Interpreting Watt, decibel
and other loudspeaker data
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 0.22%, 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 602685(2003)/EN 602685 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 nonstandard 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
602685 (previously 2685), the AES22012, the EIA RS426A, and the EIA RS426B. 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
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 602685(2003) standard for the basis, the normal listening demands in a 2025 m^{2} 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 twofold increase, a 6 dB boost may call for up to fourfold increase of the rated power, depending on the actual construction of the loudspeaker!
Firstly, we
may talk about what a decibel is. When talking about power or intensity measurements, then
the measured signal level (P_{1}) as compared to an agreed base level (P_{0})
can be expressed in decibel as follows:
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:
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 (WeberFechner 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 
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 602685 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.
According
to the IEC 602685(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:
4020,000 Hz, +/ 3 dB. The decibel range should be specified, or if it's missing, then
indicate the standard by which the range was measured.
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 onaxis frequency response curve, but
also the horizontal 30 degree and 60 degree curves are specified.
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 4020,000 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 hifi
system can be built so that to complement smaller sized main speakers, which cannot manage
deep bass, e.g. with frequency response 8020,000 Hz +/ 3 dB, one chooses a midsized
subwoofer unit, in this case to cover the 40...80 Hz range.
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.