Making sense of power requirements, decibels and sensitivity

[JustAnAudioLover]

Hi there!

I'm creating this little thread to ask a question for what is probably a very dumb question, but I can't for the life of me figure it out.

Let's say you have speakers rated for 88 dB sensitivity (2.83 V @ 1m).
The speakers' maximum SPL is 112 dB.
Their power rating is 40 to 120 W.

Now, adding 3 dB means doubling the volume. Going (112 - 88) / 3 = 8, so going from 88 dB to 112 dB is multiplying the volume by 2^8, which is 256. Am I correct on that one?

If that's true, then I don't get the numbers in the spec sheet. 1W gives you 88 dB, so to get 112 dB you should need 256W, right? If so, why is the maximum power rating 120W?

I'm sure there's some dumb mistake somewhere in my understanding of how this works, but I'm not sure why.

Could someone please explain me? Thanks

 

[staticV3]

Now, adding 3 dB means doubling the volume. Going (112 - 88) / 3 = 8, so going from 88 dB to 112 dB is multiplying the volume by 2^8, which is 256. Am I correct on that one?

See here:

Loudness volume doubling sound level change factor of perceived loudness decibel scale log compare intensities formula calculate power level noise levels volume logarithm dependence three four fold loudness sound - by what factor does level decrease

Dependance sound levels change factor perceived loudness decibel scale log compare intensities calculate power level formula noise volume doubling loudness volume - logarithm decibel 3 dBSPL 6 dB 10 dB double voltage sound pressure acoustic power loudness sound audio formula relationship...

sengpielaudio.com

If that's true, then I don't get the numbers in the spec sheet. 1W gives you 88 dB, so to get 112 dB you should need 256W, right? If so, why is the maximum power rating 120W?

Power rating might be continuous, whereas Max SPL might be a dynamic Peak value.

 

[DonH56]

First, double the power is 3 dB, but does not double the perceived volume, only increases it "a little bit". It takes 10 dB (and thus ten times the power) to double the perceived loudness (in the midrange).

Second, maximum power ratings are usually a loose measure of driver limits, time, and frequency, since different drivers have different limits (woofers handle more power than tweeters as a general rule), so the maximum power is usually at a specified frequency like 1 kHz. It is also often a continuous, not peak, rating. Ratings are often coupled to distortion so maximum power may also be a continuous rating for a maximum distortion spec, like 10% at 1 kHz or something, and maximum SPL may be for a peak short-duration power surge at some other frequency like 100 Hz. Peak SPL may require more (or less power) depending upon the frequency and speaker design. Usually max SPL is limited by driver excursion irrespective of the distortion.

Power goes as 10*log10(P2/P1) and from 88 dB to 112 dB is an increase of 24 dB (I am not sure where your division by 3 comes from). 24 dB is an increase in power of 251x, 10^(24/10) so you need 251 W at 1 m to achieve 112 dB.

Bottom line: take specs with a grain of salt.

The SPL also depends strongly upon distance from the speaker and amount of reflected energy. This online calculator provides a rough overview of what your power needs might be: http://www.hometheaterengineering.com/splcalculator.html

This old post discusses the relationship between power and SPL:

Power Needs:

For many years I have used 17 dB peak-to-average power based on an old AES article I can no longer find. Anecdotally various audio fora report 20 dB or more for movies. IME most people use much less average power than they think, but require more peak power. An online calculator can help you estimate your average power; note 80 dB is very loud to me (YMMV). Here is one:

Peak SPL Calculator

Most people think of volume in dB and most modern AVR/AVP/etc. units list dB on the volume knob. Power in dB goes as 10log10(Power_ratio) so the change in power is 10^(dB/10). Here are some reference numbers in dB and power:

1 dB is barely noticeable and requires 1.26x the power
3 dB is what most people hear as "a little louder" and requires 2x the power
6 dB is significantly louder and requires 4x the power
10 dB sounds twice as loud and requires 10x the power
17 dB is the headroom for music and requires 50x the average power
20 dB for movies requires 100x the power

If you listen at around 1 W average, then you need 50~100 W to avoid clipping on most source material. You can figure out your estimated average power from the calculator knowing your speaker's sensitivity and distance from them. Note music may be more compressed and thus require less headroom, and the loudest sounds in movies tend to be things like gun shots and explosions where a little clipping is likely unnoticeable.

HTH - Don

 

[JustAnAudioLover]

First, double the power is 3 dB, but does not double the perceived volume, only increases it "a little bit". It takes 10 dB (and thus ten times the power) to double the perceived loudness (in the midrange).

Second, maximum power ratings are usually a loose measure of driver limits, time, and frequency, since different drivers have different limits (woofers handle more power than tweeters as a general rule), so the maximum power is usually at a specified frequency like 1 kHz. It is also often a continuous, not peak, rating. Ratings are often coupled to distortion so maximum power may also be a continuous rating for a maximum distortion spec, like 10% at 1 kHz or something, and maximum SPL may be for a peak short-duration power surge at some other frequency like 100 Hz. Peak SPL may require more (or less power) depending upon the frequency and speaker design. Usually max SPL is limited by driver excursion irrespective of the distortion.

Power goes as 10*log10(P2/P1) and from 88 dB to 112 dB is an increase of 24 dB (I am not sure where your division by 3 comes from). 24 dB is an increase in power of 251x, 10^(24/10) so you need 251 W at 1 m to achieve 112 dB.

Bottom line: take specs with a grain of salt.

The SPL also depends strongly upon distance from the speaker and amount of reflected energy. This online calculator provides a rough overview of what your power needs might be: http://www.hometheaterengineering.com/splcalculator.html

This old post discusses the relationship between power and SPL:

Power Needs:

For many years I have used 17 dB peak-to-average power based on an old AES article I can no longer find. Anecdotally various audio fora report 20 dB or more for movies. IME most people use much less average power than they think, but require more peak power. An online calculator can help you estimate your average power; note 80 dB is very loud to me (YMMV). Here is one:

Peak SPL Calculator

Most people think of volume in dB and most modern AVR/AVP/etc. units list dB on the volume knob. Power in dB goes as 10log10(Power_ratio) so the change in power is 10^(dB/10). Here are some reference numbers in dB and power:

1 dB is barely noticeable and requires 1.26x the power
3 dB is what most people hear as "a little louder" and requires 2x the power
6 dB is significantly louder and requires 4x the power
10 dB sounds twice as loud and requires 10x the power
17 dB is the headroom for music and requires 50x the average power
20 dB for movies requires 100x the power

If you listen at around 1 W average, then you need 50~100 W to avoid clipping on most source material. You can figure out your estimated average power from the calculator knowing your speaker's sensitivity and distance from them. Note music may be more compressed and thus require less headroom, and the loudest sounds in movies tend to be things like gun shots and explosions where a little clipping is likely unnoticeable.

HTH - Don

Woah, that's a very detailed explanation! Very clear as well, thanks a lot for clearing things up
This makes a lot more sense now, especially the continuous power != peak power thing and the power != loudness.

(Btw that's why I love posting on these kind of forums, where you know people who actually know their stuff are gonna answer you ^^)

 

[MattHooper]

This question reminds me (and I’m having déjà vu like I asked it before…)

Many years ago, I started out with a CJ MV55 tube amp - el34s, 45w/side. I also had a locally built 28w tube amp. They worked fine for powering my Quad 63s and some smaller speakers, but when I started to get into fuller range floor standing speakers, and complex loads (eg big Thiel speakers) those amplifiers just seem to run out of steam. They didn’t control the bass very well, and the sound lacked power and dynamics. Everything just sounded underpowered.

Then I traded up to the CJ Premier 12 mono blocks, 140w/side (6550 push pull).

Once I did that everything was fine. Bass was tighter and punchier, and there was plenty of dynamics and drive. Nothing really sounded underpowered anymore.

But here’s the thing. If that’s the case, what would best explain it?

Because I generally don’t listen too loud then.
I’m guessing I was probably playing music between 70 and 80db average.

And normally, apparently, much of the time we aren’t using more than a few watts.

If that was the case, why might the smaller tube amps have sounded more tubby in the bass and less punchy and dynamic?

Could it be the difference in Transformers?
Or is essentially tripling the power rating accounting for much of that?

 

[RayDunzl]

Let's say you have speakers rated for 88 dB sensitivity (2.83 V @ 1m).
The speakers' maximum SPL is 112 dB.
Their power rating is 40 to 120 W.

A crude graphic.

I'll assume 8 ohms for the speaker:

 

[DonH56]

This question reminds me (and I’m having déjà vu like I asked it before…)

Many years ago, I started out with a CJ MV55 tube amp - el34s, 45w/side. I also had a locally built 28w tube amp. They worked fine for powering my Quad 63s and some smaller speakers, but when I started to get into fuller range floor standing speakers, and complex loads (eg big Thiel speakers) those amplifiers just seem to run out of steam. They didn’t control the bass very well, and the sound lacked power and dynamics. Everything just sounded underpowered.

Then I traded up to the CJ Premier 12 mono blocks, 140w/side (6550 push pull).

Once I did that everything was fine. Bass was tighter and punchier, and there was plenty of dynamics and drive. Nothing really sounded underpowered anymore.

But here’s the thing. If that’s the case, what would best explain it?

Because I generally don’t listen too loud then.
I’m guessing I was probably playing music between 70 and 80db average.

And normally, apparently, much of the time we aren’t using more than a few watts.

If that was the case, why might the smaller tube amps have sounded more tubby in the bass and less punchy and dynamic?

Could it be the difference in Transformers?
Or is essentially tripling the power rating accounting for much of that?

Most likely IMO is the higher-power amplifier had better transformers and higher feedback (more loop gain) resulting in much lower output impedance (much higher damping factor). Here is an article on amplifier output impedance and speaker interaction that includes some tube amplifiers: https://www.audiosciencereview.com/...amping-factor-and-speakers.23968/#post-807327 The differences in frequency response are clear.

 

[amirm]

You only need a moderate amount of power to get adequate loudness. You need a ton of power to get really loud! Get as much power as you can. If the speaker can't handle it, it will tell you (severe distortion).

 

[Old_School_Brad]

The only thing I’d add to the already well-covered answers above is that it’s quite common to see a 20 dB difference between the dBA average and the C-weighted peak when listening to modern music -especially genres with deeper bass content like some pop, house, or EDM. It is not just isolated to movie LFE content.

So keep that in mind when fiddling with the power calculators.

 

[MattHooper]

Most likely IMO is the higher-power amplifier had better transformers and higher feedback (more loop gain) resulting in much lower output impedance (much higher damping factor). Here is an article on amplifier output impedance and speaker interaction that includes some tube amplifiers: https://www.audiosciencereview.com/...amping-factor-and-speakers.23968/#post-807327 The differences in frequency response are clear.

Thanks, Don. I don’t think I had seen that thread before. I’m just going through it now.
When I had a Bryston 4B3 amplifier a while back to compare to my Premier 12s, it was clear that even the 12s didn’t control the bass as tightly as the Bryston amp. Though I found things about the bass character of each combination that I liked.

I have another question, but perhaps it’s more suitable to the thread that you linked, so I will add it there.

 

[Anton S]

You only need a moderate amount of power to get adequate loudness. You need a ton of power to get really loud! Get as much power as you can. If the speaker can't handle it, it will tell you (severe distortion).

Absolutely! Many more drivers incur damage/destruction due to clipping than because of too much power. Ever since the mid-70's, the smallest amp I've used to drive my main L/R speakers has been 250 WPC rms.

 

[Blumlein 88]

Thanks, Don. I don’t think I had seen that thread before. I’m just going through it now.
When I had a Bryston 4B3 amplifier a while back to compare to my Premier 12s, it was clear that even the 12s didn’t control the bass as tightly as the Bryston amp. Though I found things about the bass character of each combination that I liked.

I have another question, but perhaps it’s more suitable to the thread that you linked, so I will add it there.

I forget if the Premier 11 or 12 amps were used in that Carver amp challenge way back when. The final thing Bob Carver did to match the sound of the C-J Premier amp was to reduce damping in the bass frequencies and lower the power output below 100 hz because the Premiers had that issue in an audible way compared to his SS amp. I don't recall what he did to do this. I think it was altering feedback in the lower frequencies.

 

[Old_School_Brad]

Absolutely! Many more drivers incur damage/destruction due to clipping than because of too much power. Ever since the mid-70's, the smallest amp I've used to drive my main L/R speakers has been 250 WPC rms.

Technically speaking, it's always power -not clipping itself, that damages drivers.

Brain fart edit.

 

[J.M. Noble]

Technically speaking, it's always power -not clipping itself, that damages drivers.

For example, if your 25 W amplifier clips, but your tweeter can handle 40 W, no damage will occur because the amplifier can't deliver more than 25 W, even when clipping.

An amplifier rated for 25W RMS (i.e. a 14.14Vrms sine wave) into 8 ohms will have power supply rails of +/- 20V. If you put a square wave through that same amplifier, you can theoretically deliver 50 watts into that same 8 ohms.

 

[Old_School_Brad]

An amplifier rated for 25W RMS (i.e. a 14.14Vrms sine wave) into 8 ohms will have power supply rails of +/- 20V. If you put a square wave through that same amplifier, you can theoretically deliver 50 watts into that same 8 ohms.

That’s true -in theory, and assuming a regulated power supply.
In practice, however, those voltage rails will sag noticeably when the amplifier enters an overload condition. And before that, even.

 

[J.M. Noble]

That’s true -in theory, and assuming a regulated power supply.
In practice, however, those voltage rails will sag noticeably when the amplifier enters an overload condition. And before that, even.

That 25W rating is continuous RMS unless we're playing games here. Dynamic power will be much higher. We're not talking about switchmode amps if "sag" is part of the conversation. (with a full wave rectifier, 20,000μF supply capacitance, and 20V rails, ripple is around 730mV @ 1.414A and 1V @ 2A; the transformer has probably done most of its "sag" by 25W and now we're in the process of overheating it, which will take longer than it takes to fry the tweeter.)

It's also worth pointing out that the power rating of many tweeters is based on a specified pink noise signal voltage level at a specified crossover frequency/slope: that "40 watt" tweeter is getting at most 3 octaves of that signal ... and the voice coil will heat up, which increases resistance & reduces power delivered for a given input signal "power" (really voltage) level.

The tweeter's voice coil is probably wound with #32AWG or smaller copper wire, which is only rated for about half an amp (chassis wiring)--which works out to 2 watts for an 8 ohm tweeter. We accept higher temps in voice coils, of course, so maybe we can double that to 4 watts actually dissipated. If you've ever had to design or specify a heatsink, you'll realize that's a lot of heat to dump out of a low mass coil in a confined space.

 

[Anton S]

Is it not true that, once the capability of an amp's power supply rails is surpassed and the waveforms are clipped, a lot of high frequency harmonics are produced, and this is what generally blows a driver?

 

[J.M. Noble]

Is it not true that, once the capability of an amp's power supply rails is surpassed and the waveforms are clipped, a lot of high frequency harmonics are produced, and this is what generally blows a driver?

For tweeters specifically ... maybe, in extreme cases. Rod Elliott has some interesting analysis of this and other potential failure modes.

As someone who worked in car audio and replaced a lot of tweeters, I'm not quite as dismissive as he is.

 

[Anton S]

For tweeters specifically ... maybe, in extreme cases. Rod Elliott has some interesting analysis of this and other potential failure modes.

As someone who worked in car audio and replaced a lot of tweeters, I'm not quite as dismissive as he is.

Another page of Elliott's site is also worth a read, as well. He believes that the IM distortion in amplifier clipping is the predominant factor. Not sure I completely agree with that, but I am certainly in agreement with his conclusion:

"The moral of the story is to avoid clipping at all times - even momentary (supposedly inaudible) clipping will generate an unwanted low frequency or subsonic signal whose frequency will be completely unrelated to anything in the programme material. All it will achieve is cone displacement and increased intermodulation distortion. Unfortunately, it's simply not possible to avoid clipping completely unless your power amplifiers are rated for far more power output than your speakers can handle. Should a very powerful amplifier still be driven to clipping, your loudspeakers will have a very short life."

 

[DanielT]

I posted this in another thread but it might fit better in this one. An example with a piece of music. Mostly to show that it may also be necessary to have a lot of amp power in the higher frequencies. If it is dynamic music that requires it, that is:

I will use the track Michael Ruff - Speaking in Melodies - Wishing Well (well-recorded fusion) as an example, as there are several high-frequency peaks that require a lot of power from the amplifier. First, the voltage, current and power for the entire signal are shown:

As you can see, we get an active power of 710 Wp at most.

Then we only look at frequencies above 7 kHz (HP filtering with 3rd order Butterworth):

For frequencies above 7 kHz, we get an active power of about 425 Wp. In addition, the strongest high-frequency peak does not occur at the same time as the strongest peak for the total signal.


We can also look only at frequencies above 10 kHz (HP filtering with 3rd order Butterworth):

For frequencies above 10 kHz we get an active power of about 225 Wp. Furthermore, the strongest high-frequency peak does not occur at the same time as the strongest peak for the total signal.

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