Loudspeakers & Power Ratings: What's the Deal Part II Continued?

As we can see from the half section view of the loudspeaker, the dimensions of the magnet, voice coil and steel magnetic parts (which complete the magnetic circuit) will set the amount the speaker can move before it collides its own parts together, sometimes called bottoming, a mechanical affect not related to the drop off in (B*L).

BL reduced from 19 to 12

Let us look at an example where the B*L falls off by about 37%, a very modest and realistic figure for a VC coming slightly out of the gap. In the graph above, the orange line represents a speaker with a BL product of 19 T-M versus the yellow line which is 12 T-M (37% less). As we can see from this model, we need the speaker with the 12 TM to move 42mm (1.65 inches off center in each direction) if we attempt to drive it with 1000 watts at 20 Hz in a box tuned at 40 Hz. This would require a VC on the order of 100 mm in height (not diameter) but VC height. (See diagram below)

Voice Coil

A typical VC is around 1 inch in height, and has perhaps 8-10 mm (about 0.35 inches) of excursion available by virtue of its height exceeding the top plate thickness. (We call this overhang). So what will happen if we attempt to power 1000 watts into this typical speaker at 20 Hz? In all likelihood it will break by smashing its parts together (bottoming) long before the VC even has a chance to get hot.

At the outset, I said there were two ways to destroy a speaker, thermally or mechanically. The mechanical limits to what a speaker can do must be considered if one is to obtain a picture of “how much power can it handle?” In fact, once we start making subwoofers with VC diameters of 3 inches or more, the likelihood of seeing a thermal failure falls way off relative to the likelihood of seeing a mechanical failure. Some conventional power handling tests use signals from the speakers resonant frequency up to a frequency 10 times as high, (The AES standard is an example). This will give us little indication of how much power a subwoofer can handle in real life, when it is rarely used above 120 Hz. 400 watts is not 400 watts when it comes to power handling. Unless you know the details of the signal used, then you know little about what the speaker can do. In part one, I said I would show you how we can take a speaker with a power handling of 500 watts and make it handle 1000 or break with 100 watts. Here is an example.

Speaker Failure Example at Various Power Levels

Let us say we have a woofer which we know when excited with pink noise, set from 50 to 500 Hz can handle 500 watts before it will burn. Let it be a given.

We know from the earlier example at middle and high frequencies the excursion is small and as we go lower, the excursion increases dramatically. If the signal used is placing its power across the full bandwidth of the audible spectrum in varying amounts (as it should be) then this signal will most likely burn the VC before it breaks the speaker. Suppose now, we go back to the earlier example of the vented speaker tuned at 40 Hz and drive it at 20 Hz.

1000 watts @ 20 Hz

We notice that at 20 Hz, the excursion of this speaker is predicted to reach 42 mm at 1000 watts. I said predicted, because the program running the model assumes (as most of these programs do) that the speaker can actually move that far without destroying itself. Well, it cannot. In short, we are asking this speaker to destroy itself. Suppose instead of using a continuous signal of 20 Hz, we simply use a tone burst. Ten cycles on, Ninety cycles off. That means for 90 percent of the time, the power applied is zero watts. Since we need to break this speaker with 100 watts, we will make the tone burst (during its short duration) 1000 watts. Divide that by 10, and this averages to 100 watts RMS over the course of the power test (which is hours long). Since the crest factor of a single frequency continuous tone (sine wave) is 3db, and the signal is 1000 watts RMS (for 10% of the time) the peak power is 2000 watts, and the RMS is 100 watts, so the crest factor (ratio of peak to RMS power) of this test is 13 db. This crest factor is not standard or similar to power test signals at all, but it is not unlike music either. The spectrum however, is definitely unlike music, and designed in concert with the crest factor to BREAK this speaker.

Choosing the Test Signal

OK, we have proven we can be cruel, now let’s be kind to the speaker and give it a really big number (we want to make the boss and his customers happy). Instead of using a standard such as the EIA RS-426A spectrum, (Circa 1980, and this has been replaced by standard “B” which has more LF energy) let's use simple white noise (that stuff you hear in between FM radio stations or when your TV station goes out.)

EIA RS426A Measured Noise Spectrum

Editorial Note on White & Pink Noise

White noise is so called because it is like white light in that it has equal energy per unit hertz. Pink noise is white noise RED shifted (so now it is pink). When you red shift a spectrum, you bias it toward low frequencies, as in a source (like a train) which is moving away from you so that its motion increases the distance between the sound pressure waves, making the sound lower as the source moves away from you (Doppler shift). Pink noise has equal energy per octave, so the energy from 100 to 200 Hz is equivalent to the energy from 200 to 400 Hz White noise on the other hand, will have twice the energy (+3db) from 200 to 400 Hz, than it contains from 100 to 200 Hz

White Noise vs Pink Noise

So, if we suddenly use white noise to test a woofer, and we let the frequencies go from 20Hz to 20KHz, half of the energy is contained above 10kHz where the speakers Impedance is VERY high, and therefore the current drawn by the speaker is VERY low. Therefore the actual power dissipated in the speaker (as opposed to apparent power which calculates power into the nominal impedance) is also VERY low. Let's consider the woofer modeled below, with a typical 2 millihenry VC inductance.

Impedance Full Range

As we can see from the Impedance magnitude graph, by the time we are at 10kHz, this speaker is already at 127 ohms. The current it is drawing is less than 7% of what it would were it actually 8 ohms (8/127 = 0.063). Since 50% of the power of this signal is actually above 10 KHz, the actual power delivered is far far less than what we would calculate into the nominal load impedance. Hence the apparent power handling is far greater than in fact the real power dissipated in the speaker. Using white noise and calculating power handling with the nominal impedance will yield a figure far greater than the 500 watts determined with EIA standard noise.

If you are asking well, who does this? The answer is no one. If the manufacturer is going to inflate his number, he likely will NOT ask engineering to go through this kind of exercise, they will simply make something up they believe is plausible and necessary for them to sell the product. The point I want to stress here is that without a knowledge of the test signal used, THE POWER HANDLING NUMBER IS MEANINGLESS!

without a knowledge of the test signal used, THE POWER HANDLING NUMBER IS MEANINGLESS!

Bass is a large signal, not a small signal phenomenon. The lower you go, the more power you need. As we go to lower and lower frequencies, our hearing becomes less and less acute. The result is as we go to lower and lower frequencies, we have less available dynamic range in our brains between the perceived low frequency, and the point at which it becomes painfully loud.

The result of this is while practically all amplifiers go down to 20Hz, very few speakers can reproduce it without producing more harmonic distortion than low fundamental frequencies. If you are pushing a compliant (soft suspension) speaker in a vented box well below the box tuning frequency (this is no different than playing it in free air) you will just end up producing lots of distortion, or simply break the speaker.

OK, this all makes some sense you say, but where is the proof? Why it is in part three of course. Stay tuned for some examples to back up the theory.

About the Author

Paul is currently President of his own Audio Consulting company, Procondev, based in Downey California, in Los Angeles County. He is actively seeking new clients and can be contacted by email by writing [email protected]