Interpreting Watt, decibel and other loudspeaker data

Watt (power)

The nominal power rating on the data sheet of a loudspeaker is not the acoustical power delivered by the loudspeaker, but the maximal undistorted sinus power of the amplifier which drives the speaker with the waveform defined in the standard. Since the efficiency of most of the drivers used in home audio loudspeakers is only 0.2-2%, in case of dynamic speakers the majority of the power fed by the amplifier only heats the voice coil of the speakers (except for mechanical and eddy current losses. If too high a power is applied to a speaker, the voice coil may get so hot that it comes away from the carrier and so it is damaged. However it may be that the voice coil excursion gets too high even at a lower power and the voice coil hits against the inner structure of the speaker and it peels off of the cone due to the serious forces coming into play. So there are two limiting factors for the applied input power: a "temperature limit" and a "mechanical limit" (or "excursion limit").

It is customary to interpret the power rating specified by the manufacturer that it is the "recommended maximal amplifier power", which may be used to drive the loudspeaker without damage. This interpretation seems to deal with the problem of both the temperature limit and the mechanical limit, but it is only true as long as the amplifier in not overdriven into clipping. Unfortunately if a lower power amplifier is used which doesn't have enough supply voltage to deliver the required signal in its integrity and is therefore overdriven, then this clipping increases the RMS relative to peak voltage of the signal. Therefore a lower power amplifier may deliver comparable power to a higher power amplifier (at least at musical signals with high crest factor), which could have amplified the required signal without clipping. Moreover as the clipping increases the high frequency content in the output signal, an undersized power amplifier may damage the tweeter more "efficiently" than a higher power amplifier!

So we don't have a cushy time. The IEC 60268-5(2003)/EN 60268-5 standard includes specification for "rated noise power". But this is not the only standard in use. Making use of this chaos, manufacturers like to present a showy high value for the power rating of their loudspeakers, it may well be that they specify the result of some non-standard measurement method, one that has an "easy" waveform (e.g. the peak power of short burst signals with long breaks) differing from the pink noise with a defined crest factor and defined frequency distribution appearing in the standards. We have to conclude that what the different manufacturers simply call "rated power" may not be comparable. Therefore it is expedient to inquire from the manufacturer, what exactly covered by their "rated power," and by what standard it is measured. The next figure shows the frequency distribution of the noise signals of the most frequently used standards for measuring rated power: the IEC 60268-5 (previously 268-5), the AES2-2012, the EIA RS-426-A, and the EIA RS-426-B. You can see the significant differences between them, which makes comparing impossible.

Further information on different standards of loudspeaker rated power: http://www.doctorproaudio.com/doctor/temas/powerhandling.htm

What is the minimal loudspeaker rated power for home listening?

The rated power must be evaluated together with sensitivity and impedance, and it depends on room size, and even the listener distance from the loudspeaker. A larger room generally requires a higher loudspeaker power for the same perception of loudness, when one listens to the loudspeaker from afar. Sensitivity is generally measured with a 2.83 V RMS voltage, which imposes 1 W on a 8 Ω loudspeaker, 1.5 W on a 6 Ω loudspeaker, and 2 W on a 4 Ω loudspeaker. Therefore if different impedance loudspeakers are to be compared "power proportionately," relative to a 8 Ω loudspeaker, the sensitivity of a 6 Ω loudspeaker must be decreased by 1.8 dB, while the sensitivity of a 4 Ω loudspeaker must be decreased by 3 dB. In this way the sensitivity will be given in dB/W. After applying this correction, any loudspeaker with a 3 dB higher sensitivity needs half the electrical input power for achieving the same sound pressure (loudness). It works vice versa: a loudspeaker with 3 dB less sensitivity needs double electrical power to achieve the same loudness. Taking the rated power of the IEC 60268-5(2003) standard for the basis, the normal listening demands in a 20-25 m2 room containing a usual amount of sound absorbing appointments and assuming a 87 dB SPL/ 1 W sensitivity loudspeaker listened to at a distance of 2 m is more than adequately served by an only 10...20 W rated loudspeaker for almost any kind of music. Naturally, a loudspeaker with 3 dB higher sensitivity (90 dB/W) needs only half of this power, that is 5...10 W for the same max. loudness, and a loudspeaker with 3 dB less sensitivity (84 dB/W) will need 20...40 W. But beware! If the bass or treble needs to be boosted with the tone control, then a 3 dB boost may call for up to two-fold increase, a 6 dB boost may call for up to four-fold increase of the rated power, depending on the actual construction of the loudspeaker!

Decibel (sensitivity)

Firstly, we may talk about what a decibel is. When talking about power or intensity measurements, then the measured signal level (P1) as compared to an agreed base level (P0) can be expressed in decibel as follows:

L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,

When talking about measurements, which have their square proportionate to power or intensity, for example voltage, current, sound pressure, then the equation takes on the following form:

L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{A_1^2}{A_0^2}\bigg) = 20 \log_{10} \bigg(\frac{A_1}{A_0}\bigg). \,

This equation can be called the "20 logarithm" rule, while the equation for the power can be called the "10 logarithm" rule.

Using the decibel is useful where one needs to work with great ratios. Because of the logarithmic scale, these ratios can be expressed with a convenient figure. On top of that the sound and light intensity as observed and assessed by human sense organs is closer to the logarithm of the intensity (Weber-Fechner law), rather than the intensity, so the decibel is very useful to indicate numerically the level differences perceived by sense organs.

In acoustics, the (dB) refers to sound pressure (correctly "dB SPL", where SPL stands for "sound pressure level"). The base level of acoustics is 0.0002 µbar (2×10−5 Pa), which is approximately the hearing threshold of a healthy human ear at 1 kHz.

Now let's cover the sensitivity specification of a loudspeaker stated in decibel.

Formerly the sensitivity was specified as "X dB/W/m". But the sound pressure is proportional to voltage, not to power. A double sound pressure increase necessitates double voltage and quadruple power. So the sensitivity should be specified as "X dB SPL/2.83 V RMS/m" (the measure is not 1 V RMS but 2.83 V RMS, because this way the expression is consistent with the outdated dB/W for 8 Ω loudspeakers, as 2.83 V RMS impresses just 1 W on a 8 Ω resistor).

Let's assume now that two loudspeakers are specified correctly as "X dB SPL/2.83V RMS/ m". How do they compare? If the sensitivity of a loudspeaker is x dB higher than that of another loudspeaker, then the sensitivity proportion between them can be calculated by the equation 10(x/20). The next table contains what proportions the positive and negative decibel differences correspond to. (Remark: Our hearing perceives not double sound pressure as double loudness. To human hearing a 2...3 dB is just audible, and approximately a 10 dB change is heard as double loudness.)


Positive change (+dB)

Negative change (-dB)

0 dB

1x

1x

1 dB

1.12x

0.89x

2 dB

1.26x

0.79x

3 dB

1.41x

0.71x

6 dB

2x

0.5x

10 dB

3.16x

0.32x

20 dB

10x

0.1x

40 dB

100x

0.01x

60 dB

1000x

0.001x

Ohm (impedance)

The loudspeaker impedance is frequency dependent. How can it be expressed with a single figure then? The "nominal impedance" of a loudspeaker is a plain ohmic resistance, which is supplied by the manufacturer for calculation purposes. This definition is not exactly what the IEC 60268-5 standard says, but it will do. The standard states that in the specified frequency range, the minimum impedance may not be lower than 0.8 times the nominal impedance, and if it's lower than this outside the specified frequency range (incuding DC, that is 0 Hz), then the manufacturer must denote it separately. Since at DC, the impedance is really often lower then in the passband, this should be separately specified, but most manufacturers refuse to do this.

To determine the nominal impedance, the manufacturer should measure a series of impedance values in the nominal frequency range, determine its minimum, and calculate its average. If the minimum is lower than 0.8 times this average, then the nominal impedance will be 1.25 times (= 1/0.8) the minimum, otherwise it will be the average. Nevertheless the manufacturers usually simplify this, and instead of the accurate value they specify 4, 6, or 8 Ω. They may do this to not confuse the customers, but in this way precise calculations cannot be made.

Hertz (frequency range)

According to the IEC 60268-5(2003) standard, the frequency range must be calculated as follows: 1) The frequency response of the loudspeaker must be recorded in the reference axis with sinusoidal signal. 2) Around the maximum sound pressure, the curve must be averaged in an 1 octave width. This averaged signal level is the sensitivity. 3) The frequency range is specified as the interval where the sound pressure is down by 10 dB compared to the sensitivity level. In the frequency response, dips smaller than 1/9 octave can be disregarded.

Unfortunately, there is no consensus among the manufacturers, because there are other standards. Everybody wants to specify a wider frequency range. A correct specification can be for example: 40-20,000 Hz, +/- 3 dB. The decibel range should be specified, or if it's missing, then indicate the standard by which the range was measured.

If the frequency response curve is specified

In a real living room the sound reflected from the walls will contain not only the forward propagated sound but also sound components reflected from other directions. All this is perceived by our ears. It is better if not only the on-axis frequency response curve, but also the horizontal 30 degree and 60 degree curves are specified.

What loudspeaker to buy in terms of frequency response?

Music usually doesn't contain frequencies lower than 40 Hz, except for organ music, where the lowest pipes go under this value. Human hearing is limited to about 20,000 Hz even in young age, and above 35 years old, the sensing of high frequencies is gradually impaired. So if you only listen to music, then it is enough to buy a loudspeaker with a frequency range of 40-20,000 Hz +/- 3 dB. But the home cinema effects often contain frequency components below 40 Hz. To radiate these, one needs a big (active) subwoofer. The hi-fi system can be built so that to complement smaller sized main speakers, which cannot manage deep bass, e.g. with frequency response 80-20,000 Hz +/- 3 dB, one chooses a mid-sized subwoofer unit, in this case to cover the 40...80 Hz range.

Conclusion

The manufacturers cannot seem to reach a consensus on how to unanimously specify performance data, and due to this two loudspeakers cannot always be compared based on the numerical values alone. Curves and diagrams tell more, but we must keep in mind that loudspeakers usually work in the complex environment of a living room, not in an anechoic chamber, where measurements were made. Besides, some loudspeaker manufacturers specify the parameters so barely, that these data are to be handled with caution. Give the loudspeakers a good listening test, do not choose them by comparing technical data alone when you buy. Check out my loudspeaker buying tips.

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