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Loudspeaker Sensitivity vs Efficiency


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DYohn 
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Joined: April 22, 2003
Location: Arizona, United States
Posted: March 05, 2006 at 11:09 AM / IP Logged  

In several discussions on here people are calculating predicted SPL values based on the "db/watt-meter" ratings given for their loudspeakers.  This is not strictly correct, and in fact may be way off.

The sensitivity of a loudspeaker is the medium sound pressure between 125 Hz to 4 kHz using a constant voltage at a specific distance; measured in dB per watt and meter. Usually 2.83 volts is used as this corresponds to 1 watt @ 8 ohms, with the SPL measured at 1 meter.

For instance the sensitivity of an 8-ohm loudspeaker might be listed as 92 dB / 2.83 volts / 1 meter. In this case the power (P = V  squared / R) = 2.83 X 2.83 / 8 = 1 watt. In a 4-ohm loudspeaker 2.83 volts will generate 2 watts. To get the actual reference value at 1 watt, you have to subtract 3 dB (power cut in half) from the sensitivity measured; if the speaker was measured at 2-ohms, you subtract 6db, etc.  Many car audio manufacturers fail to include this correction.  Some cheat it by measuring at 0.5 meter.  Some intentionally fudge the numbers or the test voltage.  Also since the value is measured at frequencies higher than normal subwoofer usage bands, it may or may not be 100% accurate below 80Hz.  Good manufacturers will do it right and give you accurate numbers, and often will include specifics about the test such as if a subwoofer was measured using standard frequency sweeps or using sub-woofer sweeps below 80Hz. 

But there are other factors contributing to the overall system efficiency and resulting output levels in a car.  The speaker enclosure adds several SPL components, especially using a ported system.  The vehicle has what’s called “cabin gain,” or the many resonances set up as the closed vehicle functions as a resonance chamber similar to what happens inside a loudspeaker enclosure.  These items might increase the system sensitivity value by as much as 6db or even more, and increase the overall system efficiency from the lowly speaker averages of 1 or 2% to 50 or 60% or more.

So a simple calculation beginning with the speaker’s sensitivity rating and working up by adding 3db for every doubling of input power will only tell you part of the story. (BTW, the raw SPL difference between 1 watt and 1000 watts is +30db.)  It only indicates what the speaker would do in a free air anechoic test chamber at 1 meter away.  A better method is to test the system after installation and determine the overall system sensitivity.  Then a calculation to determine required wattage to achieve a particular db SPL value will have much more meaning.  Also realize that SPL decreases with distance at a rate of -6db for each doubling of distance.  So if the output is 87 db at one meter, at 2 meters the output will be 81 db.  It is critical to know where the test mic will be positioned in relation to the speakers to calculate a predicted output level.

By the way, loudspeaker efficiency is a measure of how much incoming electrical energy is converted into acoustic energy.  Often speaker manufacturers will not give you this value, but for good quality loudspeakers a typical value might be between 0.2 % and 2 % and means that only 2% of the amplifier signal is actually being converted into sound, the rest is being wasted as heat.  Some high efficiency subwoofers might get as high as 10% or 15%, but high efficiency speakers like compression drivers designed for pro audio can be almost 100% efficient (100% efficiency is 112db/watt-meter.)  You can convert the listed sensitivity number into an efficiency using this formula: Efficiency = 10E(Sensitivity in dB - 112)/10

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stevdart 
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Posted: March 05, 2006 at 11:47 AM / IP Logged  

How do you calculate the function 10E X ?

Does this calculator do it right?

Build the box so that it performs well in the worst case scenario and, in return, it will reward you at all times.
DYohn 
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Posted: March 05, 2006 at 11:54 AM / IP Logged  

Sorry, the "E" means "to the power of."

That calculator seems to be pretty close, Steve.

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Steven Kephart 
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Posted: March 05, 2006 at 4:30 PM / IP Logged  
DYohn wrote:

So a simple calculation beginning with the speaker’s sensitivity rating and working up will only tell you part of the story.  It only indicates what the speaker would do in a free air anechoic test chamber at 1 meter away. 

And even that assumes a perfectly linear speaker.  Power and BL compression will greatly effect the actual results of the test as well.

DYohn wrote:
By the way, loudspeaker efficiency is a measure of how much incoming electrical energy is converted into acoustic energy.  Often speaker manufacturers will not give you this value, but for good quality loudspeakers a typical value might be between 0.2 % and 2 % and means that only 2% of the amplifier signal is actually being converted into sound, the rest is being wasted as heat.  Some high efficiency subwoofers might get as high as 10% or 15%, but high efficiency speakers like compression drivers designed for pro audio can be almost 100% efficient (100% efficiency is 112db/watt-meter.)  You can convert the listed sensitivity number into an efficiency using this formula: Efficiency = 10E(Sensitivity in dB - 112)/10

This number, if provided, is generally given as "no".  Here's a link to another paper on driver efficiency: http://www.adireaudio.com/Files/TechPapers/SPLCalculations.pdf

DYohn 
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Posted: March 05, 2006 at 5:02 PM / IP Logged  
Good old eta naught.  Thanks for the link, Steven!
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SoundAudio 
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Posted: March 06, 2006 at 8:46 AM / IP Logged  

Thanks for the good discussion guys.  The info comesnin handy for my electroacoustics class.

Good Luck!
-Thad

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