# Quality factor how is it defined?

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#### shank1207

Hello,
i have this question on quality factor after reading the paper by Small, Q is defined to be a ratio of resitance to reactance for parallel circuit. But in the electrical analogous circuit of loudspeaker there is even the inductance term why don't we use the inductance in the formula? And it is measured as Qmc=wCes*R. Also when we are adding damping according to the formula resistance should increase and Qmc is supposed increases , but he writes that Qmc is less for filled enclosure then unfilled enclosures.

Thanks

#### Ron E

It can be a little confusing, the facility with which some of these sources switch back and forth between mobility and impedance type circuits and the electrical, mechanical and acoustical analogies.

The R relating to Ces is Res, and Res is inverse, it gets bigger for less damping.
The inductor is factored in because w=1/sqrt(Les*Ces)

#### shank1207

It can be a little confusing, the facility with which some of these sources switch back and forth between mobility and impedance type circuits and the electrical, mechanical and acoustical analogies.

The R relating to Ces is Res, and Res is inverse, it gets bigger for less damping.
The inductor is factored in because w=1/sqrt(Les*Ces)
Thanks thats makes sense and when i calculate i get 2*w*Ces*Res

#### sreten

but he writes that Qmc is less for filled enclosure then unfilled enclosures.
Thanks

Hi,

Putting a driver in a box increases the Q. The increase depends on
the ratio of box size to Vas, the larger that is the less Q increases.

Stuffing a box increases its effective volume so the Q is less than
for the unstuffed box. Not by a huge amount usually, as the volume
increase is is typically about 20% for well stuffed.

However I have seen very well stuffed midranges where the
stuffing increases the mechanical resistance significantly,
and drastically reduces the effective driver Q.
xrk971's dagger mid enclosure seems to do this.

rgds, sreten.

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#### shank1207

Hi,

Stuffing a box increases its effective volume so the Q is less than
for the unstuffed box. Not by a huge amount usually, as the volume
increase is is typically about 20% for well stuffed.

rgds, sreten.
Yes i was thinking about this too like how does the stuffing increase the mass and volume at the same time, the volume seems logical because of decrease in speed of sound how about the mass is it due to the loading in the rear of the driver due to stuffing

#### sreten

Hi, Stuffing does not affect mass as far as I'm aware, rgds, sreten.

#### Ron E

Stuffing can affect mass insomuch as the fibers move with the diaphragm. You will find stuffing effects quite resistant to analysis, though, except on a very broad level. Broadly a lumped model says stuffing just acts as a dissipative element at resonance.

#### shank1207

Hi, Stuffing does not affect mass as far as I'm aware, rgds, sreten.

Mass loading due to stuffing has been documented by Mr. Small in the closed box system analysis he mentions it might be either due to constriction of air passage near the rear of the diaphragm or due to motion of material itself.

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