Sensitivity and Hofman’s Iron Law, or “why you can’t have your cake and eat it too”

floyd's iron law

by Jim Salk

in Speaker Design

If given a choice, most people would opt for a high sensitivity speaker in a small cabinet that plays extremely deep. While that may be possible (we’ll get to that shortly), this basic desire runs smack up against the laws of physics.

I’m sure you’ve probably run across that old adage, “quality, speed, low price…pick any two.” It basically states that if you want quality fast, you have to expect to pay a higher price. If you want quality at a low price, you have to be willing to wait. And if you want it fast at a low price, well…

Where driver sensitivity is concerned, there is a similar law in effect. It is called “Hofman’s Iron Law” and it offers you any two of the following: small cabinet size, deep bass and high sensitivity.

A few decades ago, amplifiers were limited in terms of power, so speakers had to be efficient. They didn’t play particularly low and the cabinets were generally quite large. Today, most speaker manufacturers want to offer small speakers with extended bass response. So driver manufacturers put most of their R & D efforts into low sensitivity drivers that can play deep in a small cabinet. Since today’s drivers tend to be less sensitive, so do today’s speakers. While perhaps these lower sensitivity ratings are less than many people would like, the wide availability of high-power amplifiers make the trade-off a reasonable one.

In the end, speaker design is all about trade-offs. If you are willing to sacrifice bass extension and live with a relatively large speaker cabinet, high sensitivity drivers are still available. But spouses don’t have much tolerance for large speakers and most consumers prefer speakers with reasonable bass extension.

To put things in perspective, consider this example: JBL manufactures a 12″ woofer that is well regarded by the high sensitivity crowd. But it doesn’t play very deep and requires a relatively large cabinet. By comparison, it is relatively easy to produce a speaker with greater bass reach using a modern 5″ or 7″ driver. This is Hoffman’s Iron Law in action.

If you are not willing to give up bass extension and simply can’t live with an overly large cabinet, there is basically only option at your disposal – multiple drivers. When you wire two woofers in parallel, you gain about 6db in sensitivity. At the same time, the impedance is cut in half. If you hook them in series, the impedance doubles, but there is no increase in sensitivity.

So if you take a driver that is, say, 84 db sensitive and you want a speaker that is over 90 db sensitive with a impedance of 8 ohms, you need four drivers (two pairs of 8-ohm drivers that are wired in series, wired in parallel). This will get you well over 90 db in sensitivity at 8 ohms and is one common approach to the problem.

But as indicated above, there are always trade-offs. When the signals from these drivers intersect somewhere out in front of the speakers, the resulting comb filtering reinforces some frequencies while attenuating others. So you end up with peaks and valleys and a jagged looking frequency response curve.

We often get calls from people who own low power amps that require high efficiency speakers. We always try and help them out. At the same time, we always make them aware of the trade-offs they must be willing to accept.

If you find yourself obsessed about sensitivity, here are some things to consider.

  • The ability of any system to produce exceptional sound will be limited mainly by the capability of the speakers
  • Today’s highly-accurate, cutting-edge drivers tend to be low sensitivity
  • If you want a speaker using these cutting-edge drivers, it will tend to be a low sensitivity design
  • Watts are cheap – high power amps are readily available

The reality is that although there are ways around it (if you are willing to accept the trade-offs), Hoffman’s Iron Law will basically stand between you and a high sensitivity speaker in a small cabinet with deep bass response. So if you’re after the high quality, full-range sound reproduction modern drivers are capable of,  you’d be better off finding a good high-power amp to drive your new low sensitivity speakers. Don’t blame me…blame Hofman.

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