Speaker efficiency vs. sensitivity
John Dunlavy
My Feb. 4th posting regarding efficiency was written in a hurry and
failed to address a few important issues.
In the meantime, on Jan. 31st, Dick Pierce posted an excellent
explanation regarding the subject; one that leaves little to add.
Dick made the statement that the efficiency of a loudspeaker is
related "only" to the efficiency of the drivers and not the
enclosure (box). This is certainly true with respect to what I might
call "absolute efficiency", defined as the ratio of the total power
radiated (integrated over the surface of a hypothetical sphere
surrounding the loudspeaker) to the total input power at the input
terminals of the loudspeaker. However, this definition, taken alone,
might be a bit confusing to those lacking Dick's technical background
and expertise.
For example, a listener comparing two loudspeakers with identical
"efficiency" ratings might perceive one sounding much louder than
the other. This might be explained on the basis of the two
loudspeakers possessing different radiation patterns, with one
radiating more acoustical energy than the other in the direction of
the listener. A good example might be a small "box" loudspeaker and
a "horn" loudspeaker, both with drivers having equal "efficiency".
The horn loudspeaker, with a relatively narrow radiation pattern will
probably deliver as much as a 10 dB louder sound to an "on-axis
listener" compared to the box loudspeaker with a nearly "spherical
directional pattern", whose dimensions are small compared to a
wavelength (throughout the frequency range being evaluated).
Another problem in relating the SPL to efficiency of a "box
loudspeaker" may be encountered at frequencies below which the system
(a closed-box plus driver) is resonant. This occurs at a frequency
that is approximately equal to the square-root of the product of the
resonant frequencies of the box and the driver. Below this system
resonance, the total acoustical energy radiated by a "closed box
design" drops at the approximate rate of 12 dB per octave (assuming
that the resonance of the box is much higher than the free-air
resonance of the driver). However, if the box is vented by means of a
"port", the system "Q" will rise (along with a rise in the level
of radiated energy) at the low frequencies affected by the port
radiation. Thus, one might conclude that the "efficiency" of a
ported enclosure is higher at some bass frequencies than that of a
non-ported design. And, this might be a valid conclusion if one
ignores radiation patterns, "stored energy" (time-domain response)
and the rate of low-frequency roll-off (often exceeding 24-30
dB/octave below resonance).
From the above comments, it might be seen that the terms SPL and
efficiency convey quite different information concerning performance
and must be well-understood if accurate comparisons are to be made
between different loudspeaker designs. This includes the effect of
"Q" (both of driver and enclosure) on the total "system"
performance, including efficiency, SPL Vs frequency (on-axis), input
impedance (which contains terms related to loss resistance, radiation
resistance and reactance).
I suspect that for many readers, all of this seems a bit complicated
and beyond their interest (if not grasp). With this in mind, I would
suggest that the use of SPL (measured on axis, anechoically, and
referenced to a specified distance, e.g. 1 metre), using some
pre-agreed upon signal such as white or pink noise (at a given RMS
voltage level at the loudspeaker input terminals), probably represents
the best means for comparing loudspeakers with respect to their
relative "efficiency".
As I said in my last posting on the subject, if anyone would like more
detailed information, let me know. My earlier suggestion for
consulting the 1934 edition of "Loudspeakers" still stands. This
truly excellent book, authored by N.W. Mc Lachlan, D.Sc. (published by
Oxford at the Clarendon Press) provides one of the best reference
sources on loudspeakers and their properties that I have ever come
across.
Best regards,
John Dunlavy