might be wondering where this Smarties business comes from, and what place it has in this serious blog. It all started when I was to address an Historical Society on historical railway matters. I was warned that I might have trouble holding the audience attention. Thus alerted, I planned out several tricks to stimulate audience involvement. Of these, the handing out of little packets of Smarties as prizes for correct answers to questions proved to be the most effective. It is amazing how competitive a room full of senior citizens can be!

So, having brought the joke into this forum, it falls to me to “pay up”. Packets of Smarties have been sent to Brian Magee and James Fenech.

I had gone into this a bit right after the first posting on the matter, and now I come back to my notes, I find that this process seems to be an interesting bit of industrial archaeology in itself. To model what was going on in the Wireless World Circuit (See my earlier posting “”), I chose to use a cubic to provide me with an anode characteristic that had the essential features of the tetrode described. I scratched around with some algebra to work out the equation for a cubic that would seem to pass through the key points. I ended up with:

I = 0.000134 * (0.678E-3 * v^3 – 0.884E-1 * v^2 + 2.9 * v)

The non canonical form of this is a product of the way I derived it. I did not attempt to simplify the presentation of the polynomial, as I could rely on the simulator to multiply out my coefficients at run time.

Here is the tetrode circuit and characteristic as published all those years ago. I have added the load line for the 20k dropper resistor.
Reas circuit 1

Here is the result of the simulation:

Not the same, but near enough to explore the key points.

Here is the simulation circuit:
Simulated Rae Circuit

Notice that I have set up my “curve tracer” by offering the cubic response generator with a voltage ramp, which I created by providing a constant current to capacitor C1. This is scaled so that the voltage rises one volt every second. This means that a time domain plot with a time scale marked out in seconds can be read as if the horizontal scale is a voltage scale. The current B1 is the tetrode anode current, and current B2 is for drawing the load line.

The above simulation just showed how my arbitrary function generator loaded with a cubic represented the key features of the tetrode plate characteristic. Then I put that tetrode in the circuit.

You can see that the voltage rises to the first crossing point of the anode characteristic and the load line (round about 17.38 volts).

On the other hand, if we power the anode circuit from a low impedance supply at 45 volts, we might get the successful oscillator circuit that was originally wanted.

If we run this, we get the Anode Voltage coming out like this:

Which is what was wanted in the first place.

More on this in another post later.

31 Cathode Ray Oscilloscope

In 1965, when I was in Matric (we used to call it 6th form then: both designations that have been replaced) I gave a talk to the physics class on how a radio receiver works. The Physics teacher gave me a very old CRO tube as payment. It has been lovely to have all these years, but I have nowhere to display it, and I have to reduce my stuff.

This post is a call to readers for help in finding a good home for it. Quite apart from historical interest, this tube is made in a way that makes all the inner workings clear. Much more so than with what we would have called a “modern one” before oscilloscopes went over to liquid crystal display. It is what we would have called a “five inch” screen, and the tube is about 410 mm long.IMG_0511bis

This is what it looks like. The terminals for the deflection plates are brought straight out through the tube wall and have caps the size of the anode caps on an 807.


The operation of the deflection plates is easily explained when the form of them is a clear as this!


Not as if it is from an obscure manufacturer! The only designation on it is hand written.


I have conducted various searches for the identity of this tube but to no good effect. When it was presented to me, the tube had been wired up by another student in a circuit spread out on a sheet of plywood. It did work then.

Anyone got a good idea of where I could find a good home for this?


30 Negative Resistance

I remember that when I was a youngster, my grandmother commented that “they” were saying that transistors would take over from valves. I reported that I had read in the magazine “Radio and Hobbies” that the transistor was predicted to be taken over by a new device called the “Tunnel Diode”. The tunnel diode dates from 1958, and was in production in 1960. It earned its stripes as an active device, even though it had only two leads, by having a “negative resistance” region in its voltage/current characteristic.

Tunnel Diode

Exploiting or avoiding negative resistance regions had become well established in valve (vacuum tube) days. I had read many explanations of the history of growth of the number of grids in the thermionic valve. The explanations (or was it my youthful, impatient eye) seemed to gloss over the number two. We went from triodes to pentodes, with a very scanty look at tetrodes. There was mention of secondary emission and negative resistance with tetrodes, but these notions were quickly glossed over.

The Radiotron Designer’s Handbook (mine is 4th edition; 1955 but this matter might not have been revised since the first edition in 1934.) mentions secondary emission from the anode in a tetrode (pp7) but in that section does not mention that this can give rise to negative impedance at the anode. In the chapter on oscillators, there is mention of a “Negative transconductance oscillator”, but the design described does not utilize the negative impedance of the anode in a tetrode. (The Radiotron Designer’s Handbook might not be considered children’s reading, but nevertheless, I wish the Father Christmas had been on to it in the early ’60s.)

I remember one construction article in which tetrode characteristics were wanted, and this was achieved by selecting a pentode in which the suppressor grid was connected to a separate pin, rather than connected internally to the cathode. Youngsters who are not familiar with this talk and are interested might like to check the Wikipedia article ( on this which is mostly good stuff, and very little piffle.

I remember a discussion amongst juvenile philosophers at a railway volunteer work party in which we discussed negative resistance, but dismissed it as impossible as it implied that the device was a source of energy. We had not learned to distinguish between E/I and dv/di.

Negative resistance characteristic of tetrodes was exploited in trigger circuits, which could be configured to “snap” between stable states if set up so that the negative resistance region imposed an “S” bend over the load line.

In his book “Time Bases” (1943) Puckle gives several examples of peculiar bias arrangements of tetrodes to obtain a characteristic curve with a negative resistance region in it. The earliest citation for a work describing ways of obtaining negative resistance was from 1935. The motivation in those days was the ability to build a trigger circuit with only one valve. There were many two valve trigger circuits in those days: one of course being the well known one by Schmitt which used two triodes. Schmitt’s trigger had particular features that distinguished it from the several alternatives available to the designer in those days. These features are mostly absent from the arrangements of positive feedback around a comparator or op-amp that is commonly called a Schmitt Trigger today.

The motivation to “use only one valve” must have been very strong in the days when a valve cost about £1/-/- and the average weekly wage was about £20/-/-. This would put its cost in today’s (2014, Australia) money at about $29.00.

One circuit used the MS4 tetrode.

MS4 Valve

This MS4 Valve picture is from the National Valve Museum This motivation to use tetrodes in this way was overcome by the introduction of integrated circuits, although we didn’t use that term then. The trick was to put two triodes in one bottle. A Schmitt Trigger could then be built using “one valve”.

Schmitts Trigger

Two triodes in one bottle. Enabled a Schmitt’s trigger to be built with “one valve” and killed the tetrode “negative resistance” trigger.


As an aside, in modern circuitry, we could be justified in calling this:

Transistor Schmitt trigger

a Schmitt Trigger, but not really this:

Not Schmitts Trigger

In spite of the fact that this circuit comes from the Wikipedia page for “Schmitt Trigger”, it owes nothing to Scmitt’s circuit. It is a lost cause, but it would have been better if such a circuit were called an “hysteretic trigger’ or just a “trigger”. (Sigh!)

Note that the transistor circuit (above) seems to have been derived from Schmitt’s two triode circuit without much thought. It will generally be found that the VCE(SAT) of the first transistor is less than the VBE of the second. R1 and R2 are thus both unnecessary. Replace R1 with a short, and R2 with an open circuit.

This negative resistance business is important in modern electronics engineering. I gave an example in my post number 14 “Is a skim across the top worse than no analysis at all?” and number 15 “Load Line” (both October 2013). Another example arises in the use of a resistor for “soft start” of a switched mode supply. I might treat this in another post. I will finish this post with a last blast from the past.

For a recent post, I was looking up M. G. Scroggie (“Cathode Ray”)

and I came across this delightful conundrum.

Henry Farrad 1Henry Farrad 2Henry Farrad 3

I will leave this hanging in the air just for now. I will give my explanation for Mr Lea’s problem next post. In the meantime, I offer a packet of Smarties for the best reader’s solution.

29 I did the Test Question – and Failed!

I mentioned in my last post that M.G. Scroggie, writing under the pseudonym “Cathode Ray” wrote reminiscences of years of interviewing in an article in “Wireless World”. Many “Cathode Ray” articles can be found at the site, but not, as far as I can tell, this particular one.

Like me, Scroggie found that the simplest questions can be useful for distinguishing between candidates on the most subtle points. He had a favourite question. He would present the candidate with this circuit:

Scroggie Circuit

His question was “What is the Voltage Gain of this circuit?”

Nearly all candidates would have a crack at it and write:


Voltage Gain = ———–


Scroggie would reply: “No. That is not what I want.”

The candidate would then try complicating the matter in all sorts of ways. They would offer a more complicated expression that took into account the finite gain of the op-amp. They would introduce the op-amp dominant pole frequency and derive an equation that was an expression of frequency.

To all these efforts, Scroggie would say “No”.

In the end he had to tell them what he was after: a minus sign!

If the circuit is inverting, then the voltage gain is a negative number. Scroggie was a stickler for details such as this, and I learned several rules from him for conventions that can help me from making errors by such means as getting the sign of an expression wrong.

That Scroggie article appeared many years ago, but I have never forgotten the lesson. Thus when James posed his question, which I repeat here:

“Design a one transistor amplifier with a gain of three.

 – 9V supply rail.
– 5k drive impedance to drive YOUR amplifier.

 – 22k load impedance driven from YOUR amplifier.

 – 20-20kHz operation.

 – gain of 3.

 – AC coupling required.

 – Output voltage of 1Vp-p.

 – 1 transistor only.”

“This is reasonably easy,” he wrote, “but requires getting a lot of things in line.”

I was alerted to possible complications when I read the “requires a lot of things in line” bit.

I interpreted this as a potentially tricky question because the required gain is a positive number. This indicates that the amplifier is to be non-inverting. The alternative interpretation, that James (like Scroggie’s candidates) had simply ignored the sign, seemed less likely in the face of those warning words. So I had a crack at it. Here is my effort.

Gain  of 3 page 1

Gain of 3 page 2

Gain of 3 page 3

Gain of 3 page 4

gain of 3 page 5

Gain of 3 page 6

Gain of 3 page 7

Now, first of all, I will mark my own work. What you see above is what I was able to do in examination conditions, although I have written it out again more neatly for you.

In the hand written text above, I have used the term “Transresistance” which is WRONG! What I meant was “Reciprocal of Transconductance” which is not the same thing!

I realized later that I could reduce the collector current, and consequently the volt drop in the collector load resistor just by increasing the value of the emitter load resistor. Indeed, after I had put it up on the simulator, I did increase the emitter load to 9k1, and the small signal response did not change at all. There would have been a little more headroom without transistor saturation, and although I have not even estimated the effect of temperature, the more room to move the circuit has, the more it will be tolerant of changed bias conditions as the VBE changes.

So I sort of had a circuit together in my quick single session with a note pad and a calculator. I was certainly able to make some minor improvements over the next couple of hours, but those hours would not have been available in a job interview test!

How did I do?

My Circuit

Here is the circuit in LTspice before I changed the emitter load resistor.



My circuit No Inversion

It has a gain of 3 with no inversion.



Mycircuit Linear gain

This is not a Bode plot. The vertical axis is linear. ALMOST made a gain of 3! Could quickly tweak this in a real world situation, of course.



My Circuit Bode

Here is a Bode plot showing how well I did at setting the bandwidth limits.

All this is all very well, but it turns out that I took myself (and you) up a wattle, as this was NOT what the examiner wanted. James was not being pedantic about the minus sign!  He wrote to me later to show what he wanted. Here it is:

James (600 x 461)

Oh Well! I guess I failed that test!


28 Interviewing for a Job

Before I get down to the subject in hand, I need to draw your attention to a much improved power cable based hi-fi equipment enhancer. If the placebo effect (see comment from Nigel Machin to last post) works as he says, then this must be much more effective than the item I wrote about last time. Is there any limit to this?

And now, for something completely different.

I recently had a little innocent fun reading blogs that I had been referred to by an employment agency. There was lots of interesting advice for the job applicant. There was not much advice offered for the applicant interviewer/selector. They are both difficult – being an applicant and being a person who must choose between the applicants.

I have done a bit of both over the years, and if I had not been taking the outcome so seriously, I would have found the process of observing the person across the desk from me very interesting. The interest arises from reflecting on the experience later.

There are many aspects of this that do not relate to the technical aspects of the job of being an electronics engineer. The psychology of both roles is interesting. The way both parties give so much more away then they realise is something that can only really be grasped much later, often when the experience of many of these encounters can be brought to bear. I reserve discussion of the non-engineering aspects for another forum, but there are some interesting points relating directly to the question of just what grasp of electronics the candidate has.

I have been the interviewer/selector more times than I have been the candidate, and will share some lines of questioning that I liked to use.

Here are two circuits that I have used many times over the years when interviewing candidates for junior engineer or technician positions. One of the reasons that I stuck with these circuits was that I discovered that after I had used them a number of times, I picked up patterns of response. Once I had calibrated these circuits, the candidates betrayed an awful lot about themselves very quickly. I had been reluctant to publish these in the past, because I did not want to encounter candidates who had swatted up on them. I think that that is unlikely now. Possibly these circuits are a little dated. Perhaps anyone wanting to use circuits such as these as test questions might want to change them a little to suit modern conditions. There is one analogue and one digital.

Analogue Circuit.

Analogue Circuit

I didn’t come to the interview with this circuit printed out: I would sketch it in front of the candidate. Thus the candidate would have the time it takes to draw this freehand to take it in.

My first question would be “What is this?”

This is not the sort of question that has only one answer, but it is a question that gives the candidate plenty of scope to show how she understands what is shown.

I showed this to Ed Cherry when he was still at Monash. He told me that the Monash students did not study the “Concertina” circuit, as if that somehow made it a bit unfair to ask them about it. I reckon that what makes this circuit a really good interview question is that it gives the candidate who has never seen such a thing before a chance to show how she figures it out.

(Concertina circuit: The circuit was also called the “cathodyne” in valve days

My next question would be, “What dc voltages would you expect to see on each of the terminals of the transistor?”

This immediately separated the sheep from the goats. I have had all sorts of weird responses to this question. I have even had a candidate attempting to work this out starting from the collector. I would often be asked about how accurate an answer I needed. I would say “Imagine that this had just been prototyped, and I asked you to check that the dc conditions seemed to be ok. You make measurements, but what do you expect? How do you judge if the measurements indicate a problem or not?

The next matter was small signal performance. I drew a small sine wave on voltage/time axes at the input, and two vacant sets of axes beside the outputs, and asked the candidate to show me what signals, to the same scale, I would expect to see on the outputs.

Analogue Circuit2

This is such a simple circuit, and yet at this point it had shown huge discriminating power amongst the hundred or so candidates that I have put it to over the years. For the candidate who seemed to be finding it easy sailing, I would propose some capacitative load on each output and ask for some indication on an asymptotic (straight line) bode plot of what effect this would have.


I’ll give you a hint that I did not give them. I would like to have seen bode plots representing emitter voltage, collector current and collector voltage in that order.

A Digital Circuit.

Then I would draw a digital circuit. This is what I would draw.


Some people were not familiar with the appearance of a logic symbol with an inversion bubble on the inputs. I always felt that this was a strange sort of naivety. Nevertheless, for those who had never seen such a symbol, here was a chance to think on their feet and show how they could figure it out. This circuit was drawn using a convention that used to be common of linking outputs with inversion bubbles with inputs with inversion bubbles whenever this is possible. This circuit also shows that this is not always possible.

My first question would be, “What is this?”

This time the initial question is one with a single correct one-word answer. To get this right straight away, rated the candidate highly. For everyone else, I would ask, “How would you describe the signal D in terms of the signals A, B, and C?”

Perhaps in the case where the candidate was struggling, I would ask “Can you tell me what

DeMorgan’s Theorem states?”

( )

It always impressed me how much I could learn about a candidate with these two very simple circuits.

I was discussing these with my friend James Fenech, and he mentioned the alternative idea of giving the candidate a prepared test. That can be a good idea too. I have only sat a set test for a job application once. It was a cleverly contrived test with some tricky traps. I fell into a couple of them. James suggested that one could start with line of thinking such as my really simple analogue circuit (above) and set a task such as “Design a one transistor amplifier with a gain of three”. This reminded me of an article that was written in Wireless World by M.G. Scroggie who used to use the nom de plume “Cathode Ray”. He discussed a lifetime of interviewing young engineers and observed how the candidates had changed over the years. He had a pet question about the gain of an op amp. I don’t think that it was supposed to be a trick question, but it turned out to be a bit tricky for the modern candidate.

Was James’ question a “trick” question? To try to clarify this, I asked him for a more detailed specification. He replied:

“If I were setting such a question:

 – 9V supply rail.

 – 5k drive impedance to drive YOUR amplifier.

 – 22k load impedance driven from YOUR amplifier.

 – 20-20kHz operation.

 – gain of 3.

 – AC coupling required.

 – Output voltage of 1Vp-p.

 – 1 transistor only.”

“This is reasonably easy,” he wrote, “but requires getting a lot of things in line.”

I still couldn’t decide whether this is a trick question or not. I had a crack at it. With one interpretation of the requirement, I found that it was only just possible. maybe this is what James meant when he wrote “… requires getting a lot of things in line.”



27 Special Offer – Fetid Dingo’s Kidneys

Here is a “special Offer that I received from audio equipment retailer “Audio Trends” this afternoon, and the email I have just sent them:

Special Offer

Here is the text enlarged so you can read it:

Special Offer text

Hello Audiotrends people,
I have been a recipient of your emailouts since purchasing a Tivoli Radio from you some time ago.
This afternoon, I will be clicking on the “Unsubscribe Instantly” link, but I wanted to write to inform you of why I am doing this.
I am an electronics engineer, and am qualified to make judgements about the credibility of claims for many of your products.
The claims made for the Isotek EV03 Premier Power Lead are so far into the fetid dingo’s kidneys domain, that it would amount to theft if you were to take a gullible customer’s money for this product. I do not wish to be associated with any company who would peddle such stuff.

Richard Schurmann

26 Colour

As you all know, our colour vision works by exploiting three different spectral responses of the cone cells in the retina.

Spectral response of human cones

I found this picture somewhere, and although it gives the general idea, I am not sure how accurate it is. In particular I am not sure that the “colouring in” is right. We generally consider these spectral responses to peak at Red, Green and Blue. Note that the optics guys like to characterize light by its wavelength: not frequency so the hoizontal axis is the other way around from what we would normally expect in electronic engineering spectral work. It looks here (on my screen, anyway) that the S curve peaks in the black, and the L in the yellow. Anyway, we assign Red, Green and Blue to them and this is why we regard these as the “Primary Colours” (Not to be confused with the Cyan, Magenta and Yellow used by printers, or the approximations to them: Red Blue and Yellow used by artists.)

Those of us with a little schooling in how television works sometimes have trouble convincing our fellow TV viewers that there is no yellow light emanating from the television screen: particularly when a vivid yellow image is portrayed. Reference to the above graph might help, with the explanation that what we perceive as yellow is the condition in which the M and L cones are (roughly) equally stimulated. This can happen with narrow band spectral light (sodium vapour), or with a bimodal spectrum with a peak in the green and a peak in the red. I find it nicely intriguing that we cannot tell these apart.

If either of our M cones or our L cones are missing, or perhaps they are both there, but for some reason have identical receive spectra, then we have red/green colour blindness.

There is another phenomenon that arises from the way we generate our perception of yellow by comparing the signal strength of our Green (M) and Red (L) sensing cones.

If we are presented with a spectrally pure red light, we see it as red (or, whatever we see it as, we have come to know that the name for it is red): similarly for spectrally pure green light. The intensity of the light has no bearing on the perceived colour. On the other hand, when we are subjected to light containing both red and green spectral lines, our perceived colour depends on the relative intensity of the two spectral lines.

If the relative sensitivity of the M and L cones varies from person to person, or perhaps the location of the spectral peaks of their sensitivity varies, then those effects will have little or no effect on the colour perception of red or green light, but will directly effect the colour perception of light containing both red and green lines.

My first awareness of this arose when reading the biography of Lord Rayleigh. When I write “Lord Rayleigh”, I mean the 3rd baron Rayleigh. His surname was Strutt. My interest in him was sparked in the days when my primary work interest was acoustics. Rayleigh made many advances in that field. Rayleigh’s son wrote a biography of his father, which I have and which I read every few years. In his time, the son became Lord Rayleigh himself, but to avoid confusion, I will restrict the name to the 3rd baron.

Rayleigh investigated red/green colour blindness (important because of the choice of red and green for railway signals) He made a significant observation (Page 46)


Lord Rayleigh P46

That this could be a “new” discovery may seem strange to those of us who are familiar with how colour television (or colour computer monitors) work, but here it is. No date given in the biography, but probably about 200 years after Newton’s work with a prism.

Lord Rayleigh P174
Lord Rayleigh P175
The fourth Baron was writing here as if the population (of people) could be divided into two groups, one of which had Lord Rayleigh as a member, and the other had the Balfours.

There is a delightful similarity here with Lord Rayleigh’s discovery of Argon. In an era when air was believed to consist of water vapour, carbon dioxide, oxygen and nitrogen, it followed naturally that nitrogen could be obtained by removing the other constituents from air. Rayleigh had set himself the task of weighing gasses, and he discovered that chemically produced nitrogen was lighter then nitrogen thus derived from the atmosphere. This led to the discovery that there was another gas present. This was produced by removing all the known constituents from air. What remained was named “Argon”. In the account of this discovery by his son, there is no mention of the possibility that this “Argon” might have more than one constituent.

Wikipedia says:
Constituents of Air
Lord Rayleigh’s Argon was mostly argon (99.7%), but it was 0.19% neon, 0.056% helium and 0.019% methane. You can’t really blame Lord Rayleigh for not noticing the others.

Similarly, Lord Rayleigh assumed that there were people with normal eyesight, and then one group (“this peculiarity”) (which included those Balfour brothers) which was different.

As with the argon, he was right to identify an anomaly, but wrong to assume that there was only one. The feature that Lord Rayleigh noticed in the Balfours is these days called Anomalous trichromacy. Wikipedia says:

Anomalous trichromacy is a common type of inherited color vision deficiency, occurring when one of the three cone pigments is altered in its spectral sensitivity. This results in an impairment, rather than loss, of trichromacy (normal three-dimensional color vision).
Protanomaly is a mild color vision defect in which an altered spectral sensitivity of red retinal receptors (closer to green receptor response) results in poor red–green hue discrimination. It is hereditary, sex-linked, and present in 1% of males.
Deuteranomaly, caused by a similar shift in the green retinal receptors, is by far the most common type of color vision deficiency, mildly affecting red–green hue discrimination in 5% of European males. It is hereditary and sex-linked.
Tritanomaly is a rare, hereditary color vision deficiency affecting blue–green and yellow–red/pink hue discrimination. Unlike most other forms, it is not sex-linked, it is related to Chromosome “7”.
Here is a summary of the frequencies of occurrence (not agreeing exactly with the above text.)
Anomalous Trichromacy Table
Two Consequences for us

Consequence 1.
Years ago, I was putting the finishing touches to a design that has three LEDs on the front panel. These were red, yellow and green. As the LEDs of different colours have different forward volt drops, one would never imagine that they would have the same value of series resistor. Factors of variation in LED brightness, and variations in the sensitivity of the human eye were to be considered as well. I had read Lord Rayleigh’s biography many years before, but did not think of it then. I selected the resistors to give much the same brightness to the three LEDs (to my eyes). I proudly submitted my work to my mate Tino Vescovi, who was my boss at that time. He asked why I had set the brightness of the three LEDs the way I had. I told him that I had set them for equal brightness. “No”, he exclaimed, “The brightnesses are so very different.” Tino changed the resistor values so that the brightnesses looked the same to him. They now looked very different to me. Unfortunately, I do not recall whether Tino’s changes made the red look brighter than the green or the other way around. I conclude that either Tino or I (or both) have anomalous trichromacy.

The lesson is, when you set the brightness of LED lamps like this, get a consensus of your work mates. Don’t rely on one person’s view. It is better to optimize your product for 96.665% of the population than the other 3.335%. You cannot get it right for everybody.

Consequence 2.
These days most people in the photography game are using digital equipment. They view their work on a computer monitor (often a very expensive “calibrated” one) which uses red, green blue primary colours. Then they print it out with a colour printer that uses cyan, magenta yellow and black inks.

No matter how well calibrated the monitors are, they cannot (even in principle) provide an image that will look the same as the printed one for 100% of the population. I suppose pleasing 96.665% is good enough. However it would be good if people whose profession is the presentation of colour understood this.

CIR Chromaticity Diagram

CIR Chromaticity

Somehow I love this. The diagram is presented as occupying x – y axes. Of course there is a z axis representing brightness. I have drawn in a triangle. I understand that if the screen has three phosphors (red, green and blue) then the colour on the screen can be any colour within the triangle.

Somehow the shape of the curve must follow from the spectral response curves of the S, M and L cones (first picture in this post). See

I wonder if it would be practical to use a similar “colour space” in other communication systems which used a three channel receiver with partly overlapping passbands. Hmmmmm!?


Flame Loudspeaker

Recently, I was sorting out some old material and I came across a few documents from what now seems to be the distant past. It is hard to believe this these days, but before the days of the personal computer, blokes generally did not type for themselves, and if a document was required to be well presented, one had to find a friendly typist to type it out. In 1975, which just before the “Personal Computer revolution”, it was my job to write programs for a Wang personal computer. The term “Personal Computer” wasn’t even coined then, and they called it a “Programmable Calculator”. It was programmed in BASIC. So great was perception of the barrier between a male “user” of this machine, and the qwerty keyboard, that Wang sold this machine with two keyboards: one of conventional “qwerty” style, and one in which the keys were in alphabetical order. Each key doubled as a BASIC command name when used with the <Ctrl> key.

So in 1973, if one wasn’t a typist (and the vast majority of us were not) then one wrote out a document in long hand first.

My interest had been aroused by an item in a column called “Real and Imaginary” by “Vector”, in the August 1973 issue of Wireless World. In those days, it was very common in Britain for regular contributors to magazines to use a nom-de-plume. I don’t know why this was, but “Cathode Ray”, “Vector”, and in another magazine, “Tubal Caine”, “Duplex” (This was actually two people who shared the name), “LBSC” (and others) became well known. I wonder where this idea came from.

Here is the item:


I determined to try it. I had an oxy torch, and it was in at work for some reason at the time. I do not have a copy of the typewritten letter: indeed it might not have been copied. Here is my handwritten report.

flame spkr letter

For you young blokes who are not familiar with the common arrangements of valve a.m. radio circuit, I include one here. It was universal to have a radio that provided for a.m. only, as there were no FM broadcast transmissions in those days!


This circuit is much older than the one I used, but all the essential features are there. It will be seen that if one of the wires to the speaker is cut, then the last valve has just an inductor (the speaker transformer primary) for a load. A connection to that anode provides a high voltage audio signal superimposed on a d.c. bias (in this case 250 volts). This is a good first guess for the signal requirements for the flame speaker.

Here was a speaker with no moving mechanical parts, and thus no resonances of moving mass and mass suspension stiffness. Yet…. completely impractical!

flame0003 (800 x 1037)

Flux Strap / Flux Band

You know the thing I am referring to. A strip of metal (usually copper) is wrapped around a transformer to provide a shorted turn to stray field. A Flux Strap or Flux Band?

 Transformer 2
Transformer with Flux Strap or is it a Transformer with a Flux Band?

What do you call it?

I have searched in vain for a Standard way of depicting this thing (whatever you call it) on the schematic symbol. In the face of this vacuum, I have adopted my own which seems to be clear to people who have never seen the symbol before. This is an advantage over some other attempts to depict it, which have been misinterpreted as a metal shield between primary and secondary.

Flux band symbol (500 x 435)My way of depicting a Flux Strap on the schematic symbol

Are any readers aware of a Standard way of showing this, or even one that is commonly accepted in some circles?

20-07-2014 I return to report that nobody did come back to me with the details of a Standard way of depicting a flux strap, so I used the style of depiction that I had sketched out above. Here it is as used in my work.

Circuit Diagram