A 1 kHz sine tone played at 89.3 dBA SPL measured at the Mouth Reference Point (MRP) is
recorded by a calibrated Type 4938 B&K reference microphone. The RMS level of the recorded
signal is noted.

各位大侠，谁能告诉我一下，RMS到底是怎么定义的？非常感谢！

额定功率,长期老化功率实验公式

Root mean square

In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids.

It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a special case of the power mean with the exponent p = 2.

Definition

$x_\text{rms} = \sqrt{ \langle x^2 \rangle} \,\!$ (where $\langle \ldots \rangle$ denotes the arithmetic mean)

Ways of calculating the root mean square

The RMS of a collection of $n$ values $\{x_1,x_2,\dots,x_n\}$ is

$x_{\mathrm{rms}} = \sqrt {{1 \over n} \sum_{i=1}^{n} x_i^2} = \sqrt {{x_1^2 + x_2^2 + \cdots + x_n^2} \over n}$

The corresponding formula for a continuous function $f (t)$ defined over the interval $T_1 \le t=$ is

$f_{\mathrm{rms}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {[f(t)]}^2\, dt}}$

The RMS of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a series of equally spaced samples. Additionally, the RMS value of various waveforms can also be determined without calculus, as shown by Cartwright

Uses

The RMS value of a function is often used in physics and electrical engineering.

Average electrical power

Engineers often need to know the power, $P$ , dissipated by an electrical resistance, $R$ . It is easy to do the calculation when a constant current, $I$ flows through the resistance. For a load of R ohms, power is defined simply as:

$图片点击可在新窗口打开查看$

However, if the current is a time-varying function, $I (t)$ , this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. If the function is periodic (such as household AC power), it is nonetheless still meaningful to talk about the average power dissipated over time, which we calculate by taking the simple average of the power at each instant in the waveform or, equivalently, the squared current. That is,

$图片点击可在新窗口打开查看$	$图片点击可在新窗口打开查看$ (where $图片点击可在新窗口打开查看$ denotes the mean of a function)
	$图片点击可在新窗口打开查看$ (as R does not vary over time it can be factored out)
	$图片点击可在新窗口打开查看$ (by definition of RMS)

So, the RMS value, $I RMS$ , of the function $I (t)$ is the constant signal that yields the same average power dissipation.

We can also show by the same method that for a time-varying voltage, $V (t)$ , with RMS value $V RMS$ ,

$图片点击可在新窗口打开查看$

This equation can be used for any periodic waveform, such as a sinusoidal or sawtooth waveform, allowing us to calculate the mean power delivered into a specified load.

By taking the square root of both these equations and multiplying them together, we get the equation

$图片点击可在新窗口打开查看$

Both derivations depend on voltage and current being proportional (i.e., the load, R, is purely resistive). Reactive loads (i.e., loads capable of not just dissipating energy but also storing it) are discussed under the topic of AC power.

In the common case of alternating current when $I (t)$ is a sinusoidal current, as is approximately true for mains power, the RMS value is easy to calculate from the continuous case equation above. If we define $I p$ to be the amplitude of the current, then:

$图片点击可在新窗口打开查看$

where t is time and ω is the angular frequency (ω = 2π/T, whereT is the period of the wave).

Since $I p$ is a positive constant:

$图片点击可在新窗口打开查看$

Using a trigonomentric identity to eliminate squaring of trig function:

$图片点击可在新窗口打开查看$

but since the interval is a whole number of complete cycles (per definition of RMS), the $sin$ terms will cancel, leaving:

$图片点击可在新窗口打开查看$

A similar analysis leads to the analogous equation for voltage:

$图片点击可在新窗口打开查看$

Because of their usefulness in carrying out power calculations, listed voltages for power outlets, e.g. 120 V (USA) or 230 V (Europe), are almost always quoted in RMS values, and not peak values. Peak values can be calculated from RMS values from the above formula, which implies V_p = V_RMS × √2, assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 × √2, or about 170 volts. The peak-to-peak voltage, being twice this, is about 340 volts. A similar calculation indicates that the peak-to-peak mains voltage in Europe is about 650 volts.

It is also possible to calculate the RMS power of a signal. By analogy with RMS voltage and RMS current, RMS power is the square root of the mean of the square of the power over some specified time period. This quantity, which would be expressed in units of watts (RMS), has no physical significance. However, the term "RMS power" is sometimes used in the audio industry as a synonym for "mean power" or "average power". For a discussion of audio power measurements and their shortcomings, see Audio power.

Measurements of AC magnitude

So far we know that AC voltage alternates in polarity and AC current alternates in direction. We also know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a "waveform." We can measure the rate of alternation by measuring the time it takes for a wave to evolve before it repeats itself (the "period"), and express this as cycles per unit time, or "frequency." In music, frequency is the same as pitch, which is the essential property distinguishing one note from another.

However, we encounter a measurement problem if we try to express how large or small an AC quantity is. With DC, where quantities of voltage and current are generally stable, we have little trouble expressing how much voltage or current we have in any part of a circuit. But how do you grant a single measurement of magnitude to something that is constantly changing?

One way to express the intensity, or magnitude (also called the amplitude), of an AC quantity is to measure its peak height on a waveform graph. This is known as the peak or crest value of an AC waveform:

图片点击可在新窗口打开查看

Another way is to measure the total height between opposite peaks. This is known as the peak-to-peak (P-P) value of an AC waveform:

图片点击可在新窗口打开查看

Unfortunately, either one of these expressions of waveform amplitude can be misleading when comparing two different types of waves. For example, a square wave peaking at 10 volts is obviously a greater amount of voltage for a greater amount of time than a triangle wave peaking at 10 volts. The effects of these two AC voltages powering a load would be quite different:

图片点击可在新窗口打开查看

One way of expressing the amplitude of different waveshapes in a more equivalent fashion is to mathematically average the values of all the points on a waveform's graph to a single, aggregate number. This amplitude measure is known simply as the average value of the waveform. If we average all the points on the waveform algebraically (that is, to consider their sign, either positive or negative), the average value for most waveforms is technically zero, because all the positive points cancel out all the negative points over a full cycle:

图片点击可在新窗口打开查看

This, of course, will be true for any waveform having equal-area portions above and below the "zero" line of a plot. However, as a practical measure of a waveform's aggregate value, "average" is usually defined as the mathematical mean of all the points' absolute values over a cycle. In other words, we calculate the practical average value of the waveform by considering all points on the wave as positive quantities, as if the waveform looked like this:

图片点击可在新窗口打开查看

Polarity-insensitive mechanical meter movements (meters designed to respond equally to the positive and negative half-cycles of an alternating voltage or current) register in proportion to the waveform's (practical) average value, because the inertia of the pointer against the tension of the spring naturally averages the force produced by the varying voltage/current values over time. Conversely, polarity-sensitive meter movements vibrate uselessly if exposed to AC voltage or current, their needles oscillating rapidly about the zero mark, indicating the true (algebraic) average value of zero for a symmetrical waveform. When the "average" value of a waveform is referenced in this text, it will be assumed that the "practical" definition of average is intended unless otherwise specified.

Another method of deriving an aggregate value for waveform amplitude is based on the waveform's ability to do useful work when applied to a load resistance. Unfortunately, an AC measurement based on work performed by a waveform is not the same as that waveform's "average" value, because the power dissipated by a given load (work performed per unit time) is not directly proportional to the magnitude of either the voltage or current impressed upon it. Rather, power is proportional to the square of the voltage or current applied to a resistance (P = E²/R, and P = I²R). Although the mathematics of such an amplitude measurement might not be straightforward, the utility of it is.

Consider a bandsaw and a jigsaw, two pieces of modern woodworking equipment. Both types of saws cut with a thin, toothed, motor-powered metal blade to cut wood. But while the bandsaw uses a continuous motion of the blade to cut, the jigsaw uses a back-and-forth motion. The comparison of alternating current (AC) to direct current (DC) may be likened to the comparison of these two saw types:

The problem of trying to describe the changing quantities of AC voltage or current in a single, aggregate measurement is also present in this saw analogy: how might we express the speed of a jigsaw blade? A bandsaw blade moves with a constant speed, similar to the way DC voltage pushes or DC current moves with a constant magnitude. A jigsaw blade, on the other hand, moves back and forth, its blade speed constantly changing. What is more, the back-and-forth motion of any two jigsaws may not be of the same type, depending on the mechanical design of the saws. One jigsaw might move its blade with a sine-wave motion, while another with a triangle-wave motion. To rate a jigsaw based on its peak blade speed would be quite misleading when comparing one jigsaw to another (or a jigsaw with a bandsaw!). Despite the fact that these different saws move their blades in different manners, they are equal in one respect: they all cut wood, and a quantitative comparison of this common function can serve as a common basis for which to rate blade speed.

Picture a jigsaw and bandsaw side-by-side, equipped with identical blades (same tooth pitch, angle, etc.), equally capable of cutting the same thickness of the same type of wood at the same rate. We might say that the two saws were equivalent or equal in their cutting capacity. Might this comparison be used to assign a "bandsaw equivalent" blade speed to the jigsaw's back-and-forth blade motion; to relate the wood-cutting effectiveness of one to the other? This is the general idea used to assign a "DC equivalent" measurement to any AC voltage or current: whatever magnitude of DC voltage or current would produce the same amount of heat energy dissipation through an equal resistance:

In the two circuits above, we have the same amount of load resistance (2 Ω) dissipating the same amount of power in the form of heat (50 watts), one powered by AC and the other by DC. Because the AC voltage source pictured above is equivalent (in terms of power delivered to a load) to a 10 volt DC battery, we would call this a "10 volt" AC source. More specifically, we would denote its voltage value as being 10 volts RMS. The qualifier "RMS" stands for Root Mean Square, the algorithm used to obtain the DC equivalent value from points on a graph (essentially, the procedure consists of squaring all the positive and negative points on a waveform graph, averaging those squared values, then taking the square root of that average to obtain the final answer). Sometimes the alternative terms equivalent or DC equivalent are used instead of "RMS," but the quantity and principle are both the same.

RMS amplitude measurement is the best way to relate AC quantities to DC quantities, or other AC quantities of differing waveform shapes, when dealing with measurements of electric power. For other considerations, peak or peak-to-peak measurements may be the best to employ. For instance, when determining the proper size of wire (ampacity) to conduct electric power from a source to a load, RMS current measurement is the best to use, because the principal concern with current is overheating of the wire, which is a function of power dissipation caused by current through the resistance of the wire. However, when rating insulators for service in high-voltage AC applications, peak voltage measurements are the most appropriate, because the principal concern here is insulator "flashover" caused by brief spikes of voltage, irrespective of time.

Peak and peak-to-peak measurements are best performed with an oscilloscope, which can capture the crests of the waveform with a high degree of accuracy due to the fast action of the cathode-ray-tube in response to changes in voltage. For RMS measurements, analog meter movements (D'Arsonval, Weston, iron vane, electrodynamometer) will work so long as they have been calibrated in RMS figures. Because the mechanical inertia and dampening effects of an electromechanical meter movement makes the deflection of the needle naturally proportional to the average value of the AC, not the true RMS value, analog meters must be specifically calibrated (or mis-calibrated, depending on how you look at it) to indicate voltage or current in RMS units. The accuracy of this calibration depends on an assumed waveshape, usually a sine wave.

Electronic meters specifically designed for RMS measurement are best for the task. Some instrument manufacturers have designed ingenious methods for determining the RMS value of any waveform. One such manufacturer produces "True-RMS" meters with a tiny resistive heating element powered by a voltage proportional to that being measured. The heating effect of that resistance element is measured thermally to give a true RMS value with no mathematical calculations whatsoever, just the laws of physics in action in fulfillment of the definition of RMS. The accuracy of this type of RMS measurement is independent of waveshape.

For "pure" waveforms, simple conversion coefficients exist for equating Peak, Peak-to-Peak, Average (practical, not algebraic), and RMS measurements to one another:

In addition to RMS, average, peak (crest), and peak-to-peak measures of an AC waveform, there are ratios expressing the proportionality between some of these fundamental measurements. The crest factor of an AC waveform, for instance, is the ratio of its peak (crest) value divided by its RMS value. The form factor of an AC waveform is the ratio of its peak value divided by its average value. Square-shaped waveforms always have crest and form factors equal to 1, since the peak is the same as the RMS and average values. Sinusoidal waveforms have crest factors of 1.414 (the square root of 2) and form factors of 1.571 (π/2). Triangle- and sawtooth-shaped waveforms have crest values of 1.732 (the square root of 3) and form factors of 2.

Bear in mind that the conversion constants shown here for peak, RMS, and average amplitudes of sine waves, square waves, and triangle waves hold true only for pure forms of these waveshapes. The RMS and average values of distorted waveshapes are not related by the same ratios:

This is a very important concept to understand when using an analog meter movement to measure AC voltage or current. An analog movement, calibrated to indicate sine-wave RMS amplitude, will only be accurate when measuring pure sine waves. If the waveform of the voltage or current being measured is anything but a pure sine wave, the indication given by the meter will not be the true RMS value of the waveform, because the degree of needle deflection in an analog meter movement is proportional to the average value of the waveform, not the RMS. RMS meter calibration is obtained by "skewing" the span of the meter so that it displays a small multiple of the average value, which will be equal to be the RMS value for a particular waveshape and a particular waveshape only.

Since the sine-wave shape is most common in electrical measurements, it is the waveshape assumed for analog meter calibration, and the small multiple used in the calibration of the meter is 1.1107 (the form factor π/2 divided by the crest factor 1.414: the ratio of RMS divided by average for a sinusoidal waveform). Any waveshape other than a pure sine wave will have a different ratio of RMS and average values, and thus a meter calibrated for sine-wave voltage or current will not indicate true RMS when reading a non-sinusoidal wave. Bear in mind that this limitation applies only to simple, analog AC meters not employing "True-RMS" technology.

REVIEW:
The amplitude of an AC waveform is its height as depicted on a graph over time. An amplitude measurement can take the form of peak, peak-to-peak, average, or RMS quantity.
Peak amplitude is the height of an AC waveform as measured from the zero mark to the highest positive or lowest negative point on a graph. Also known as the crest amplitude of a wave.
Peak-to-peak amplitude is the total height of an AC waveform as measured from maximum positive to maximum negative peaks on a graph. Often abbreviated as "P-P".
Average amplitude is the mathematical "mean" of all a waveform's points over the period of one cycle. Technically, the average amplitude of any waveform with equal-area portions above and below the "zero" line on a graph is zero. However, as a practical measure of amplitude, a waveform's average value is often calculated as the mathematical mean of all the points' absolute values (taking all the negative values and considering them as positive). For a sine wave, the average value so calculated is approximately 0.637 of its peak value.
"RMS" stands for Root Mean Square, and is a way of expressing an AC quantity of voltage or current in terms functionally equivalent to DC. For example, 10 volts AC RMS is the amount of voltage that would produce the same amount of heat dissipation across a resistor of given value as a 10 volt DC power supply. Also known as the "equivalent" or "DC equivalent" value of an AC voltage or current. For a sine wave, the RMS value is approximately 0.707 of its peak value.
The crest factor of an AC waveform is the ratio of its peak (crest) to its RMS value.
The form factor of an AC waveform is the ratio of its peak (crest) value to its average value.
Analog, electromechanical meter movements respond proportionally to the average value of an AC voltage or current. When RMS indication is desired, the meter's calibration must be "skewed" accordingly. This means that the accuracy of an electromechanical meter's RMS indication is dependent on the purity of the waveform: whether it is the exact same waveshape as the waveform used in calibrating.

Audio power

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:^[1]

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

For a purely resistive load, a simpler equation can be used, based on the root mean square 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) 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.^[2]

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.^[3]

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.

In common use RMS, when applied to power measurements, has come to mean "sine-wave power." A 100 Watt "RMS" amplifier can produce a 100 Watt sine-wave into its load. With music, the total actual power would be less. With a square-wave, it would be more. Citation from epanorama.net

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).

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 measure, 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 of 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.^{[citation needed]}

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) small changes in output power produce much smaller changes 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 Program 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 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. [1]
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) [2] 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 world.

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.

Audio quality measurement

Audio quality measurement seeks to quantify the various forms of corruption present in an audio system or device. The results of such measurement are used to maintain standards in broadcasting, to compile specifications, and to compare pieces of equipment.
The need for measurement

Measurement allows limits to be set and maintained for equipment and signal paths, and different pieces of equipment to be compared. While the issue of measurement is controversial, to the extent that Hi-Fi magazines these days tend to shun measurement in favour of listening tests, it is important to realise that audio quality measurement has in the past got a bad name by failing to produce results that correlated well with listening tests.^{[citation needed]} This was because certain basic measurements were used, such as THD measurement, and A-weighted noise measurement, without any proper consideration of whether these related to subjective effects. The proper approach to measurement, which is largely adopted by broadcasters and other audio professionals, is to first devise measurements that can quantify the various forms of corruption in terms of subjective annoyance to a human listener, ideally the most critical listener based on tests using many suitably rested subjects.^{[citation needed]} Once this is done, measurement has the advantage of not being dependent on a particular listener, or his state of hearing on a given day. It also has the advantage of being able to quantify corruption levels that would not be audible to even the most sensitive ear, which is important because a typical audio path from source to listener can involve many items of equipment, and just listening to each is not a guarantee that they will still sound acceptable when cascaded so that all their deficiencies add up.

Automated sequence testing

Sequence testing uses a specific sequence of test signals, for frequency response, noise, distortion etc, generated and measured automatically to carry out a complete quality check on a piece of equipment or signal path. A single 32-second sequence was standardised by the EBU in 1985, incorporating 13 tones (40 Hz–15 kHz at ?12 dB) for frequency response measurement, two tones for distortion (1024 Hz/60 Hz at +9 dB) plus crosstalk and compander tests. This sequence, which began with a 110-baud FSK signal for synchronising purposes, also became CCITT standard 0.33 in 1985.^{[citation needed]}

Lindos Electronics expanded the concept, retaining the FSK concept, and inventing segmented sequence testing, which separated each test into a 'segment' starting with an identifying character transmitted as 110-baud FSK so that these could be regarded as 'building blocks' for a complete test suited to a particular situation. Regardless of the mix chosen, the FSK provides both identification and synchronisation for each segment, so that sequence tests sent over networks and even satellite links are automatically responded to by measuring equipment. Thus TUND represents a sequence made up of four segments which test the alignment level, frequency response, noise and distortion in less than a minute, with many other tests, such as Wow and flutter, Headroom, and Crosstalk also available in segments.^{[citation needed]}

The Lindos sequence test system is now a 'de-facto' standard^{[citation needed]}in broadcasting and many other areas of audio testing, with over 25 different segments recognised by Lindos test sets, and the EBU standard is no longer used.

Multitone testing

Another approach to automated testing uses a special multitone signal to assess all parameters simultaneously, by analysing the spectrum of the output from the device under test. It relies on the fact that with appropriate choice of frequencies, distortion components and noise can be made to appear between the tones, and measured using digital comb filtering. Even noise and wow and flutter can be extracted from the spectrum in principle.^{[citation needed]}

In practice, though the use of a single brief test is attractive, and might even be used between programmes, this method presents several problems.^{[citation needed]} Digital distortions produce a fine spectrum which can swamp the measurement of true noise in the absence of signal. The composite signal also has a high peak to mean ratio, with peak levels occurring whenever all the tones hit maximum simultaneously. Although the Probability density function can be controlled to some extent, it is not possible to separate out distortion at high level, from low level distortion. Quite high amounts of the former can be considered acceptable, but low level distortion is more critical.

Fast sequence tests are possible, and there have been attempts to make these appear like jingles for incorporation into broadcast programmes.^{[citation needed]}

Measurements needed

Crosstalk measurement
Flutter measurement (on analog tape systems)
Rumble measurement
Jitter (on digital systems)
Impulse response (speakers) (Waterfall plots, MLSSA) (colouration)
Latency (satellite links and codecs) (sound for live video)

LMS就听过，哪有什么RMS？L,R,L,R,L,R,烦

楼上太狠了，好大一堆英文字母，，，，全部都认得我，我不认得他。
RMS即有效值？即某个类型的波形的信号（交流或者脉冲的都可）流过某个电阻后，时间T在电阻上产生的功，等于××V的直流电在同样长的时间T时在该电阻产生的功。我们叫这个信号的RMS值就等于这个XX值。

例如，一个交变电压信号为 311×cos（2×50×pi×t），经积分运算或者实际测量表明，它通过某个电阻后产生的功率，等于220V的直流电通过该电阻产生的功率。
因此我们称这个交变电压信号的有效值为220V。

1楼楼主看懂了没有？我是没看明白

非常感谢新绿这么系统的资料！
其实简单来说，RMS就是一个均方根值！

这位是不是搞立体声信号研究的？LRLRLR？呵呵

主题：关于RMS

Measurements of AC magnitude

Audio power