March 16, 2012

Let's talk about woofer speed

Woofer speed is an entirely hairy topic, but I'm going to discuss here one aspect briefly - transient response. It is commonly thought that driver moving mass and motor strength are critical aspect of the time it takes for a woofer to respond to a transient signal. Some take a narrow view and look only at moving mass. Others will argue that this can be overcome by a powerful motor. It seems in reality neither are directly related to transient response.

In the past, Dan Wiggins of Adire Audio had an article on this topic on his website, which is no longer online, but can be found on the Way Back Machine:

Woofer speed by Dan Wiggins >

This post is essentially a summary of that paper - the short version.

We start with the basic equation that we all learn in Physics class:

F = ma

which means

Force = mass x acceleration

The force is provided by the driver motor and we know it as BL factor multiplied by the current i. The mass in question is the moving mass of the driver (mms). So we can now rewrite the equation in speaker terms:

BL x i = mms x a

BL is time invariant - that is, it doesn't change with time
Current (i) on the other hand, does change with time as it carries the audio signal
mms is also a constant and does not vary with time

So we see that both BL and mms are time invariant and don't change with time, hence they are not real factors in the equation. The two critical factors are in fact current and acceleration which we are seeking to investigate.

So we see that the ability of a driver to respond quickly to a transient signal is proportional to the current supplied. If we could make the current increase infinitely fast, then the driver would respond in kind. However, we can't increase the current infinitely fast. The reason is that the voice coil is in fact an inductor, and it turns out that the inductor is the bottleneck in this equation. Inductors don't like the current flowing through them to change. The bigger the inductor, the longer it will hold onto the current. So in a nutshell, we now have an answer - the critical determinant of how quickly a woofer will respond to a transient signal is the voice coil inductance.

So if you want to know something about the transient response of a woofer or subwoofer, consider the voice coil inductance.

In a real room, the lack of bass damping will often be a more sigificant factor, but once this is dealt with via treatment, this aspect is something to consider. In a recent comparison of an Acoustic Elegance TD18 woofer and my Eminance Magnum 18" woofers I noticed an obvious difference in the perceived transient response. I used some EQ to match the frequency response and there was a clear improvement with the TD18H which has a much lower inductance.

So what happens if the mms is made very very heavy? The fs is pushed down and the driver becomes very inefficient. Taken too far it will perform quite poorly for reasons other than transient response.


  1. Thanks Paul.

    This should be clear from reading the Acoustic Elegance site but they have not explained it like you have.

    Good one and something to keep in mind.


  2. As woofers LTI systems inside normal operating conditions a 'fast' woofer is just one with extended high frequancy response.

  3. Hi Paul,
    This is an interesting subject. In addition to what James says: unless your woofer is a full range driver, you will always find a big inductance in the filter between the amp and the driver.
    A high rise in current is a powerful signal, and/or a high frequency.
    But I can't ignore the perception of speed that people find when they hear high efficiency woofers or closed box systems. I think it has little to do with how fast the cone jumps from zero movement to high excursion. For reproducing a low frequency of 100Hz the woofer has all the time in the world to follow that signal. My opinion is, that we have to find the answer in what happens after the signal stops. Then some high Q/high mass systems still sing, they don't stop moving directly but swing out. They have stored energy.
    Let's imagine a high compliant (' weak' ) spring and hang a relatively high mass on it and then let it swing. It takes some force to let it stop from swinging instantly. If we do with a low mass on a low compliant spring, it will stop moving more easily/rapidly.
    So a heavy cone with high compliant surrounds with low Fs will likely have a high Q on it's resonance frequency and have a not very perfect transient response. But a typical high efficiency woofer (like we see in PA or studio's) usually has a lighter cone and less compliant swing-system due to the reliable cloth surrounds, double spiders and so on, have a relatively high Fs, don't produce very-low bass but sound "fast" because they have a better transient response. For bass horns this is even more the case.

    Arjan Hofstee.

  4. What James wanted to say - this argument in this article is simply wrong. Dan Wiggins claims that two minimum phase system exhibiting the same frequency response have a differing transient response. This is incorrect. As James said, the transient response of a minimum phase transducer is mutually related to its frequency response.

  5. Do you have something to back up your assertions?

  6. My English came out a little garbled but basically what svenr said. Its basic signals stuff. To an electronic engineer your argument seems backward as impulse (transient) response is just another representation of frequency response in this system. An ideal impulse response from a transducer would be achieved by a transducer with flat frequency response over all frequency, this transducer would produce all spectral components of the impulse correctly and therefore reproduce the original impulse. A woofer with 'good' transient response is just closer to the ideal frequency response and therefore has extended high frequency performance, this is usually achieved like how you point out by decreasing voice coil inductance via shorting rings and the like.

  7. This is a good course on signals stuff that will allow for understanding of this viewpoint:


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