loudspeaker equivalent circuit - representation of acoustic power

[Malcolm Irving]

A 100dB guitar speaker has an efficiency of about 6%. In other words 94% of the electrical power supplied to the speaker is dissipated as heat, and only 6% is converted into acoustic power.

A loudspeaker equivalent circuit includes various resistances, inductances and capacitances. Pure inductances and capacitances cannot dissipate any power, so 100% of the input power must be dissipated in the equivalent circuit resistances.

My question is:
Can we (and should we) separate ‘acoustic power dissipation’ from ‘heat dissipation’ in the equivalent circuit?
For example, if we decide that all the acoustic energy is included in the dissipation of a particular 16 ohm resistor in the equivalent circuit, we could split that resistor into a series combination of 1 ohm and 15 ohms. We could then say the heat dissipated in the 1 ohm resistor represents acoustic power dissipation while the heat produced in the 15 ohms and any other resistors represents heating (in the real speaker).

Two further questions then arise:
There are usually three or more resistors in the equivalent circuit – how should acoustic power be proportioned among them?
If we do this, could the voltage signal(s) across the ‘acoustic resistors’ be a good source for a line out to a PA or other re-amping system? (Since it could be a good representation of the sound produced by the real speaker?)

[Helmholtz]

Did you read this thread:
https://music-electronics-forum.com/...ad.php?t=47723 ?

The part of the speaker emulating impedance representing acoustic power dissipation certainly must be real/dissipative/resistive. But I think its value must change with frequency, prohibiting a simple separation. A fixed series resistor would just reflect current variation over frequency dictated by the total complex impedance.

[Old Tele man]

SOUND is modulated air pressure.

Electrical POWER is modulating VOLTS-times-AMPS (and could be reactive).

[J M Fahey]

If we do this, could the voltage signal(s) across the ‘acoustic resistors’ be a good source for a line out to a PA or other re-amping system? (Since it could be a good representation of the sound produced by the real speaker?)

What voltage?

An acoustic resistor is *acoustic*, it deals with pressure, speed, mass, airflow, etc. units.
No voltage anywhere.

Practical example: bolt a 12" speaker to a piece of plywood, but instead of an 11" hole , just drill a 1/4" one inh the center.

That is an acoustic resistor.

Play music, then grab your trusty multimeter and put probes anywhere in or around it: across diameter, from inside face to outside face, whatever ... will you measure a voltage anywhere?

It is NOT a resistor in any electrical way, just an analogy, a model, to help explain certain things to certain people.

[Malcolm Irving]

I used to work in electrical power systems engineering. We had various equivalent circuits for transmission lines, underground cables, transformers, generators, motors, etc.
A motor converts electrical power to rotational mechanical power. The equivalent circuit for an induction motor (for example) includes resistances which represent heating of the windings, heating of the magnetic parts and in particular a resistance which represents the mechanical energy output.
That resistance is a very significant one, since induction motors have energy efficiencies in the region of 95%. Interestingly, the value of that resistance depends on the speed of the motor, which I think ties in with the point Helmholtz has made.

In a loudspeaker, energy transferred out as sound is much less significant (since speakers are so inefficient). Nevertheless, I have always wondered whether there should be a resistor or resistors somewhere in the loudspeaker equivalent circuit that represent acoustic energy output. It seems to be worth having, even if it is relatively insignificant, as the sound output is the raison d’etre of the whole device.

In a typical loudspeaker equivalent circuit we have:
Shunt capacitance and inductance (analogous to cone mechanical inertia and compliance) together with a shunt resistance (to represent mechanical damping of the cone movement).
Series resistance and inductance (representing the voice coil). Also, a parallel resistance across the coil inductance (to represent energy loss in the magnetic parts).
But what part of the energy loss in each of these resistances represents energy dissipated as sound?

[J M Fahey]

Ok, please post the equivalent speaker circuit showing all impedance elements.

One of them must be representing the air load and since part of it is dissipative , power sent to it "goes away and does not return", that is the "resistor" you are interested in.

All of these models are called "equivalent" for good reason, they allow us to simplify analysis by "treating everything as if it were Electrical" using the same or very similar sets of equations, but we must always remember "the map is not the territory".

In your electric motor example: if it is connected to mains, it will pull current (and so power) from it.
An electrical model will explain that.

Now you activate a clutch or a gearbox and that motor starts pumping water, lifting a lift, sawing wood, whatever mechanical load.

Mains current/power will increase, "as if" a resistor were connected in parallel to mains.
That resistor MUST be shown somewhere in the equivalent circuit or the model is useless.

Same with speakers, which are nothing but an electric motor driving a load.

FWIW we handle Electrical models so well that we apply them to almost everything, from Medicine to Chemistry to Sociology and Economics

I have seen Electrical models explaining and predicting sales vs. price and publicity investment, the price of gold vs. unemployment, etc. and even voting polls results prediction, go figure.

I guess it´s easier to write software to model and simulate data if "translated" to Electrical values.

[Mike Sulzer]

If you measure the impedance looking into a motor driving various loads, you see electrical effect of the various loads because the motor is efficient, as MI said. If you measure the impedance of a speaker, you do not see anything that can be easily attributed to the power transmitted into the air as a function of frequency, and therefore you ignore it when modeling the circuit.

[Leo_Gnardo]

FWIW we handle Electrical models so well that we apply them to almost everything, from Medicine to Chemistry to Sociology and Economics

I have seen Electrical models explaining and predicting sales vs. price and publicity investment, the price of gold vs. unemployment, etc. and even voting polls results prediction, go figure.

I guess it´s easier to write software to model and simulate data if "translated" to Electrical values.

Thanks for mentioning this Juan.

FWIW: The "equivalency" of engineering regimes was the basis of undergrad education at the college I attended. "All the equations are the same, the variables are just assigned different letters." Maybe that's so, but I wasn't much impressed with the notion I'd have to take 3 years of generalized engineering courses before finally "specializing" in electronics in the senior year. So I switched to Physics and got a swell introduction to electronics, plus an on campus job, in my second year at school. Let's just say, I wasn't much looking forward to analyzing the forces on pin truss bridges (already 100 years obsolete) for 2 more years, then finally getting a look at what electrical circuits do.

Handing out a bunch of thumbsups this morning to you three brain trust guys. Good reading! Extra credit to Malcolm for "raison d'etre."

Yes it is a mystery that the conversion of speaker energy to air movement isn't a factor in modeling impedance. Certainly for many/most efficiency is 5% or less. But there are some - for instance Electrovoice speaker/cab combination designs like the 50 year old "Eliminator" folded horn and I'm sure others besides - that claim an efficiency around 25% and that's not insignificant.

[Helmholtz]

If you measure the impedance looking into a motor driving various loads, you see electrical effect of the various loads because the motor is efficient, as MI said. If you measure the impedance of a speaker, you do not see anything that can be easily attributed to the power transmitted into the air as a function of frequency, and therefore you ignore it when modeling the circuit.

Yes it is a mystery that the conversion of speaker energy to air movement isn't a factor in modeling impedance. Certainly for many/most efficiency is 5% or less. But there are some - for instance Electrovoice speaker/cab combination designs like the 50 year old "Eliminator" folded horn and I'm sure others besides - that claim an efficiency around 25% and that's not insignificant.

According to electrical systems theory Malcolm's principal idea is correct. The acoustic power must have an electrical equivalent and should show in the speakers impedance. More precisely in its real part, the AC resistance. As conversion efficiency is low, the influence on impedance is low. But it is measurable. At least in principle. A speaker's impedance changes with its acoustic load. I could measure an increase of the series AC resistance (Rs) of a free standing speaker by 3.5%@1kHz when covering it partly with a heavy towel. The series inductance however did not change noticeably.

As a well designed speaker impedance emulation is based on measurements of a real speaker built into a cab, the acoustic loss is an inherent but distributed part/property of the total circuit.

[glebert]

I have always been curious about the linearity of the acoustic load part. With increased volume the speaker moves farther, and has to push more air faster. Air resistance is normally a square law effect, so it seems like there is a nonlinearity there. Additionally, as the speaker gets towards the excursion limits there will be more nonlinearity there, although that is not technically acoustic load.

[Helmholtz]

I have always been curious about the linearity of the acoustic load part. With increased volume the speaker moves farther, and has to push more air faster. Air resistance is normally a square law effect, so it seems like there is a nonlinearity there. Additionally, as the speaker gets towards the excursion limits there will be more nonlinearity there, although that is not technically acoustic load.

Me too.
But I have never seen a comparison between speaker frequency responses or impedances at low and high levels.
I don't see a realistic chance to incorporate such non-linear effects into the simple passive speaker impedance model.

Speakers also develop partial cone modes/resonances (cone "break-up"), showing in a number of peaks and dips at higher frequencies of the response.
But I did not see them in the impedance.

[Mike Sulzer]

I have always been curious about the linearity of the acoustic load part. With increased volume the speaker moves farther, and has to push more air faster. Air resistance is normally a square law effect, so it seems like there is a nonlinearity there. Additionally, as the speaker gets towards the excursion limits there will be more nonlinearity there, although that is not technically acoustic load.

You sure "air resistance" is the proper model? I think all you are doing is compressing and uncompressing the air with a diaphragm that moves well under the speed of sound. Thus the compressions and uncompressions propagate away nicely at the speed of sound.

( I tried to find a link explaining this, but I gave up when I went to a site called physics.org and found a very stupid explanation of how a speaker works.)

[glebert]

You sure "air resistance" is the proper model? I think all you are doing is compressing and uncompressing the air with a diaphragm that moves well under the speed of sound. Thus the compressions and uncompressions propagate away nicely at the speed of sound.

( I tried to find a link explaining this, but I gave up when I went to a site called physics.org and found a very stupid explanation of how a speaker works.)

Nope, that is why I said I was curious.

[Malcolm Irving]

Ok, please post the equivalent speaker circuit showing all impedance elements.
....

I wasn't think of any particular one, but Aitken's reactive dummy loads are a good example:
http://www.aikenamps.com/index.php/d...-load-emulator

[Malcolm Irving]

…. A speaker's impedance changes with its acoustic load. I could measure an increase of the series AC resistance (Rs) of a free standing speaker by 3.5%@1kHz when covering it partly with a heavy towel. The series inductance however did not change noticeably.
…

Not easy to do in practice, but operating a speaker in a vacuum would be an interesting experiment because all the acoustic load would be eliminated.
Comparing the measured impedance curve in vacuum with that in air, we could see which resistive elements of the equivalent circuit model have been reduced.