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by John L. Murphy

Subject: Speaker Inefficiency
(posted 14Apr99 to Bass List)
Jason wrote:

>>What makes speakers so inefficient?  Is there a poor transfer of
>>electric energy to movement of the cone (if this is so, shouldn't a
>>contrabass be extremely efficient?), or is most of my power being
>>wasted from the cone to the air?  The answer is probably a
>>combination of both.  Can someone explain which is greater, and

>>I was once told that the ideal transducer has a matching
>>impedance with the fluid, and air is very difficult to match.  Can
>>someone explain impedance?  I am sure this has something to do
>>with the answer to my first question.

The loss of efficiency occurs as the speaker cone converts its mechanical
energy of motion into acoustical energy.  The main problem is the impedance
mismatch as Jason notes.  Just as an audio power amp needs to be "loaded" in
order to transfer electrical power from the amp to the load so to does a
speaker need to be "loaded" to transfer acoustical power into the air.

Consider a typical 100 Watt audio amp that delivers it's rated power into an
8 Ohm load.  That requires about 28.28 Volts (rms).  The same amp can only
deliver about half its rated power, or 50 W, into 16 Ohms.  Into a 32 Ohm
load the amp only delivers a quarter of its power, or 25 W.  As the load on
the amp is reduced the maximum power it can deliver is also reduced.  On the
other hand, if we load the amp more heavily than its rating we can get more
than its rated power output.  If our 100 W amp can take it, a 4 Ohm load
would result in 200 W of power transfer (assuming the amp can still deliver
28.28 Vrms into our 4 Ohm load.)  Most real amps will deviate from these
numbers due to power supply voltages varying with the load . . . but you get
the picture.

One way we can specify the "radiation impedance", or acoustic load, seen by
a speaker is to specify the "spatial load".  That is, the solid angle into
which the speaker radiates.  The lightest load would be "full space." That
is equivalent to placing the speaker in a tiny enclosure and suspending it
in the air well away from any reflecting surface.  The next most stiff load
would be half space, or mounting the speaker on a very large plane surface
such as a wall.  Quarter space loading would be stiffer yet followed by
eighth space and eventually horn loading the speaker into even smaller solid

By the way a 100% efficient speaker would convert 1 Watt of electrical
energy into 1 Watt of acoustical energy to produce 112.1 dB SPL at 1 meter
when radiating into half space.  This same 100% efficient speaker would
achieve only 106.1 dB SPL radiating into full space.  We encounter this
shift from half space load to full space load in our listening rooms as our
speakers change from half space loading by the baffle at mid frequencies to
full space loading at bass frequencies.  The result is "diffraction loss" or
the "6  dB baffle step" as some would say.  The acoustic load is more stiff
at mid frequencies and is reduced at lower frequencies.

We can also interpret the room modes in terms of radiation impedance.  Where
the room has a resonance it presents a stiff load to the speaker over a
narrow frequency range thereby drawing too much power from the system.  The
result is a peak in frequency response at the room mode frequency.  Ideally
we would like to have our speakers presented with an acoustic load that is
constant with frequency, then our speakers would achieve the nice flat
response we predict when we model our systems assuming a half space load.
Auto cabins and small rooms exhibit a striking bass boost due to "cavity
effect" as the room load becomes more stiff with falling frequency.

For more on spatial loads (and some illustrations of the basic loads) see my
Tech Topic titled "Loudspeaker Spatial Loading" at the True Audio web site.



John L. Murphy
Physicist/Audio Engineer
True Audio
Check out my new book "Introduction to Loudspeaker Design" at Amazon.com


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Andersonville TN 37705

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