# Electrical power rating ?

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#### shank1207

Hi,

There is a relation between displacement limited rating of acoustic and electrical power (Par)with effeciency(eta):eta=Par/Per. I wanted to knw what is the relation of thermal power capacity Pe(max). (I am looking for a formula since i am making a small matlab program)?

Since i am already asking a question i was also looking for a relation between Qtco(Q when source resistance is zero) and Qtc of the closed box is there any?

#### TBTL

I wanted to knw what is the relation of thermal power capacity Pe(max).
Relation to what?

Since i am already asking a question i was also looking for a relation between Qtco(Q when source resistance is zero) and Qtc of the closed box is there any?
I do not understand your question but maybe the answer is on this page: www.diysubwoofers.org/sld/sealed1.htm. Can you define what Qtco and Qtc refer to?

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#### shank1207

Relation to what?

I do not understand your question but maybe the answer is on this page: www.diysubwoofers.org/sld/sealed1.htm. Can you define what Qtco and Qtc refer to?

Hello thanks for your reply i am sorry i should have rephrased my question the notation are from Thiele and Small's paper, Qtc is the the total Q of the sealed box and Qtco is the total Q when source resitance is zero. I want to find out the electrical power that i need to feed the driver. Because when i am doing the calculation for small driver(1", fs=180) in a small volume(200cm3) i am getting incredibly high input power rating.Thats why i wanted to find out how do you calculated the electical power limit to the driver in relation to driver T/S parameters.

#### sine143

you cannot "calculate" thermal power handling. it is determined via aes standard testing (band limited, compressed pink noise with 6db crest factor run for 2 hours).

#### Ron E

As to your first question, drivers are either displacement limited or thermally limited. You calculate excursion for a given input and extrapolate. Problem is the large signal behavior is nonlinear.

Qts=ws*Mms/(Bl^2/(Re+Rg)+Rms)
Rg is source resistance

Qtc/Qts=Fc/Fs=sqrt(1+Vas/Vb) for no damping case.

There are probably a million m-files out there if you search.
You should really program this up in Simulink and then you can go nonlinear ;P

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#### shank1207

As to your first question, drivers are either displacement limited or thermally limited. You calculate excursion for a given input and extrapolate. Problem is the large signal behavior is nonlinear.

Qts=ws*Mms/(Bl^2/(Re+Rg)+Rms)
Rg is source resistance

Qtc/Qts=Fc/Fs=sqrt(1+Vas/Vb) for no damping case.

There are probably a million m-files out there if you search.
You should really program this up in Simulink and then you can go nonlinear ;P

So we have the relation between displacement limited Acoustic power (Par)and electric power(Per) through effeciency, accordingly the electric power should not exceed this limit. Is this the power limit of the amplifier that i should use and make note not to exceed it?

And about the Qtc (with damping) there is no relation between Qtco (case without damping) ?. And the ratio of Qtc/Qts is different then the that of sqrt(1+alpha) guess it is normal considering the effect of damping and stifness

#### shank1207

you cannot "calculate" thermal power handling. it is determined via aes standard testing (band limited, compressed pink noise with 6db crest factor run for 2 hours).
Thanks for the information for the expected displacement limited electric power do the driver have to have some specified thermal limited electric power?

#### sreten

Hi,

The thermally limited input power is basically at what temperature
does the driver self destruct, the coils cooling time constant and
the history of the input signal to the driver. E.g. A midrange can
easily take 500W transients, no hope in hell of 500W sine waves.

However as this is in subwoofers, bass in not known for transients.
For subwoofers generally speaking if you have an amplifier capable
of exceeding the drivers thermal limits, you also have an amplifier
far too powerful for the drivers excursion limitations. Basically if
you match the used power to the excursion limitations that will
pretty much guarantee that thermal issues do not matter.

rgds, sreten.

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#### Ron E

So we have the relation between displacement limited Acoustic power (Par)and electric power(Per) through effeciency, accordingly the electric power should not exceed this limit. Is this the power limit of the amplifier that i should use and make note not to exceed it?

112.1+20*log10(Par) is SPL
112.1+20*log10(eta_0) is SPL at 1watt into Re

The exercise is left to the reader. You will find that Par is not a very useful measure. You could have a 500W rated subwoofer that in some box could be destroyed by a 50W amplifier at 10-20Hz

And about the Qtc (with damping) there is no relation between Qtco (case without damping) ?. And the ratio of Qtc/Qts is different then the that of sqrt(1+alpha) guess it is normal considering the effect of damping and stifness

I don't understand the question. The effect of damping is essentially a notch filter at Fc. Not worth getting hung up over, IMO. Just use sqrt(1+alpha) You could read small-margolis article in 1981 JAES...

#### shank1207

112.1+20*log10(Par) is SPL
112.1+20*log10(eta_0) is SPL at 1watt into Re

The exercise is left to the reader. You will find that Par is not a very useful measure. You could have a 500W rated subwoofer that in some box could be destroyed by a 50W amplifier at 10-20Hz

I don't understand the question. The effect of damping is essentially a notch filter at Fc. Not worth getting hung up over, IMO. Just use sqrt(1+alpha) You could read small-margolis article in 1981 JAES...
Thats cool thanks . About Qtc i just wanted to know if the Q of the closed box with and without damping are related in a equations.

For the electrical power rating I am still confused with interpreting them when mentioned in specs for example what does this mean maximum power input 8W and rated power input 4W how does this apply to acoustical perfomance? Giving a thought it must be through efficiency.

#### Ron E

eta_0 is efficiency (0 to 1)
power ratings are marketing.

It sounds like you are trying to find some deterministic solution and this problem is not that simple,

#### AndrewT

As to your first question, drivers are either displacement limited or thermally limited. ................
Ron drove the nail in all the way to it's head.

You the user must recognise both power limits.
You limit the power delivered by setting the control knobs so that the driver sounds as though it is not being overloaded.
You can use some limiting electronics to help with protecting drivers from abusive users. but listening is usually adequate.

Many amplifier manufacturers and many speaker manufacturers often recommend amplifier power ratings upto roughly double the speaker's long term "no thermal damage" rating.
eg the speaker is rated @ 100W long term for pink noise when above the LF excursion limited frequency. This speaker may have an LF limit of just a few watts to extreme low frequency signals.
Yet the recommended amplifier could be 200W.

#### shank1207

Ok thanks i get the idea.

#### shank1207

I had read this in the paper by Small so i was thinking there is a relation between thermal limited power and displacement limited power

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#### Ron E

112.1+20*log10(Par) is SPL
112.1+20*log10(eta_0) is SPL at 1watt into Re

The exercise is left to the reader. You will find that Par is not a very useful measure. You could have a 500W rated subwoofer that in some box could be destroyed by a 50W amplifier at 10-20Hz

Run these numbers.

As far as your 71 vs 22 watt he is saying only that peak is about 3.5 times average = or about 10*log10(71.5/22.5)~5dB

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#### shank1207

Run these numbers.

As far as your 71 vs 22 watt he is saying only that peak is about 3.5 times average = or about 10*log10(71.5/22.5)~5dB
Ok thank you very much Ron.

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