# Max Voltage for Speaker of Given Power Rating

I have been looking into the design of loudspeaker drivers and would like to know how to determine the maximum voltage which can be delivered to a given speaker.

From Ohm's law we know that P = V^2 / R. Therefore with for a speaker of any given power rating it would seem that max voltage could be determined by the formula:

V = sqrt(P * R)

Therefore for an 8ohm speaker with a power rating of 10 watts, it would seem that max voltage is around 9 volts. (sqrt(8 * 10 = 80) = 8.944 ~= 9)

What I'd like to know is which voltage measurement this refers to out of the following:

-Peak (where the speaker could handle a range of 0v -> 9v)

-RMS (where the speaker could handle an RMS value of 9v)

-Peak-to-peak (where the speaker could handle a range of -9v -> 9v)

If anyone could clarify this for me I'd greatly appreciate it.

• Depends on the units in which speaker power rating was specified, peak or RMS. To me RMS is the only valid value you should use. Al this peak stuff is just advertising. – Oldfart Apr 26 '18 at 3:15
• A power supply has to supply peak voltages and peak currents into the load. So the voltage rails have to be sufficient for that. Power dissipation is related to RMS voltages and currents and not peak values. So the calculation is different. You will need $\pm\sqrt{2\cdot P\cdot R}$ for the supply rails (plus enough margin on both sides for the circuits to operate well.) So $5\:\text{W}$ into $8\:\Omega$ suggests $\pm 9\:\text{V}$, plus perhaps an added two to three volts for circuitry. A $\pm 12\:\text{V}$ power supply would be enough. (Bridging has a different answer.) – jonk Apr 26 '18 at 3:19
• @jonk I suggest you turn that into an answer. – Oldfart Apr 26 '18 at 3:24
• The answer depends which "power rating" the specs have in mind. Depending on that, the question text already contains the answer. – Ale..chenski Apr 26 '18 at 3:30
• – jonk Apr 26 '18 at 3:33

As oldfart commented, use of the word 'peak' in audio is just marketing hype. What is real is true RMS watts into a given load of 4 to 8 ohms, with some amplifiers giving specs for a 1 or 2 ohm load. This is proved by testing with an audio spectrum/THD analyzer and documented.

At no time did I ever do 'peak' testing because it is ambiguous at best, and usually miss-leading the consumer. True 'peak' testing usually involved amplifier clipping distortion and/or speaker thumping or gritty sounds. An amplifier that match's or is a bit stronger than the speakers RMS rating is ok. It means no distortion until the speaker pops or sounds gritty.

This game of 'peak' value is just that. The reason is that you can mathematically play games with time and say things like for 10 mS (1/100th) of a second this amplifier can put out 50% to 100% more power. Heck, for 1 mS the power supply could dump several times its RMS load.

RMS refers to continuous power at a certain THD level into a defined load, and is the only rating to be trusted. The same scenario in terms of peak power has no meaning, as the marketing guru's are talking about very brief periods of time that do not relate to what the continuous volume can be.

Peak power is not to be confused with 'headroom', which is less abstract and means the power supply is over built by 20% or so, so at full volume sudden peaks in music volume from 24 bit or 32 bit audios enormous dynamic range do not overload the amps power supply. It is a built in safety margin when you crank up the volume to loud (but not distorted) levels.

If you hear so called 'peaks' it will be in the form of distortion from the amplifier and/or your speakers, and is fair warning to turn the volume down until it sounds very clean.

@jonk did the math that makes it clear. An 8 ohm speaker driven by a class AB (typical) amplifier with +/- 12 volt power will only give you 5 watts RMS. A 4 ohm speaker would give you 20 watts RMS. Combine them for a 2 ohm load (if the amp is rated for it) and you get 80 watts RMS. At no time was the word 'peak' mentioned, as it represents power into a abnormally low load for a mS or less, which has no meaning in real-world conditions where sustained clean sound is what counts.

• If anyone wants some great speakers, I can sell you some 10kW peak* tweeters *(peak meaning <1uS) – BeB00 Apr 27 '18 at 1:11

Typically speakers are rated for power in RMS but may be fake spec’d in peak power limits for marketing bias reasons or best case with both.

I agree with all the above (5 comments at the time of writing)

There are 3 considerations : speaker damage due to:
1) heat,
2) excessive bass travel on cone and ...
3) clipping or high THD with wide dynamic range bursts not found on highly compressed radio music. Excessive peaks can cause gross odd harmonic distortion from clipping or gradual rapid rise in THD from coil travel outside the magnet edge and reduction of magnet strength from a 40’C rise or more of sustained Max power boom box operation.

Therefore it is possible to use a 20W design amp on a 10W speaker as long as you realize the risks of pushing it to output limits and the type of music or voice demands an appreciation of what is often called the crest factor of peak / rms ratio.

Given the supply voltage demands for linear bipolar amps and single supply bridge amps and class D,E etc varies, the supply must be able to meet the peak power load and RMS load specs you define for the reasons I suggested.

The most efficient would be a Class D bridge amp with 12V single supply requiring no huge caps for AC coupling.

• It is worth noting that while RMS is useful as a metric for some things, using a power amp rated for the same RMS power as the speaker will be sub optimal with real audio content as real audio has quite a high peak to RMS ratio (Typically well over 10dB) and providing the Xmax limit (Mechanical) and thermal limits (RMS integrated over a few seconds) are not exceeded, speakers can take a hell of a lot more short term power then the RMS number would imply. Power amplifiers with thermal design for RMS rating, but 10dB or so of voltage and current headroom for short term peaks are a good thing. – Dan Mills Apr 26 '18 at 14:09
• Yes Dan thats a better explanation of the crest factor or desired Peak/rms ratio – Sunnyskyguy EE75 Apr 26 '18 at 14:28

Given that music signals might easily have a 10db dynamic range between peak and average sound levels, a music signal might have a 10 watt average level and also 100 watt peak transients. If a 20 watt amplifier is trying to produce that signal there will be significant clipping distortion.

The frequency distribution of that clipping distortion will be almost entirely outside the range of signal that your speaker can respond to. Therefore that distortion will be almost entirely converted to heat instead of sound.

In that case it is possible to blow out a 30 watt speaker while using a 20 watt amplifier on a signal with an average of 10 watts. Or you could have used a 100 watt amplifier to play that same signal through a 30 watt speaker and experience no problems at all.

In broad generalities, you can use a higher amplifier rating with less speaker danger than a lower amplifier rating. With too much power, you have a danger of slamming the speaker voice coil into the magnet like a castanet on bass tones (a very obvious sound most people never experience). With too little power you have a danger of melting voice coils from high frequency distortion (almost never happens in the 10 watt neighborhood).

Also a speaker's DC resistance is not very representative of it's AC impedance

That's just a long winded way of saying that the voltage limit of an amplifier is not the best way to determine if an amplifier is a good match to a speaker. If I was designing a speaker driver, I would base my voltage target on whatever power supply I could easily obtain. The bigger, the better, within cost restraints. 5 volts is quietly acceptable especially for speech or other non-musical signals (think about the various music players that run on USB), 12 volts is reasonably loud and easy (car stereos), etc.

On the other hand, if a speaker is rated at 10 watts, you can assume that a 10 watt amplifier should be 'loud enough' as long as you don't try to turn it up to eleven. Even if your power calculations are off by double, the logarithmic nature of sound will overwhelm the difference if all you are worried about is if you will be able to hear the signal.