August 2008


Speaker Efficiency: An Initial Review
Article By Peter W. Mitchell
From BAS August 1973

  For many people buying stereo equipment, the question of whether to spend an additional $50 - $100 to get a 60-watt rather than 30-watt amplifier is an important one. Yet few people consider the fact that the choice of loudspeaker can completely offset that doubling of amplifier power. How many audiophiles are aware, for example, that KLH-17s driven by a 20-watt amplifier can play louder than Small Advents driven by a 60-waft amp? If, like many listeners, you never play music louder than a 90-dB sound pressure level, then this difference is irrelevant; any speaker on the market can be driven comfortably to 90 dB in a living room by a good 20-watt-per-channel amplifier. So you can select loudspeakers on the basis of their sound character, bass range, size, appearance, and cost. But if you want to reproduce the 100-dB levels of a full orchestra in a concert hall or a grand piano in a salon, you ought to consider the speaker’s efficiency as well as its other parameters, or else be prepared to buy a big amp.

Probably the reason why people don’t consider loudspeaker efficiency carefully is that manufacturers have made useful data on relative efficiency hard to obtain. The Standards Committee of the Institute of High Fidelity, which is responsible for defining how manufacturers and test labs should measure the performance parameters of high-fidelity equipment, has standardized the specifications of amplifiers and is currently revising its FM tuner specification standards, but has never standardized any speaker measurement techniques, not even for speaker efficiency. So manufacturers don’t advertise efficiency, magazine test reports have not generally measured efficiency, and the buying consumer is left in the lurch. Of course the IHF is a manufacturers’ association, not a consumer-oriented body, and the IHF Standards Committee operates at the manufacturers’ bidding. There is some disagreement among industry members about how best to measure speaker predominance parameters, and apparently the IHF would rather leave consumers completely ignorant than specify tests which might  produce a misleading result once in a while.

However there are four ways in which at least approximate values of relative loudspeaker efficiency can be obtained. I have used all of these in compiling the attached table.

     (1) Since mid-1970 High Fidelity’s speaker test reports have included response measurements in an anechoic chamber, taken all around the speaker at a microphone distance of 1 meter and processed with a, small computer to produce three response curves. One of these is the on-axis frequency response, but the curve of interest here is the solid line representing the speaker’s total acoustic power output, for an electrical input of one watt, averaged over all directions. To represent the speaker’s efficiency, I take the average output in the range from 100 Hz to 2 kHz (where most of the acoustic power in music occurs).

I add 3 dB to the number obtained from High Fidelity’s graph, and the resulting number turns out to represent with pretty fair accuracy the sound pressure level (SPL) obtained at an average location in a room of 2000-cubic-feet volume and moderately live acoustics, for a one-watt input. Then, knowing the SPL produced by one watt of amplifier power, the power required to produce a sound level of 100 dB can be calculated from the equation: P = antilog (100 - SPL).

     (2) Consumer’s Union, whose reports on high-fidelity gear have to be taken with a grain of salt in some respects, do include in their loudspeaker evaluations a “required power” figure which can be taken as an indication of relative speaker efficiency. CU do not specify how their power figures are obtained, but I find that doublino their numbers gives results which agree roughly with the power figure ~or 100 dB which I derive from High Fidelity.

     (3) Estimates of relative efficiency can be obtained from comparative listening tests in showrooms or at home, but great care must be taken, If 8-ohm and 4-ohm speakers are compared and sound equally loud at the same volume control setting (or at the same reading on an amplifier’s "power" meter). the lower-impedance speaker is actual a absorbing more power and so is about 3 dB less efficient. If equally efficient 8-ohm and 4-ohm speakers are compared, the 4-ohm speaker will sound louder at the same volume control setting. Another problem with listening comparisons is that a speaker with an upper-midrange peak will sound subjectively loud and so more efficient than it really is.

     (4) Most loudspeakers obey a physical relationship between low-frequency response, cabinet size, and efficiency. This relationship was established about 15 years ago at Acoustic Research; Henry Kloss calls it Hoffman’s Iron Law. It doesn’t apply to speakers which contain “acoustic amplification,” such as the Klipschorn and Heil’s air motion transformer, but it does apply generally to closed-box loudspeaker systems. In a form practical for calculations it can be expressed as:

Here E is the efficiency of the woofer in the frequency region where its response is flat, the efficiency is expressed as a percentage, and though the formula gives only the woofer’s efficiency the tweeter’s efficiency obviously will be matched to the woofer if the speaker sounds good. The V in the formula is the effective volume of the cabinet, in cubic feet. F is the resonant frequency of the woofer as mounted in the box not the free-air resonance). Q is the reactance/resistance ratio at resonance, in practical terms it may be taken as a number which specifies the shape of the speaker’s low-frequency response. A speaker with a Q of about 1 is approximately flat down to the resonant frequency. A Q much higher than one would mean a pronounced peak at resonance; with a Q of less than 0.8 the speaker’s low end would start rolling off at about twice the resonant frequency. Many good speakers have a Q of about one. The equation in dictates that such a speaker, with a resonant frequency of 45 Hz in a 2 cubic foot box will have an efficiency of about 1 percent (or worse if the design is not optimum). At that efficiency a speaker will produce a sound level of about 84 dB at 1-watt input, in an average room.

Incidentally, the Iron Law explains the difference between the KLH-17 and the Smaller Advent alluded to earlier. The Smaller Advent has a lower woofer resonance (43 Hz versus 60 Hz) and a smaller cabinet than the KLH-17; it pays for its deep-bass performance and compact size with a loss of efficiency.

I have compiled the following tables using all of the above methods for obtaining values. Since the data derived from High Fidelity are the most precise (probably to within ± 1 dB), those values are collected in the left-hand column. Data obtained from the other sources are listed in the right-hand column; they should be regarded as approximate and preliminary, and may not be reliable to better than ± 2 dB. All values are rounded-off to the nearest whole decibel.

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