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Speaker sensitivity, amp power calculation and bass management

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If I understand things correctly, in the world of cinema and home-cinema, the norm is that each speaker should be able to reproduce sound at a reference level of 85 dBC SPL at the main listening position, with a 20 dB headroom.

It follows that the power needed to reach that level can be determined by speaker sensitivity, distance from speaker to MLP and the associated attenuation, boundary gain etc.

My first question is: how exactly is speaker sensitivity measured? What type of signal is fed to the speaker? All I understand for now is that an 8 ohm speaker receives 1 W of power and the result is measured at 1m. BTW, what is the relationship between 2.83 V = 1W into 8 ohms since sometimes the sensitivity is given in dB/2.83V.m?

Second question: how does one correct the required amplifier power to account for bass management and the associated relief from the subwoofer?
 

solderdude

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My first question is: how exactly is speaker sensitivity measured? What type of signal is fed to the speaker? All I understand for now is that an 8 ohm speaker receives 1 W of power and the result is measured at 1m. BTW, what is the relationship between 2.83 V = 1W into 8 ohms since sometimes the sensitivity is given in dB/2.83V.m?

Yes, this is a confusing term.
But when explained it isn't that confusing anymore.
Suppose we see the following specs:
• Impedance ............................. 6 Ω
This tells us the impedance which obviously is an average impedance of the speaker at 1kHz.

• Sensitivity................................ 86 dB/2.83 Vm
The speaker puts out 86dB SPL when fed with 2.83V at 1m distance.

The 2.83V i,s as already explained above, derived from 1W into 8 Ω.

The problem is that 2.83V into 6 Ω isn't equal to 1W but is actually 1.3W.
When we would state the efficiency in dB/W the actual efficiency would be 84.9dB/W instead of 86dB/W

The thing is an amplifier is a voltage source, not a 'power' source.
This means that if we want to compare how loud a speaker goes when connected to the same source voltage.
All we want to know is how many dBSPL is present at a specified voltage level (because its a voltage source)
So... the 2.83V is 'bombarded' as reference level instead of 1 Watt into 8 Ω which is not handy as the impedance is of importance here as well as the voltage.

With this ** dB/2.83 Vm spec you can easily compare how loud a speaker is connected to a 'standardized' voltage level. (The 2.83V)

This means that 86 dB/2.83 Vm 4 Ω Ohm speaker goes equally loud compared to a 86 dB/2.83 Vm 16 Ω speaker. Both will produce 86dB SPL at 1m distance when it is fed 2.83V while seen from power efficiency and dissipated power the numbers are quite different.

It is basically the same discussion as the dB/mW versus dB/V spec. seen in the headphone world.
One can use both but the only relevant one is dB/V as we want to know how loud something plays from a voltage source and could not care less about how much power is needed to reach that.

Second question: how does one correct the required amplifier power to account for bass management and the associated relief from the subwoofer?

I have no idea what you mean. active subwoofer, passive one, driven from speaker out or line-level out, 1 or 2 subwoofers etc.
 
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Yes, this is a confusing term.
But when explained it isn't that confusing anymore.
Suppose we see the following specs:
• Impedance ............................. 6 Ω
This tells us the impedance which obviously is an average impedance of the speaker at 1kHz.

• Sensitivity................................ 86 dB/2.83 Vm
The speaker puts out 86dB SPL when fed with 2.83V at 1m distance.

The 2.83V i,s as already explained above, derived from 1W into 8 Ω.

The problem is that 2.83V into 6 Ω isn't equal to 1W but is actually 1.3W.
When we would state the efficiency in dB/W the actual efficiency would be 84.9dB/W instead of 86dB/W

The thing is an amplifier is a voltage source, not a 'power' source.
This means that if we want to compare how loud a speaker goes when connected to the same source voltage.
All we want to know is how many dBSPL is present at a specified voltage level (because its a voltage source)
So... the 2.83V is 'bombarded' as reference level instead of 1 Watt into 8 Ω which is not handy as the impedance is of importance here as well as the voltage.

With this ** dB/2.83 Vm spec you can easily compare how loud a speaker is connected to a 'standardized' voltage level. (The 2.83V)

This means that 86 dB/2.83 Vm 4 Ω Ohm speaker goes equally loud compared to a 86 dB/2.83 Vm 16 Ω speaker. Both will produce 86dB SPL at 1m distance when it is fed 2.83V while seen from power efficiency and dissipated power the numbers are quite different.

It is basically the same discussion as the dB/mW versus dB/V spec. seen in the headphone world.
One can use both but the only relevant one is dB/V as we want to know how loud something plays from a voltage source and could not care less about how much power is needed to reach that.



I have no idea what you mean. active subwoofer, passive one, driven from speaker out or line-level out, 1 or 2 subwoofers etc.

Great explanation !! I see more clearly now.

Is the sensitivity measured with a 1 kHz tone @ 2.83V?

If so, I don’t understand how one can use this value to calculate how much power you need to achieve a given SPL at the listening point using a pink noise, which contains many more frequencies?

If I am not mistaken, a homecinema setup is calibrated for each speaker to produce a steady 85 dB(C) SPL at the listening position and 105 dB(C) peak SPL, and this is done by playing a « narrow » band pink noise and measuring with a SPL meter, C weighted, slow reading.
 
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I have no idea what you mean. active subwoofer, passive one, driven from speaker out or line-level out, 1 or 2 subwoofers etc.

I am not sure what I mean either...

- for a given speaker, one can calculate how much power one needs to reach a given SPL at a given distance, using the speaker’s sensitivity figure.
- for reasons I have yet to understand, bass frequencies seem to require much more power than mids and highs?
- therefore I would expect to need less power to reach the same SPL with this speaker if the bass frequencies were redirected to another speaker?
 

solderdude

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Great explanation !! I see more clearly now.

Is the sensitivity measured with a 1 kHz tone @ 2.83V?

If so, I don’t understand how one can use this value to calculate how much power you need to achieve a given SPL at the listening point using a pink noise, which contains many more frequencies?

If I am not mistaken, a homecinema setup is calibrated for each speaker to produce a steady 85 dB(C) SPL at the listening position and 105 dB(C) peak SPL, and this is done by playing a « narrow » band pink noise and measuring with a SPL meter, C weighted, slow reading.

Sensitivity of speakers is often measured at either 500Hz or 1kHz. The listed Impedance is often measured at 1kHz.
However, the actual impedance differs from that 6 Ohm which means that 2.83V at 50Hz or 2.83V at 1kHz will yield a different efficiency (because the frequency response isn't always flat) nor will the power at 50Hz be the same as at 1kHz because the impedance can be drastically different so will also the power be.

Efficiency is measured at a 'standard' voltage so you can compare speakers with the same dB/2.83Vm directly.

Knowing the listening distance, room properties etc you can calculate the needed voltage to reach a certain SPL.
When you know that voltage you can calculate the needed power.
Since the speaker in the example was 6 Ohm one would need to calculate the power at 4 Ohm as an amp that is only specified at 8 Ohm might not reach max. voltage at 6 Ohm. 4 Ohm certainly will.

So say you calculated you need 16V then (16x16)/4 = 64Watt in 4 Ohm
 

solderdude

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I am not sure what I mean either...

- for a given speaker, one can calculate how much power one needs to reach a given SPL at a given distance, using the speaker’s sensitivity figure.
- for reasons I have yet to understand, bass frequencies seem to require much more power than mids and highs?
- therefore I would expect to need less power to reach the same SPL with this speaker if the bass frequencies were redirected to another speaker?

Yes, that is correct. It has to do with the way we are hearing. Hearing is not linear. Our ears are much less sensitive for lower frequencies.
So when we play/record/listen to music there will be much more 'energy' in the lows compared to the mids in order for us to hear it normally.
Basically you need a LOT more power for the lowest frequencies than for lower mids, mids and treble.

This also means that when you use a sub and and filter the frequencies that already go to the sub out of the signal to an amp that does the rest than there is less voltage needed. This means the amp can be less powerfull (clip at a higher power level) and the bass driver has a much easier job.

Efficiency, however, remains the same. That is in dBSPL. We hear in Phon which is not linear. When we measure SPL in dBA it is already closer to Phon but not the same.
 

Jdunk54nl

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So how much power you need can be very confusing, especially with how speakers are rated for power.
Music, much like pink noise, has about a 3db/oct roll off. You can verify this with audacity and analyze the songs. Power gets doubled or cut for every + or - 3db we go.

So if you are sending 100w at 20hz, this is what the power that each octave would need to measure a perfectly flat RTA response with REW or the like.

Power frequency chart.jpg


This also gets into speaker power rating. A 100w tweeter would fry if you send it 100w. It has a 100w rating based on music and can NEVER actually get that much power, in reality it will fry if you send it much over 5w. This has been verified multiple times. I have some good friends that torture test speakers as part of their job, when measuring how much power they receive it was like 2-3w for ear piercing levels, and 5w would fry them. This was while playing music. Hopefully, from the chart above, you can see why 2w-3w on tweeters is EAR PIERCING loud.

So, what does this all mean? Tweeters need like max 5w amps, midrange needs like 25w amps, a midbass needs like 50w-75w, so 100w total amps would be great for most people to get to ear piercing levels.

Luckily if you put a 200w amp on something, the music will never actually send the smaller speakers that much power due to the things listed above, in other words, that 200w amp is pretty much a waste of power...oh....and most of us don't drive are amps to their max volume so we hardly ever use all that power anyways....
 
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Sensitivity of speakers is often measured at either 500Hz or 1kHz. The listed Impedance is often measured at 1kHz.
However, the actual impedance differs from that 6 Ohm which means that 2.83V at 50Hz or 2.83V at 1kHz will yield a different efficiency (because the frequency response isn't always flat) nor will the power at 50Hz be the same as at 1kHz because the impedance can be drastically different so will also the power be.

Efficiency is measured at a 'standard' voltage so you can compare speakers with the same dB/2.83Vm directly.

Knowing the listening distance, room properties etc you can calculate the needed voltage to reach a certain SPL.
When you know that voltage you can calculate the needed power.
Since the speaker in the example was 6 Ohm one would need to calculate the power at 4 Ohm as an amp that is only specified at 8 Ohm might not reach max. voltage at 6 Ohm. 4 Ohm certainly will.

So say you calculated you need 16V then (16x16)/4 = 64Watt in 4 Ohm

What confuses me is if sensitivity is measured with a 1 kHz tone then how can it be relevant to calculate how much power you need to read a 85 dB(C) SPL generated from a pink noise?

Surely you would need much more power to produce a PN than a 1 kHz tone to the same SPL?
 

Jdunk54nl

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From my understanding, when test tones are used, it is usually at 0 dbfs, pink noise is not. It is 3db/oct down slope and is only 0dbfs at 20hz. I do know REW outputs pink noise at -12dbfs to account for peaks in the pink noise. Also measuring how loud something is (SPL), takes the total energy into account. Tones have all the energy at one tone, noise/music has the energy split between all of the tones and that adds together to get the SPL.

If you look at an RTA for noise, the level may be like 70 db for most frequencies, but the SPL meter may read 85db because it adds all of that energy to get that SPL reading.
 
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Yes, that is correct. It has to do with the way we are hearing. Hearing is not linear. Our ears are much less sensitive for lower frequencies.
So when we play/record/listen to music there will be much more 'energy' in the lows compared to the mids in order for us to hear it normally.
Basically you need a LOT more power for the lowest frequencies than for lower mids, mids and treble.

This also means that when you use a sub and and filter the frequencies that already go to the sub out of the signal to an amp that does the rest than there is less voltage needed. This means the amp can be less powerfull (clip at a higher power level) and the bass driver has a much easier job.

Efficiency, however, remains the same. That is in dBSPL. We hear in Phon which is not linear. When we measure SPL in dBA it is already closer to Phon but not the same.

Thanks for the explanation.

Thus, do we have any way of calculating how much of the total power we had previously calculated would be redirected to another speaker because of bass management, to find a more realistic figure that will help use choose an amplifier?
 
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From my understanding, when test tones are used, it is usually at 0db, pink noise is not. It is 3db/oct slope and is only 0db at 20hz.

I am not sure what you mean by 0 dB ?

From what I have read, a typical AVR will use a narrow band PN generated at -30 dBFS and use this to calibrate each speaker so as to read 75 dB(C) from it’s calibration mic.

This should ensure that movie content, which is recorded at a normalised -20 dBFS will be reproduced at the 85 dB(C) reference level, as intended by the artist. The narrow band PN IIRC ensures a consistent measure on speakers that have more or less limited bass extension
 

Jdunk54nl

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Edited above for 0dbfs and added the following:


I do know REW and SMAART outputs pink noise at -12dbfs to account for peaks in the pink noise. Also measuring how loud something is (SPL), takes the total energy into account. Tones have all the energy at one tone, noise/music has the energy split between all of the tones and that adds together to get the SPL.

If you look at an RTA for noise, the level may be like 70 db for most frequencies, but the SPL meter may read 85db because it adds all of that energy to get that SPL reading.

Most speaker manufacturers do not really care how they get the 1w or 2.83v as long as they get that, as in they can turn up/down the generator dbfs or turn up/down the amp.
 

EdTice

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Yes, this is a confusing term.
But when explained it isn't that confusing anymore.
Suppose we see the following specs:
• Impedance ............................. 6 Ω
This tells us the impedance which obviously is an average impedance of the speaker at 1kHz.

• Sensitivity................................ 86 dB/2.83 Vm
The speaker puts out 86dB SPL when fed with 2.83V at 1m distance.

The 2.83V i,s as already explained above, derived from 1W into 8 Ω.

The problem is that 2.83V into 6 Ω isn't equal to 1W but is actually 1.3W.
When we would state the efficiency in dB/W the actual efficiency would be 84.9dB/W instead of 86dB/W

The thing is an amplifier is a voltage source, not a 'power' source.
This means that if we want to compare how loud a speaker goes when connected to the same source voltage.
All we want to know is how many dBSPL is present at a specified voltage level (because its a voltage source)
So... the 2.83V is 'bombarded' as reference level instead of 1 Watt into 8 Ω which is not handy as the impedance is of importance here as well as the voltage.

With this ** dB/2.83 Vm spec you can easily compare how loud a speaker is connected to a 'standardized' voltage level. (The 2.83V)

This means that 86 dB/2.83 Vm 4 Ω Ohm speaker goes equally loud compared to a 86 dB/2.83 Vm 16 Ω speaker. Both will produce 86dB SPL at 1m distance when it is fed 2.83V while seen from power efficiency and dissipated power the numbers are quite different.

It is basically the same discussion as the dB/mW versus dB/V spec. seen in the headphone world.
One can use both but the only relevant one is dB/V as we want to know how loud something plays from a voltage source and could not care less about how much power is needed to reach that.



I have no idea what you mean. active subwoofer, passive one, driven from speaker out or line-level out, 1 or 2 subwoofers etc.


I understand what the OP meant so I'll try to answer although it was somewhat addressed in later posts.

Adding a subwoofer can, sometimes, reduce the load on the primary amplifier. But it depends on what kind of subwoofer. If you add a *passive* subwoofer (unpowered) to the system, you may get better bass reproduction, but it doesn't reduce load on the amplifier. (And this isn't a super-easy task). More realistically, many "active" subwoofers have speaker-level inputs (to accommodate audio equipment that doesn't have pre-outs). The subwoofer has its own internal amp, but main amplifier still has to put out the entire signal. You may or may not get better audio but, again, you don't change the load on the amplifier. In the former case, the amplifier is driving the subwoofer. In the second, it *thinks* its driving the full range and much of the amplification is wasted.</p>

I am going to ignore the "line level out" because I think what is meant here is a dedicated subwoofer out (which is admittedly at line level voltage so the terminology isn't perfectly precise but pretty clear). In that case, the AVR can be configured to do internal bass management. The low frequencies can be sent only to the subwoofer. If you do this, the amplifier won't receive the bass as input and won't have to amplify that part of the sound. This will reduce load on the amplifier.</p>
 
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I understand what the OP meant so I'll try to answer although it was somewhat addressed in later posts.

Adding a subwoofer can, sometimes, reduce the load on the primary amplifier. But it depends on what kind of subwoofer. If you add a *passive* subwoofer (unpowered) to the system, you may get better bass reproduction, but it doesn't reduce load on the amplifier. (And this isn't a super-easy task). More realistically, many "active" subwoofers have speaker-level inputs (to accommodate audio equipment that doesn't have pre-outs). The subwoofer has its own internal amp, but main amplifier still has to put out the entire signal. You may or may not get better audio but, again, you don't change the load on the amplifier. In the former case, the amplifier is driving the subwoofer. In the second, it *thinks* its driving the full range and much of the amplification is wasted.</p>

I am going to ignore the "line level out" because I think what is meant here is a dedicated subwoofer out (which is admittedly at line level voltage so the terminology isn't perfectly precise but pretty clear). In that case, the AVR can be configured to do internal bass management. The low frequencies can be sent only to the subwoofer. If you do this, the amplifier won't receive the bass as input and won't have to amplify that part of the sound. This will reduce load on the amplifier.</p>

Indeed that is what I had in mind.
 

AnalogSteph

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Surely you would need much more power to produce a PN than a 1 kHz tone to the same SPL?
If speaker sensitivity and impedance were to remain constant across the audio spectrum - i.e. flat frequency and impedance response - then actually no, you wouldn't. With a speaker of non-constant impedance, as usually found, your guess is as good as mine. You'd have to analyze this by integrating spectral power density (as a function of voltage and load impedance) over frequency. Could be lower, could be higher.
 

solderdude

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What confuses me is if sensitivity is measured with a 1 kHz tone then how can it be relevant to calculate how much power you need to read a 85 dB(C) SPL generated from a pink noise?

Surely you would need much more power to produce a PN than a 1 kHz tone to the same SPL?

Again ... its about the voltage needed. Not the power.
When you have 85dB and the frequency response is pretty flat it doesn't matter if the signal is 2.83V (average) with pink noise or a single sine.
It will produce the 85dB. The signal won't look the same though and depending on the impedance swing the actual drawn power will not be the same.
The average voltage will be, assuming you measure dBSPL so without weighting.
 
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solderdude

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Thanks for the explanation.

Thus, do we have any way of calculating how much of the total power we had previously calculated would be redirected to another speaker because of bass management, to find a more realistic figure that will help use choose an amplifier?

That would depend on the actual spectrum of the music and the crossover frequency.
When one assumes a pink noise spectrum is representative on average then you can see how many octaves is covering the lows and calculate how much power is going into this.

I would like to add that it doesn't really hurt to over-dimension the amps so when you have calculated around 70W or so a 150W or 200W amp will be fine.
 

EdTice

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Again ... its about the voltage needed. Not the power.
When you have 85dB and the frequency response is pretty flat it doesn't matter if the signal is 2.83dV (average) with pink noise or a single sine.
It will produce the 85dB. The signal won't look the same though and depending on the impedance swing the actual drawn power will not be the same.
The average voltage will be (assuming you measure dBSPL so without weighting.

I think I see why the original poster is confused. Hopefully this helps. The *rated* power of an amplifier and the *drawn* power are different. If you were to start playing a 20hz sin wave at 2.83v and then slowly increase the pitch up to say 20000hz and measure the sound level (with an SPL) and the power level (with a meter between the amp and speaker), the amount of power drawn would vary with the frequency. At some frequencies you would use more power than others. But you would always be at 2.83v. That's why speakers are hard. How can the power vary? Because the impediance isn't 8ohms at all frequencies and that throws out much of what we learned in undergraduate physics. The amp doesn't regulate power. It regulates voltage. And the characteristics of the speakers control how much current actually flows (the variation in impedance) at different frequencies. Impedance goes up with frequency (ignoring crossovers) and that means less current for the same voltage. The amplifier doesn't have to deliver the same current at higher frequencies (it will feel cooler at the end of this test if you do it slowly enough), but the output voltage is constant throughout.
 
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