# Math on power amplifier selection

#### vcl0124

##### Member
Hi All, I am new to this forum and these HiFi stuff. I am planning to buy DAC + power amplifier + speaker for my small living room. DAC probably something from Topping. I only have space for bookshelf speaker (something like Dali Oberon 1). For power amplifier, I am interesting in those Ncore model from audiophonics.fr but I don't know which one (power) should I choose. From Amirm's review, seems DAC performs best with 2~4Vrms output voltage (XLR). I tried to calculate the amplifier output power range with 2~4Vrms input with the equations on the specsheet of NCXXXMP and then calculate the speaker SPL with dpeaker spec. However, the amplifier output power seems way too high. I think maybe I don't understand the equation correctly. Can anyone show me an example on such calculation? Or the math I am doing is useless for selecting an amplifier?

#### NTK

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Welcome to ASR!

The rated output of a DAC is its maximum ouput. It is a level which you should never (or very rarely) reach during normal operation. It just happens that signal-to-noise ratio is usually the best when the DAC is at its maximum output. The reason is that noise is usually constant, and does not change with the signal output level. Therefore, the higher the output, the better the signal-to-noise ratio.

Since you aren't supposed to hit max level when you are listening to music, the average output from your DAC is much much lower than the "standard" 2 Vrms (for RCA outputs) or 4 Vrms (for XLR outputs).

To estimate amplifier power requirement, we usually start with a target maximum SPL (sound pressure level) at the listening position. 95 dB is considered loud, and 105 dB is very loud. Below is link to a web calculator. It is not perfect, but should give a close enough number.

Just a reminder — there is no downside to having more than enough power, other than cost.

#### tmtomh

##### Addicted to Fun and Learning
Welcome to ASR!

The rated output of a DAC is its maximum ouput. It is a level which you should never (or very rarely) reach during normal operation. It just happens that signal-to-noise ratio is usually the best when the DAC is at its maximum output. The reason is that noise is usually constant, and does not change with the signal output level. Therefore, the higher the output, the better the signal-to-noise ratio.

Since you aren't supposed to hit max level when you are listening to music, the average output from your DAC is much much lower than the "standard" 2 Vrms (for RCA outputs) or 4 Vrms (for XLR outputs).

To estimate amplifier power requirement, we usually start with a target maximum SPL (sound pressure level) at the listening position. 95 dB is considered loud, and 105 dB is very loud. Below is link to a web calculator. It is not perfect, but should give a close enough number.

Just a reminder — there is no downside to having more than enough power, other than cost.
Thanks for the link to that calculator! For far field listening (9 ft in my case) with speakers not near walls, it says you need only 5 watts to achieve 90dB spl at the listening position. Great for perspective.

OP
V

#### vcl0124

##### Member
Welcome to ASR!

The rated output of a DAC is its maximum ouput. It is a level which you should never (or very rarely) reach during normal operation. It just happens that signal-to-noise ratio is usually the best when the DAC is at its maximum output. The reason is that noise is usually constant, and does not change with the signal output level. Therefore, the higher the output, the better the signal-to-noise ratio.

Since you aren't supposed to hit max level when you are listening to music, the average output from your DAC is much much lower than the "standard" 2 Vrms (for RCA outputs) or 4 Vrms (for XLR outputs).

To estimate amplifier power requirement, we usually start with a target maximum SPL (sound pressure level) at the listening position. 95 dB is considered loud, and 105 dB is very loud. Below is link to a web calculator. It is not perfect, but should give a close enough number.

Just a reminder — there is no downside to having more than enough power, other than cost.

1. The rated power of amplifier is listed with 2/4/8ohm speaker, how to convert it to 6ohm speaker?

2. There are max. power and continous power for the amplifier, which should I use for the calculation?

3. XLR 2X the voltage input of RCA, will the amplifier output power became 4X (P=V^2/R)?

#### DonH56

##### Major Contributor
Technical Expert
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1. The rated power of amplifier is listed with 2/4/8ohm speaker, how to convert it to 6ohm speaker?

2. There are max. power and continous power for the amplifier, which should I use for the calculation?

3. XLR 2X the voltage input of RCA, will the amplifier output power became 4X (P=V^2/R)?
Not NTK but my guesses:

1. It does not really matter but an estimate would be to just average it: P_6ohms = (P_8ohms + P_4ohms) / 2.
2. For steady-state (long-term) levels use continuous amp power. For peaks use maximum amplifier power.
3. The gain is usually different and changing the input level does not change the maximum output level (different stages/sections inside the amplifier).

HTH - Don

#### Doodski

##### Major Contributor
Forum Donor
. XLR 2X the voltage input of RCA, will the amplifier output power became 4X (P=V^2/R)?
It is possible you are calculating wattage but not RMS wattage.

For RMS wattage

and... use BODMAS order of operations. (brackets, operations/exponents, divide, multiply, add and then subtract)

#### DonH56

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It is possible you are calculating wattage but not RMS wattage.

For RMS wattage

and... use BODMAS order of operations. (brackets, operations/exponents, divide, multiply, add and then subtract)
Technically there is no such thing as Watts rms... The product of rms current and rms voltage is average power. Rms times rms does not yield rms.

And yes I am aware that manufactures often (mis)use the term...

#### Doodski

##### Major Contributor
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Technically there is no such thing as Watts rms... The product of rms current and rms voltage is average power. Rms times rms does not yield rms.

And yes I am aware that manufactures often (mis)use the term...
I'm not totally understanding. I'm so used to using it I never question it.

#### DonH56

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I'm not totally understanding. I'm so used to using it I never question it.
While I have not tried to vet the article, this Wikipedia article appears to have the right of it: https://en.wikipedia.org/wiki/Root_mean_square

If you work (grunge) through the math you'll find an rms value times another rms value does not provide an rms result. Not linear terms...

HTH - Don

#### Doodski

##### Major Contributor
Forum Donor
Alrighty... Thanks for the primer and refresher. Why do manufacturers use a Prms instead of a proper power calculation?

#### DonH56

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Alrighty... Thanks for the primer and refresher. Why do manufacturers use a Prms instead of a proper power calculation.
You'd have to ask them that... Some of it may be history, as someone way back when (I am sure one of the real brains on site like JJ, Alan, or John can help out here) used it to represent average instead of (dynamic) peak power, but chances are it was a mistake by marketing that propagated. I have no idea. I got into a big debate with a certain well-known audiophile amplifier marketing/sales rep at a CES long ago, when I was a snot-nosed kid who knew everything, and durn near got tossed. Fortunately an engineer in the booth overheard and stepped in to say I was right, but "Watts rms" was the term everyone (consumers) used, so they let it go.

I would guess they are doing the proper calculation, just assigning the wrong units.

#### Doodski

##### Major Contributor
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You'd have to ask them that... Some of it may be history, as someone way back when (I am sure one of the real brains on site like JJ, Alan, or John can help out here) used it to represent average instead of (dynamic) peak power, but chances are it was a mistake by marketing that propagated. I have no idea. I got into a big debate with a certain well-known audiophile amplifier marketing/sales rep at a CES long ago, when I was a snot-nosed kid who knew everything, and durn near got tossed. Fortunately an engineer in the booth overheard and stepped in to say I was right, but "Watts rms" was the term everyone (consumers) used, so they let it go.

I would guess they are doing the proper calculation, just assigning the wrong units.
Yes, I googled it and found no real reason why they would deflate the power rating with a quoted imaginary RMS value.

#### Doodski

##### Major Contributor
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Yo yo yo @restorer-john have you any idea why manufacturers use a fake Prms value of (Vpeak*0.707)^2/Rload instead of a straight up Vpeak^2/Rload calculation. What purpose does power RMS rating serve to them? It seems counter-intutive because they deflate the power rating by multiplying by 0.707

OP
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#### vcl0124

##### Member
Thanks a lot for all the input! I think I understood the calculation more. I did below calculation to compare NC122MP, NC252MP and NC502MP. If my understanding is correct, higher power amplifier can use more "potential" of both DAC and speaker but we actually won't reach such extreme case for normal use at home, right? If so, seems like NC252MP is enough for my application.

#### Doodski

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higher power amplifier can use more "potential" of both DAC and speaker but we actually won't reach such extreme case for normal use at home, right? If so, seems like NC252MP is enough for my application.
What speakers are you using?

#### boXem | audio

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Yo yo yo @restorer-john have you any idea why manufacturers use a fake Prms value of (Vpeak*0.707)^2/Rload instead of a straight up Vpeak^2/Rload calculation. What purpose does power RMS rating serve to them? It seems counter-intutive because they deflate the power rating by multiplying by 0.707
Responding for John.
Power is the work over a unit of time.
For DC, P = UI
For AC, U RMS is the effective voltage over a unit of time, same for I RMS. So P = U RMS * I RMS * cos(teta). Teta being the phase angle between U and I. Since these are mesured in a resistor, teta = 0, P = U RMS * I RMS
Thanks a lot for all the input! I think I understood the calculation more. I did below calculation to compare NC122MP, NC252MP and NC502MP. If my understanding is correct, higher power amplifier can use more "potential" of both DAC and speaker but we actually won't reach such extreme case for normal use at home, right? If so, seems like NC252MP is enough for my application.

View attachment 108267
NC252MP is enough in most of cases

OP
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#### vcl0124

##### Member
What speakers are you using?
Not decided yet but will be some bookshelf speaker due to space limitation

#### Doodski

##### Major Contributor
Forum Donor
Not decided yet but will be some bookshelf speaker due to space limitation
Then the NC252MP will be power au plenty. You'll be able to drive the woofers to the end stops.

#### GeorgeBynum

##### Member
Why do manufacturers use a Prms instead of a proper power calculation?
OPINION ... as an over 70 year old EE who has designed amplifiers and read specs in my youth ... because it sounds better than average, and because the "PEAK POWER" advertised by manufacturers of junk is recognized by many as almost worthless.

I believe it is perceived as a value that can be maintained for at least multiple seconds, maybe minutes or hours. There's no science of which I'm aware to support that, though.

#### DonH56

##### Major Contributor
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OPINION ... as an over 70 year old EE who has designed amplifiers and read specs in my youth ... because it sounds better than average, and because the "PEAK POWER" advertised by manufacturers of junk is recognized by many as almost worthless.

I believe it is perceived as a value that can be maintained for at least multiple seconds, maybe minutes or hours. There's no science of which I'm aware to support that, though.
Sounds as good as any, especially no manufacturer wanting to report anything "average"...

The FTC requirement is 5 minutes. Whether that is science, I won't step into that...