Audio power

Sound measurements
Characteristic	Symbols
Sound pressure	p, SPL, LPA
Particle velocity	v, SVL
Particle displacement	δ
Sound intensity	I, SIL
Sound power	P, SWL, LWA
Sound energy	W
Sound energy density	w
Sound exposure	E, SEL
Acoustic impedance	Z
Audio frequency	AF
Transmission loss	TL

Audio power is the electrical power transferred from an audio amplifier to a loudspeaker, measured in watts. The electrical power delivered to the loudspeaker and its sensitivity determines the sound power level generated (with the rest being converted to heat).

Amplifiers are limited in the electrical energy they can amplify, loudspeakers are limited in the electrical energy they can convert to sound energy without distorting the audio signal or destroying themselves. These power ratings are important to consumers finding compatible products and comparing competitors.

Power calculations

A graph of instantaneous power over time for a waveform, with peak power labeled P₀ and average power labeled P_avg

Since the instantaneous power of an AC waveform varies over time, AC power, which includes audio power, is typically measured as an average over time. It is based on this formula:

$P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}v(t)\cdot i(t)\,dt\,$

For a purely resistive load, a simpler equation can be used, based on the root mean square (RMS) values of the voltage and current waveforms:

$P_{\mathrm {avg} }=V_{\mathrm {rms} }\cdot I_{\mathrm {rms} }\,$

In the case of a steady sinusoidal tone (not music) into a purely resistive load, this can be calculated from the peak amplitude of the voltage waveform (which is easier to measure with an oscilloscope) and the load's resistance:

$V_{\mathrm {rms} }\cdot I_{\mathrm {rms} }={\frac {V_{\mathrm {rms} }^{2}}{R}}={\frac {V_{\mathrm {peak} }^{2}}{2R}}\,$

Though a speaker is not purely resistive, these equations are often used to approximate power measurements for such a system.

Example

An ideal (100% efficient) push-pull amplifier with a 12-volt peak-to-peak supply can drive a signal with a peak amplitude of 6 V. Into an 8 ohm (see impedance) loudspeaker this would deliver:

P_peak = (6 V)² / 8 Ω = 4.5 watts peak instantaneous.

If this signal is sinusoidal, its RMS value is 6 V × 0.707 = 4.242 V(RMS). This voltage into a speaker load of 8 Ω gives a power of:

P_avg = (4.242 V)² / 8 Ω = 2.25 watts average.

Thus the output of an inexpensive car audio amplifier is limited by the voltage of the alternator. In most actual car systems, the amplifiers are connected in a bridge-tied load configuration, and speakers are no higher than 4 Ω. High-power car amplifiers use a DC-to-DC converter to generate a higher supply voltage.

Sine wave power

The term sine power is used in the specification and measurement of audio power. A meaningful and reliable measure of the maximum power output of an audio amplifier - or the power handling of a loudspeaker - is continuous average sine wave power. The peak power of a sine wave of RMS value X is √2*X; conversely, the RMS value of a sine wave of peak X is (1/√2)*X. For a resistive load, the average power is the product of the RMS current and RMS voltage.

Harmonic distortion increases with power output; the maximum continuous power output of an amplifier is always stated at a given percentage of distortion, say 1% THD+N at 1 kHz. Considerably more power can be delivered if distortion is allowed to increase; some manufacturers quote maximum power at a higher distortion, like 10%, making their equipment appear more powerful than if measured at an acceptable distortion level.

In common use, the terms "RMS power" or "watts RMS" are erroneously used to describe average power. A 100 "watt RMS" amplifier can produce a sine-wave of 100 watt average into its load. With music, the total actual power would be less. With a square-wave, it would be more.

In the US on May 3, 1974, the Amplifier Rule CFR 16 Part 432 (39 FR 15387) was instated by the Federal Trade Commission (FTC) requiring audio power and distortion ratings for home entertainment equipment to be measured in a defined manner with power stated in RMS terms. (See more in the section Standards at the end of this article). The erroneous term "watts RMS" is actually used in CE regulations.[1]

DIN power

DIN (Deutsches Institut für Normung, German Institute for Standardization) describes in DIN 45xxx several standards for measuring audio power. The DIN-standards (DIN-norms) are still in common use in Europe. Article describing the DIN-standards in broad terms.

PMPO

Peak Music Power Output (PMPO) (sometimes misused in advertising as Peak momentary performance output) is a much more dubious figure of merit, of interest more to advertising copy-writers than to consumers. The term PMPO has never been defined in any standard but it is often taken to be the sum of some sort of peak power for each amplifier in a system. Different manufacturers use different definitions, so that the ratio of PMPO to continuous power output varies widely; it is not possible to convert from one to the other. Peak power is twice the sine wave power, so, for example, a 5 channel system using amplifiers which can output 10 watts for a few milliseconds with an unspecified percentage for distortion would be specified as '100 watts PMPO'. Sometimes, an extra factor is applied to get an even higher figure. The term PMPO is considered misleading and meaningless by audio professionals. Most amplifiers can sustain their PMPO for only a very short time; loudspeakers are not designed to withstand their stated PMPO for anything but a momentary peak without serious damage. Sometimes the PMPO which can be delivered into an unrealistic resistive load, rather than a real loudspeaker, is quoted. There have been genuine attempts to measure 'peak music power' as described below, but in general the term is not at all useful.

The true power output of an amplifier can be estimated by examining the input current. Linear amplifiers tend to be about 60% efficient at best. A switch-mode amplifier (known as class D) can achieve much higher efficiency, sometimes as high as 95%. A linear car amplifier labeled "500 W PMPO" but fitted with a 5-amp fuse can, at most, deliver an average power of 5 A × 14.4 V × 60%, or about 43 watts. (100% efficiency is always used for PMPO)

Peak momentary power output and peak music power output are two different measurements with different specifications and should not be used interchangeably. Every time a manufacturer uses different words such as pulse or performance they do so to reflect some non standard system of measurement of their own, where only they know what it means. The Federal Trade Commission is putting an end to this with Federal Trade Commission (FTC) Rule 46 CFR 432 (1974), affecting Power Output Claims for Amplifiers Utilized in Home Entertainment Products.
Remembering that neither spec is universally standardized and as stated before different companies use different definitions, The typically understood differences between Peak Momentary and Peak Music Power Output are as follows. Peak Momentary Power Output is measured by the components ability to pass a single peak or a short train of peaks, usually less than ten contiguous wave cycles, without distortion or loss in power output. Whereas Peak Music Power Output is measured by the components ability to pass at least ten contiguous wave cycles without distortion or loss in power output. RADAR amplifiers only care about peak momentary impulse power and CW Linear amplifiers only care about RMS because a continuous sine wave is all they produce.

Power and loudness in the real world

Perceived "loudness" varies logarithmically with output power (other inversely proportionate factors are; frequency, number and material of objects through which the sound waves must travel, as well as distance between source and receiver) a given change in output power produces a much smaller change in perceived loudness. Consequently it is useful and accurate to express perceived loudness in the logarithmic decibel (dB) scale; a change of 1 dB, which corresponds to a 25.9% change in power level, is considered to be the smallest change in sound power level perceivable by the average human ear under idealized test conditions. An increase/decrease of 3 dB corresponds to a doubling/halving of power and distance of average perceivability. The sensitivity of loudspeakers, rather than merely the often-quoted power-handling capacity, is important. Many high quality domestic speakers have a sensitivity of 84 dB for 1 W at 1 meter, but professional speakers can have a figure of 90 dB for 1 W or even 100 dB (especially for some large-coned woofers). I.E., An '84 dB' source "speaker" would require a 400-watt amplifier (assuming it didn't burn out) to produce the same audio energy as a '90 dB' source being driven by a 100-watt amplifier, or a '100 dB' source being driven by a 9.92 watt amplifier(though in practice modern sub-woofers are often driven by high power amps to overcome the restriction of a small enclosure through the use of equalization). This does not mean a bigger speaker can produce more sound with less overall power. Just that a larger speaker can typically handle more initial power and so requires less amplification to achieve the same high level of output. This means using a speaker with a higher dB rating can be more advantageous as many amplifiers inevitably produce a certain amount of distortion for a given level of amplification. So, (more speaker)+(less amp.)=(same "loudness")+(less distortion).

A better measure of the 'power' of a system is therefore a plot of maximum loudness before clipping, in dB SPL, at the listening position intended, over the audible frequency spectrum. A good system should be capable of generating higher sound levels below 100 Hz before clipping, as the human ear is less sensitive to low frequencies, as indicated by Equal-loudness contours.

'Music power' — the real issues

The term "Music Power" has been used in relation to both amplifiers and loudspeakers with some validity. When live music is recorded without amplitude compression or limiting, the resulting signal contains brief peaks of very much higher amplitude (20 dB or more) than the mean, and since power is proportional to the square of signal voltage their reproduction would require an amplifier capable of providing brief peaks of power around a hundred times greater than the average level. Thus the ideal 100-watt audio system would need to be capable of handling brief peaks of 10,000 watts in order to avoid clipping (see Programme levels). Most loudspeakers are in fact capable of withstanding peaks of several times their continuous rating (though not a hundred times), since thermal inertia prevents the voice coils from burning out on short bursts. It is therefore acceptable, and desirable, to drive a loudspeaker from a power amplifier with a higher continuous rating several times the steady power that the speaker can withstand, but only if care is taken not to overheat it; this is difficult, especially on modern recordings which tend to be heavily compressed and so can be played at high levels without the obvious distortion that would result from an uncompressed recording when the amplifier started clipping.

An amplifier can be designed with an audio output circuitry capable of generating a certain power level, but with a power supply unable to supply sufficient power for more than a very short time, and with heat sinking that will overheat dangerously if full output power is maintained for long. This makes good technical and commercial sense, as the amplifier can handle music with a relatively low mean power, but with brief peaks; a high 'music power' output can be advertised (and delivered), and money saved on the power supply and heat sink. Program sources that are significantly compressed are more likely to cause trouble, as the mean power can be much higher for the same peak power. Circuitry which protects the amplifier and power supply can prevent equipment damage in the case of sustained high power operation.

More sophisticated equipment usually used in a professional context has advanced circuitry which can handle high peak power levels without delivering more average power to the speakers than they and the amplifier can handle safely.

Power handling in 'active' speakers

Active speakers comprise two or three speakers per channel, each fitted with its own amplifier, and preceded by an electronic crossover filter to separate the low-level audio signal into the frequency bands to be handled by each speaker. This approach enables complex active filters to be used on the low level signal, without the need to use passive crossovers of high power-handling capability but limited rolloff and with large and expensive inductors and capacitors. An additional advantage is that peak power handling is greater if the signal has simultaneous peaks in two different frequency bands. A single amplifier has to handle the peak power when both signal voltages are at their crest; as power is proportional to the square of voltage, the peak power when both signals are at the same peak voltage is proportional to the square of the sum of the voltages. If separate amplifiers are used, each must handle the square of the peak voltage in its own band. For example, if bass and midrange each has a signal corresponding to 10 W of output, a single amplifier capable of handling a 40 W peak would be needed, but a bass and a treble amplifier each capable of handling 10 W would be sufficient. This is relevant when peaks of comparable amplitude occur in different frequency bands, as with wideband percussion and high-amplitude bass notes.

For most audio applications more power is needed at low frequencies. This requires a high-power amplifier for low freqencies (e.g., 200 watts for 20-200 Hz band), lower power amplifier for the midrange (e.g., 50 watts for 200 to 1000 Hz), and even less the high end (e.g. 5 watts for 1000-20000 Hz). Proper design of a bi/tri amplifier system requires a study of driver (speaker) frequency response and sensitivities to determine optimal crossover frequencies and power amplifier powers.

Standards

In response to a Federal Trade Commission order, the Consumer Electronics Association has established a clear and concise measure of audio power for consumer electronics. They have posted an FTC approved product marking template on their web site and the full standard is available for a fee. Many believe this will resolve much of the ambiguity and confusion in amplifier ratings. There will be ratings for speaker and powered speaker system too. This specification only applies to audio amplifiers. A UE counterpart is expected and all equipment sold in the US and Europe will be identically tested and rated. [2]
CEA-490-A Title: Test Methods of Measurement for Audio Amplifiers
Federal Trade Commission (FTC) Rule, Power Output Claims for Amplifiers Utilized in Home Entertainment Products, 46 CFR 432 (1974).

In the US on May 3, 1974, the Amplifier Rule CFR 16 Part 432 (39 FR 15387) [3] was instated by the Federal Trade Commission (FTC) requiring audio power and distortion ratings for home entertainment equipment to be measured in a defined manner with power stated in RMS terms. This rule was amended in 1998 to cover self-powered speakers such as are commonly used with personal computers (see examples below).

This regulation did not cover automobile entertainment systems, which consequently still suffer from power ratings confusion. However, a new regulation called CEA 2006 includes car electronics, and is being slowly phased into the market by many manufacturers.

There are no similar laws in much of the rest of the earth.

Actual ratings compared

To get an idea of the relationship between PMPO watts and watts "RMS", consider the following numbers advertised for some current loudspeakers. These models have been selected at random, and inclusion in or exclusion from this list is neither a recommendation nor a criticism.

• Teac PM-100 3D surround-sound speakers: 16 W RMS, 180 W PMPO
• Kinyo "200 W" PC speakers: 3 W RMS, 200 W PMPO
• Philips Fun Power Plus MMS-102 PC speakers: 10 W RMS, 120 W PMPO (The Philips data sheet mentions only the "RMS" value; the PMPO value is claimed by retailers.)

This list shows that PMPO figures are hugely exaggerated compared with the "RMS" values used by professionals. It also shows that there is little consistency in how much the figures are exaggerated making them almost totally meaningless.

See also

• Programme levels
• Audio quality measurement

External links

• Amplifier Power Ratings (and How to calculate satisfactory PMPO values) by Rod Elliott
• Understanding amplifier power ratings
• The so called "RMS Power"
• Meaningless RMS Power - Why there is no such thing as 'RMS watts' or 'watts RMS' and never has been
• Audio power and the corresponding factors: Subjectivly sensed loudness (volume), objectively measured sound pressure (voltage), and theoretically calculated sound intensity (acoustic power)