Bl/Mms = Nonsense

[Julian 641]

Bl/Mms is constantly turning up everywhere to describe the "acceleration factor" of a driver. This is totally wrong! The "acceleration factor" or "speed" of a driver is determined only by the bandwidth of the driver and nothing else. In reality the "fastest" driver or the one with the quickest rise time is one that can play the highest frequencies! Here we will use a picture to help explain the situation. In the following we show time from left to right, and amplitude from top to bottom.

- Picture courtesy of Cool Edit 96 -

www.syntrillium.com

We have 3 complete sine wave cycles showing with a period of silence between each. The first one we shall say is 20hz, the second one is 40hz, and the third one is 80hz. However they could also be 200hz, 400hz, and 800hz. Or they could also be 500hz, 1Khz, and 2Khz. Or even 5Khz, 10Khz, and 20Khz. It is the octave relationship that is the same, that is each wave is half the time to complete a full cycle than the one before it.

So the "speed" is needed in moving the driver back and forth to match these waves. Now look at the first wave, we need to move the driver from the middle point out to a maximum peak, then pull it back to the middle, then to the opposite peak, then back to the middle.

In the second wave we have to do this twice as quick.

In the third wave we have to do this 4 times faster!

But what have we done in reality when we moved the driver faster? We have only changed the output frequency! We see that for a driver to cover all these varying speeds, it is exactly the same thing as covering a wider bandwidth of frequencies. Nothing more!

The acceleration of a driver is described by;

Force/Mass

Many people and even other speaker companies confuse this and say the force is equal to the Bl parameter of a speaker. After all it is called the "Force Factor" right? However the real force equation for a magnetic speaker motor is equal to;

Force = magnetic flux in gap ( B ) * Length of wire in gap ( l ) * current in the wire ( i )

You cannot forget the current, without the current the wire does nothing in the gap!

This means you cannot look at Bl without also including the resistance or Re of the speaker at the same time. They are directly related to each other in a speaker, one does not do anything on its own. Bl means nothing without Re, this is a very important point to understand with relation to driver parameters.

Now let us look at a speaker motor playing a wide bandwidth of frequencies. First we have to assume that if the voice coil is in the gap, both the B and the l of Bl do not change. However, to get the same amount of force ( B * l * i ) across the entire frequency bandwidth, you need to keep the same amount of current at all frequencies. To do this you need to keep the same impedance at all frequencies to keep the same current. The main limiting factor preventing the voice coil from having a flat impedance above the resonance peak and doing this is its self inductance. This is the real determinate of driver "speed"!

This self inductance increases the impedance of the voice coil the higher in frequency it goes. The current goes down, and hence the Force has to go down as the current goes down. Eventually you will come to a frequency that no current can flow in the driver! Now since lower frequency drivers need more voice coil wire to get more xmax, they also create more self inductance as a byproduct. Thus when you hear someone talk about "slow" drivers, what they really are describing are drivers that are bandwidth limited.

Now there are other issues to the bandwidth, it is not just the self inductance. There are issues with the diameter of the diaphragm, the shape and depth of the diaphragm, the diameter of the voice coil, etc. However the self inductance is the majority contributor for 99% of loudspeakers.

So in conclusion to get the Force needed for a "fast" driver, you need to get the lowest inductance as possible first. Bl/Mms does not show anything about a driver's response, rather it is total nonsense that should be placed in the GARBAGE!

I thought this was rather interesting

(Source)

[Duran 387]

Very good read

[95Honda 486]

I thought it was common knowlege that Bl and Mms relates to effeciency, not transient response.

This was one of the main points touted in XBL2, underhung, etc technology, high stroke with a small (short) coil with low Le (preserved transients)....

I wouldn't call them nonsense at all, though.....