FAQs: Loudspeakerboxes / Lautsprecherboxen

OK, here are the Frequently Asked Questions about Loudspeakers in english.

Hier sind die meistgestellten Fragen zum Selbstbau von Lautsprechern in deutsch.

1. How can I calculate the capacity/volume of my loudspeaker-box?
If you don't have the exact parameters you can't simulate or calculate the volume or length of tube etc. Parameters... this doesn't mean only diameter, and max. Power, these parameters are called Thiele-Small-Parameters or TSPs. You need them for calculation.

2. What are Thiele-Small-Parameters?
The TSPs describe the acoustic and electrical behavior of a loudspeaker in a special case.
The most importent params are the resonance-frequency fs, the equivalent-volume Vas and the quality/grade Qts of the woofer. You need these specifications for calculation of the capacity of a box. The most important params are:

• Z : the impedance is the rounded AC-resistance of the speaker, almost 4 or 8 ohms. Z depends on measure-frequency.
• fs : is the resonance-frequency (in Hertz, Hz) of the chassis: this means the first maximum of Z in free-field
• Re : is the DC-resistance of the speaker-coil (in ohms), mostly it's about twenty percent smaller than Z.
• Qes : is electrical quality, the ratio of Z to Re at fs.  So Q has never a unit.
• Qms : is mechanical quality, this value describes the ratio of deflection at fs.
• Qts : is the total (and acoustical!) Quality. Qts-value is the reciprocal attenuation of the membrane and decribes how hard is the suspension.
Qts=1/(1/Qes+1/Qms)
• Sd : the effective Surface of the membrane in square-centimeters (cm², qcm) or square-inches of the loudspeaker
• Vas : is the das equivalent-volume (in liters or cubic-foot) and describes the suppression of a loudspeaker in comparison with an air-capacity.
• SPL : this Sound-Pressure-Level is the indirect efficiency and defines how powerful is the pressure in decibel (dB SPL) with one watt in a distance of one meter. (about 40 inches)
• Rms : is the mechanical Resistance of the suspension in kg/s (kilogramms per second). Smaller values are better.
• Mms : is thy dynamic Mass of membrane in gramms (g).
• Cms : the mech. compliance in mm/N (millimeters per newton) is the reciprocal spring-constant of suspension.
• Le : This is the inductivity in mH (milli-henry) of the coil and important for calculation of passive filters.  This inductivity is the reason for rising impedance with higher frequency.

That's the look of the AC-Resistance of a 4 ohms-Bass-Speaker in dependence of the frequency. The DC-Resistance (0 Hertz) Re is 3.1 ohms. At freefield-resonance-frequency fs (here 30 Hz) the impedance increases to its first maximum, so you get a quality Qts of  about 0.400. The increase of Z to higher frequencies is the result of the inductivity of the speaker-coil and is here about 3 mH.

3. How can I calculate something with the TSPs?

For decision is the EBP useful: The Efficiency-Bandwidth-Product is quotient of fs and Qes

or you use this: X = fs/Qts
With X you can recognize the best or a good combination of the loudspeaker to the acoustic system.

X <= 40 Transmissionline (TML)
X about. 50 (40...80) contained systems / geschlossene Systeme
X about. 60 (50...100) contained bandpass-systems / geschlossene Bandpässe
X about 100 (80...120) Reflex / Bassreflex (BR)
X>= 120 for Horn systems

• Qtc=0.5 (Linkwitz-characteristic) super precision and impulsivity, very bad depth (level of sound-pressure at low frequency)
• Qtc=0.577 (Bessel) very good precision, bad depth
• Qtc=0.707 (Butterworth), good precision, good depth
• Qtc>0.707 (Chebycheff), bad precision, high pressure (with higher Qtc you have worse precision)

Calculating of Bandpass- and reflex-systems isn't so easy. The best way for that, using a simulation-software, like the Freeware BassCADe.
You need a Qts of 0.3...0.4, for best performance, lower values does not produce enough low frequency sound pressure, higher values will increase the volume of the box for a good sound.

OK, here the formula for the Helmholtz-resonance-frequency:

sqrt... square-root, Quadratwurzel

4. I don't have the TSPs. How can I get them?
They are different ways:
1st: the manufacter gives you the most important values (often you can find them on the manufact.-page)
2nd: Maybe they are on my side, here If you can't find them, please do not mail me, I don't have these TSPs.
3rd: search in other sources (maybe in web or cataloges)
4th: The final way (but the best) : You can measure and calculate for yourself. How? You need two impedance-graphs, then the software calculate the parameters. SW like BassCADe or you know the formulas...
They exist software (like Hobbybox) they can measure the parameters with help of PC-soundcard.

5. I got the TSPs from the manufactor of the speaker. But the values are different from the table on your site. What's right?
Sometimes manufactor change the speaker and keep the name. You don't know how was the measurement of the speaker. Usually you should measure with cold coil and soft membrane-hanger. But the values are not so exact, because lifetime and temperature have an importent influence of the parameters. So you get high tolerances.
Often some manufactures specify for their speakers low Vas- and Qts-values. For Marketing? Some comparriosons an further TSPs (manually measured) on www.northcreekmusic.com.