Why 2.5 ohms impedance?

[Peter.N.]

In the early days of transistor radios some speakers had a very high impedance, 30 ohms or so but this was to match them to the output stage without a transformer, probably done for cheapness and lightness.

Peter

[G6Tanuki]

Yes, small transistor radios often used 35 or sometimes even 80-Ohm speakers; these were inevitably used with wither single-ended [driver-transformer but no output-transformer] 'totem-pole' push-pull, or the later complementary-symmetry transformerless style output stages.

Many larger radios of the era used 15-Ohm speakers; a pair of OC81s running off 9 volts will still give quite decent volume into a 15-Ohm speaker without an output transformer.

[val33vo]

Low impedance speakers can be made more robust with thicker wire and if it's valve the impedance is not so important as they need an output transformer anyway.

[ms660]

Mag page 256, The Output Stage...Effect of Matching on Frequency Response by A.W. Stanley, W.W. August 1946:

https://www.americanradiohistory.com...ld-1946-08.pdf

I found the ref to the above when reading through Section 1 of RDH4 Chapter 21.

It says that the acoustic power given by the loudspeaker is dependant on the turns ratio of the matching (output) transformer, I reckon that the common use of 3 ohm (ish) loudspeakers was an all round compromise that satisfied the power output versus distortion from the valve in conjunction with an optimum turns ratio for the transformer for acoustic power, basically dictated by ra (anode resistance) and the optimum turns ratio for acoustic power.....sort of.

Lawrence.

[kalee20]

Originally Posted by Radio Wrangler

...people have pointed out that coils are inductive. But the pole pieces are not laminated, so this inductance will get lossy with increasing frequency...

I'm with you Dave on almost all of this, except the above bit!

I agree that the pole-pieces are not laminated (it adds extra cost), but the reason for laminating cores is to reduce eddy current losses due to varying fields. In a loudspeaker, the field is constant. Any signal going into the voice coil makes it move, rather than changes the field. As you say the coil velocity is ideally proportional to applied voltage. This can only happen in a constant magnetic field.

So, with a constant field, there's no need to laminate the pole-pieces!

In fact, as an inductance, it will be lossy (very!) because energy is transferred to the air. But that's a different mechanism from what you indicated.

I tend to agree with posters-to-date that 2 - 3 ohms was chosen because it's easy and quick to wind. 15 ohms would be used only if the speaker is a significant distance from the amplifier, when a lower impedance would make the resistance of connecting cables more significant - and distant speakers use is generally in the high-quality environment.

I would have thought that two layers would be optimum, you have to get the wire back to the start after all.

[Argus25]

Maybe the answer is too obvious.

I think the main reason why low impedance speakers are used is because of low supply voltages in transistor audio output applications.

In the case of no output transformer, it is the speaker impedance which limits the maximum available power deliverable to the load by the output stage, from any supply voltage, before clipping occurs.

To give an example, the output stage, running from say 12V, has a voltage peak swing of 6v (before clipping) the rms voltage is about 4.3V. So the max power you can get out of that amplifier (before clipping) becomes limited by the speaker impedance to 4.3^2/Z , where Z is the speaker impedance.

This was and always has been a gremlin in car audio design and why 4 ohm rather than 8 or 16 ohm speakers are used with car radios. The max power from a standard transformerless output stage into a 4R load, was limited to 4.3^2/4 or about 4.6 watts. The only common way to fix that was to either parallel speakers to get 2 Ohms and double the power delivery that way, or go to a bridge output stage, doubling the rms voltage and quadrupling the power that way.

In short, the lower the operating voltage of the transformerless transistor amplifier, the lower the speaker impedance should ideally be, so a low Z speaker is quite appropriate & helpful.

If a transformer is used, or required to transform the impedance, you could have practically any impedance speaker you wanted transformed as the load presented to the output stage. For a transistor output stage (or valve) the load presented to it must be low enough in impedance to get the maximum output power just before the stage clips.

So low Z speakers are very helpful, especially if the available power supply voltage for the amplifier is relatively low, as often is the case, in low voltage operated transistor circuits.

[John10b]

All very interesting and a good debate, but do remember I started by asking about vintage Radio sets with valves.
Thanks to a member(Mike) I have discovered a wealth of information from the bbc training archives, if you search BBC Wood Norton you will find a history of training with access to training notes, all very interesting.
Cheers
John

[G6Tanuki]

It's worth noting that in quite a number of radios produced up until the end of WWII - both 'communications' receivers like the HRO and upmarket consumer-radios (and some radiograms) the speaker (often more than one - with switching to let you listen to the radio in different rooms) was a separately purchased item and in such cases often the output-transformer was seen as being part of the speaker not part of the radio.

I guess if you've only got limited amounts of audio power available, distributing this at high voltage is likely to incur fewer losses than if you had the OPT in the radio and long low-impedance wires to the speaker (see '100V line' distribution).

The only downside of this approach is that if the leads to the speaker/output-transformer become open-circuit and you're using a tetrode or pentode output-valve you're likely to melt the screen-grid.

[Radio Wrangler]

Originally Posted by kalee20

So, with a constant field, there's no need to laminate the pole-pieces!

Indeed!

Sorry, my fault,

I wasn't clear. With the continuous flux of the field magnet the pole pieces do not need to be laminated. I was just thinking of the voice coil within the pole pieces with no field applied.

David

[Synchrodyne]

The attached excerpt from Briggs, “Loudspeakers”, 5th edition gives some background, bearing in mind that this was written during the valve era.



My take on that is that once output transformers became the norm, there was some, although not complete freedom to choose loudspeaker voice coil resistance and so consequent nominal impedance.

In the (valved) domestic radio receiver case, where connecting leads were very short, the economic/performance trade-off evidently favoured a low value, hence 2 to 3 ohms as probably being at the low end of what was practicable. The economics of having multiple suppliers would have favoured a degree of standardization, whether industry de jure, as in the US RMA case, or de facto, as might have been the case in the UK. (Although conceivably BREMA might have had a say in the matter.)

Accordingly the setmakers would have come to regard 2.5 ohms (or thereabouts) as the default choice, already demonstrated as providing the best economics, and probably would not have spent too much time on the matter unless they were looking for enhanced performance for their top-of-the-line models (where one does find some variations.)

To some extent that might address the original question. Even if the “hard” analysis and synthesis is not available, it is supported by the empirical evidence of what was actually done.

For the hi-fi and PA cases, higher voice coil resistances were appropriate, as explained by Briggs. 15 to 16 ohms nominal impedance was a norm in the valve era, with 7 to 8 ohms more used in the USA than the UK as far as I know. Again a measure of standardization was useful in the amplifier makers could then provide a limited number (2 or 3) secondary taps on their output transformers to address virtually all of the situations that might be encountered.

With the advent of transistors there was a paradigm shift. In the hi-fi case, in the early days around 8 ohms nominal speaker impedance was found to be a good trade-off between making good use of available amplifier power and not overstressing current capacity of the output devices and circuitry then available. From around 1970 or thereabouts generally lower (or at least lower at some frequencies) speaker impedances started appearing along with amplifiers with much higher current capacities, so at that stage, all bets were off, so as to speak.


Cheers,

[John10b]

I read the extrac from “Briggs”, very interesting. Did I misunderstand, but did they use Aluminium wire for voice coils?
Cheers
John

[Radio Wrangler]

That page also shows Gilbert Briggs' delightful writing style. The book is worth reading for this as well the insight it gives.

If I waved my magic wand and replaced an aluminium or copper voice coil winding with unobtainium, which has much lower resistivity but keep the same dimensions, turns, and magnet, the DC resistance will plummet. But the force per amp will stay the same, and the velocity per volt. The voltage to velocity characteristic will imrove.

The DC resistance is one of the electrical losses making up a loudspeaker's remarkable inefficiency. The emission of sound power is represented by one real resistive term which only comes into play in the AC impedance.

3 Ohm, 8 Ohm etc speaker names are useful for amplifier makers, but not so useful for thinking about sound output. You could get a higher speaker DC resistance by using nichrome wire.

It's like the way we used to rate light bulbs by the electricity they consumed rather than by the light they gave.

David

[Synchrodyne]

Originally Posted by John10b

I read the extrac from “Briggs”, very interesting. Did I misunderstand, but did they use Aluminium wire for voice coils?
Cheers
John

Yes. Some more from the book for background:




Cheers,

[Radio Wrangler]

Another trick found in speaker voice coils is the use of square cross section wire, which is carefully wound to place turns with flat face to flat face. This gives a better fill factor and lower resistance for a given height (therefore given magnetic gap width)

Aluminium coil formers and other tricks have been employed to get the heat out of the coil and out to where it can be spread into the environment, usually in high power stage and PA speakers.

David.

[John10b]

Very interesting, l thought I would buy a book 5th edition from Amazon but at £82 decided against it.
What wire do they use today?
Cheers
John

[kalee20]

Originally Posted by John10b

I read the extrac from “Briggs”, very interesting. Did I misunderstand, but did they use Aluminium wire for voice coils?

Yes, some manufacturers did.

The ideal driver is massless, so all the applied force goes into shifting the air rather than accelerating the mass of the cone and coil. That can't be achieved, of course, but an aluminium coil is much lighter than a copper coil (even after allowing for the fact that you have to use thicker aluminium to get the same DC resistance). Frequently, flat narrow aluminium tape was used.

Originally Posted by Radio Wrangler

If I waved my magic wand and replaced an aluminium or copper voice coil winding with unobtainium, which has much lower resistivity but keep the same dimensions, turns, and magnet, the DC resistance will plummet. But the force per amp will stay the same, and the velocity per volt. The voltage to velocity characteristic will imrove.

It's interesting to note that these two quantities, the force per amp, and the velocity per volt, are numerically equal! The units look quite different (newtons per amp, and metres per second per volt) but breaking these down into fundamental units reveals them to be the same.

The idea of reducing resistance so that the volts 'lost' in the coil's resistance becomes negligible, so that the terminal voltage does actually determine coil velocity, is super! Failing the supply of your unobtanium, I have seen ideas to use positive current feedback in an amplifier, to give a negative output resistance. If this is made equal to the speaker's coil resistance, then in principle we have what we want. But I have never used it myself (or seen it used by others) in practice.

[G8HQP Dave]

Originally Posted by ms660

It says that the acoustic power given by the loudspeaker is dependant on the turns ratio of the matching (output) transformer, I reckon that the common use of 3 ohm (ish) loudspeakers was an all round compromise that satisfied the power output versus distortion from the valve in conjunction with an optimum turns ratio for the transformer for acoustic power, basically dictated by ra (anode resistance) and the optimum turns ratio for acoustic power.....sort of.

The optimum turns ratio depends on the speaker impedance and the optimum load impedance required by the valve (not the anode resistance), so any reasonable impedance can be handled. There is no reason why 3 ohms is better than any other impedance, as far as the OPT is concerned.

The article is somewhat misleading in saying that acoustic power depends on turns ratio; the truth is that acoustic power depends on how far the turns ratio departs from the optimum turns ratio, which depends on the speaker impedance. There is no optimum turns ratio independent of speaker impedance. That is, we don't pick 40:1 because that is a good turns ratio and then find that our speaker needs to be 3 ohms in order to match a 5k valve; on the contrary, we choose 3 ohms (for other reasons) and then find that our turns ratio needs to be 40:1.

[David Simpson]

In simple terms Impedance is a sort of frequency dependant resistance factor. Its designated Z, & Z = the sq. root of (Xl squared + R squared)(For speakers). Where Xl is the inductive reactance & = 2Pi fL. L is the Inductance(usually in milli Henrys for small speakers). f = the frequency. For speech it could be from 30Hz to 3KHz. For Music it could be up to 8KHz.
Booring old maths, eh. But speaker manufacturers need to take account of these factors. They also need to take into account the radio manufacturer's requirements for the AF o/p transformer's characteristics. Sadly, that involves more booring maths relating to valves & their output circuitry. i.e. Gain G = Ra divided by ra + Ra, multiplied by mu. Not to mention transformer calculations.
A speaker's Resistance & Inductance can be measured on a modern hand-held cheapo LCR Meter,(as can a transformer's). But LCR meters just work on a fixed frequency.
I'm sure that the more academic Forum members could explain the maths & other electronic factors much better than I.


Regards, David

[Neutrino]

Moving coil loudspeakers, like moving coil galvanometers, are different from most electrical machines in that the windings are in the air gap instead of on a magnetic core.

A magnetic core, such as in a transformer or motor, allows the designer flexibility to provide space for the coils and to fill the available space with a large number of turns of thin wire or a smaller number of turns of thicker wire to suit the application. Furthermore, most of the forces are exerted on the magnetic core rather than on the windings.

In a moving coil loudspeaker the windings are in the air gap. The designer needs to minimise the size of the air gap because a larger air gap requires a bigger, heavier and more expensive magnet. In addition the mechanical forces generated are exerted on the coil.

The design of the windings for a moving coil loudspeaker is therefore more constrained than the design of windings for most other electrical machines due to the need to not only minimise the weight of the coil but also to minimise the air gap and make the coil robust enough to withstand the forces generated.

David