Hoffman's Iron Law


I love Iron Laws. Why? Well, they are so succinctly and aptly named: they are infact, iron. Good luck breaking them!

If you've been a browsing member of the online audio community for a while, you have no doubt heard about Hoffman's Iron Law. What's it all about? Well, it is quite simply, "You can have low end extension, high efficiency, or small enclosure size. Pick two."

Please note that while many people use this statement related to enclosures, it applies to the speaker you're using as well So what does that mean and why is that the case? Well, as you may have heard me say once before, speaker design and engineering is a game of compromises. The best speaker (if there truly is such thing) is the one that has the lowest impacting compromises.

Let's say you you drive a little Dodge Sprint or another vehicle with a relatively small cabin and little-to-no room for an enclosure. Of course, you're a bass head and you want to hear those lower notes banged out with some authority. To top it off, you're a cheap bugger and want a lot of sound without buying an expensive amplifier. You build your miracle enclosure, install everything, power it up, and surprise! Those low notes just aren't there. You tried to have your cake and eat it too, which just doesn't work in the real world. Naturally, you think there must be something wrong with the sub or amplifier. Now you have switched every product imaginable in and out. The good news is that an amplifier rated much higher than the RMS of your sub has given you that low end beat you're looking for. The bad news is that you just cooked a voice coil.

This is Hoffman's Iron Law at it's finest. If you want a low end monster, you had better step up the power or build a behemoth enclosure. If you want to keep your amplifier costs to a minimum, you had better build a huge enclosure or accept a very high rolloff with very little low end. If you want a small enclosure, be prepared to buy a big amp or give up that low end you love.

What is the specific relation between these by-products? The efficiency of any speaker system is directly proportional to the enclosure volume and the cube of the f3 (the frequency at which SPL is down 3dB). If you halve the efficiency of your speaker system, you may also halve the volume of the enclosure. However, if you decrease the f3 of your speaker system by a factor of two while retaining the same efficiency, you would have to increase the enclosure volume by a factor of 8 (2^3=8). Let's say you have an enclosure with an efficiency of 90dB/w/m that is 2 cubic feet in size. Suppose the f3 of this system is 30hz. However, you've decided you want a heavy bottom end and wish to drop the f3 to 15hz. Without decreasing efficiency, this change would require an enclosure measuring 16 cubic feet in size! That is quite a change, and hardly affordable in a vehicle.

With a lot of preamble, I think that adequately explains how things work on the enclosure side. But as I mentioned earlier, this applies to a normal speaker prior to installation as well. I'll cover this when I get a chance, but to provide a starting point:

where n0 = reference efficiency (% based)
Fs = the resonant frequency of the driver (measured in Hz)
Vas = Volume of air which, when acted upon by a piston of area Sd, has the same compliance as the driver's suspension (measured in m^3)
Qes = electrical "Q" of the driver at Fs (unitless)

n0 = (9.614 * 10^-7 * Fs^3 * Vas)/Qes * 100



Neil @ SSA