Calculating the amplifier power required for good dynamic range...

[humblebee]

It is often said that more power means more dynamic sound..
But the question is how much power for how much dynamic sound...
I mean how much power will be sufficient to produce how much dynamic range...is there a way to know this?
(This question becomes imp in this age of affordable Multibit DACs esp from like Schiit Audio...)

But there are also other factors...

So, with my limited knowledge I try to come up with an Amp Power Requirements Calculator of sorts...
Its incomplete...so please chip in...
Please add/remove/correct this list of factors...

Factor 1
Efficiency (actual wattage vs advertised)
American 50% (so an amp advertised at 120wpc will actually be 60wpc)
British 80% (here 120wpc wull mean 96wpc)
Lets say we have advertised wattage /2 or (lets abbreviate to AW)

Factor 2
Amp sounds best at 50% volume
So at -6db
So at 1/4 wattage
So, AW/4

Factor 3
Dynamic Range variation in music from avg levels
15db max for classical (read it online)
So, 3x5=15db
So, 2^5=32times the wattage is required for good dynamic range variation
So, AW/32

Factor 4
2 speakers means doubling of volume levels
So, AWx2

Factor 5
176khz requires quadrupling of power [look at time domain optimization (vs frequency domain optimization) by Rob Watts of Chord Electronics. This quadrupling is what I conclude naturally from that]
So, AW/4

Factor 6
Good amps have 4 times reserve
So, 400% watts
So, AWx4

Thus, a 128watts per channel amp, will be good at producing...
128 2 4 32 2 4 4 = 1watt at speaker spl
That is if spkr has sensitivity of 85db then a 128 watt amp will produce a good sound at 85db avg level (100db max sounds, as 85+15=100; factor 3)

Now, relating it to dynamic range
16 bits of sound (digital music) means 96db
So, how does it relate to an amp power....

I mean to arrive at an amp power figure that corresponds to dynamic range it will produce as originally stated...
i.e something like ... a 128wpc amp will produce 16 bits of dynamic range sufficiently loud (max 100db sounds)

Thanks in advance

 

[jls001]

Regarding dynamic range, I think one should consider the ambient noise floor of the room, the comfortable sound pressure level at which one listens, and then the power available in the amplifier.

The dynamic range is the difference between the quietest passage and the loudest passage in music. Your ability to hear the quietest passage in music depends on background noise in the room. In a very quiet room, you'll be able to hear fainter sound. For the sake of illustration, let's assume we have a speaker playing at 86 dB SPL, and the speaker is 86 dB efficient. So with 1W of power at 1m distance from speakers we have 86 dB SPL. Let's assume further that with that SPL we can hear the quietest passages in the music. Unless we know the exact ambient noise floor of a room it is impossible to say what is the quietest passage that one can hear, but for the sake of our argument we'll assume that we are halfway of the dynamic range when playing at 86 dB SPL. So we need to increase amplifier output to take the music from 86 dB SPL to 15/2 = 7.5 dB more, meaning 93.5 dB SPL.

Raising power by 3 dB to 2W will raise the output power to twice, BUT we need to raise the output power by 6 dB to double SPL. So 4W is needed to double SPL from 1W.

We're now at 86+3=89 dB SPL. Raising power by another 6 dB to 16W will take the SPL to 92 dB SPL. Upping power output further by 6 dB to 64W will take SPL to 95, etc.

However, the above does not say anything about the ability to play music to a certain target SPL level without distortion, which is probably what we're more interested in.

Note the differences in the use of dB and dB SPL. Also "loudness" being a subjective term, is not used. Only measurable parameters are used in the description to avoid ambiguity.

 

[square_wave]

Adding to what Prem said,

In laymans terms, what gives you dynamic range depends a lot on matching the right amp to the right speaker technically. Sensitivity and freq vs impedence curves, phase angle are all important factors that contributes to the match. Bake this information with the ambient noise in your room and you will get the full picture.

A well designed 10 watt per channel SET amp matched to a speaker designed to function well with such an amp may sound more dynamic than a mega watt amp connected to a power hungry speaker.

If you peer at the spec sheet, this can look very strange.

Theoretically, you can figure all this out with specs ( the right kind ). But most mainstream marketing does not divulge these kind of specs.

Also bear in mind that there are good reasons why some speakers are designed in a certain way which might make it a tough load on an amplifier. And vice versa too. It all finally boils down to what kind of sound you are looking for. You need to weigh the pros and cons to see what floats your boat. There is no replacement for actually walking the street and experiencing it for yourself.

 

[prem]

Squarewave I didn't say anything It was jls001 who had responded

 

[square_wave]

Sorry Prem.. please excuse the typo

 

[humblebee]

Thanks for clarifying all this. It makes sense and I now know that I was thinking in the right direction. I also was thinking something similar but was making the mistake of taking db for db spl.

Regarding dynamic range, I think one should consider the ambient noise floor of the room, the comfortable sound pressure level at which one listens, and then the power available in the amplifier.

Unless we know the exact ambient noise floor of a room it is impossible to say what is the quietest passage that one can hear, but for the sake of our argument we'll assume that we are halfway of the dynamic range when playing at 86 dB SPL. So we need to increase amplifier output to take the music from 86 dB SPL to 15/2 = 7.5 dB more, meaning 93.5 dB SPL.

2 questions regarding your answer...
- How do we measure room noise floor? In a decent system isn't the system's own noise floor at like 0db?
- You say ... assume that we are half way there. Some power must have been required to take us half way there. Isn't that the other 64watts? Making the total to 128 watts.

An alternative line of thinking is that every 10db increase in volume is equal to doubling of perceived sound. And that requires 10 times the power.
So for 20db variation, we require 100wpc.

 

[jls001]

2 questions regarding your answer...
- How do we measure room noise floor? In a decent system isn't the system's own noise floor at like 0db?
- You say ... assume that we are half way there. Some power must have been required to take us half way there. Isn't that the other 64watts? Making the total to 128 watts.

An alternative line of thinking is that every 10db increase in volume is equal to doubling of perceived sound. And that requires 10 times the power.
So for 20db variation, we require 100wpc.

For measuring room noise floor we can use a calibrated microphone connected to a sound card. A very quiet room will be typically 40-50 dB SPL. To get a rough idea, use Android or iOS app for SPL measurement. Not very accurate, but will give you ballpark figures. An Android app on my old phone showed my room ambient noise as ~55 dB. This is with all windows closed, fans switched off, no music playing.

A modern equipment's noise floor will be typically in the range of -90 to -100 dB or even better, BUT we need to know how high are the harmonics above the noise floor. For example, if the first harmonic is at -80 dB, then I think the effective noise floor is -80 dB.

In the example calculation, it was assumped that 1W of power had already taken us to 86 dB SPL. We need 64 Watts more to take us to 95 dB SPL.

For perceived loudness doubling, 10 dB is NOT ten times in linear scale.