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Understanding the Thiele/Small Parameters

Prerequisites:
If you haven't already read the speakers page of this site. I would strongly recommend reading it before you continue with this page.

fs:
fs is the resonant frequency of a speaker in free air (not in an enclosure). At resonance, the speaker's impedance increases dramatically. The speaker's impedance may go from 4 ohms to more than 20 ohms at resonance. The image below shows how a speaker's impedance changes across the audio spectrum.

Impedance curve

Put your mouse/cursor over the different frequencies below the following impedance curve. You can see by the bar graph that the current flow through the voice coil is the least at resonance. The voltage applied to the speaker is constant for all frequencies.

first.gif
Relative
Current
Flow
Through
Voice Coil
Impedance Curve
          15Hz 25Hz 35Hz 45Hz 55Hz 65Hz 75Hz 85Hz 95Hz

fc:
fc is the resonant frequency of the driver in a sealed enclosure. The fc is higher than the fs with a given driver. The image below shows the impedance curve with a woofer in 1 ft^3 and in an infinitely large enclosure. You can see how the resonant frequency shifts when the driver is mounted in an enclosure. Enclosures of different sizes will produce different resonant frequencies.

Resonance infinite baffle and 1ft^3 sealed enclosure

This image (below) shows the impedance curve for a ported enclosure. You should notice that, unlike sealed enclosures, the impedance is lowest at the resonant frequency.

Resonance in a ported enclosure

Vas:
Vas is the volume of air that has the same compliance as the speaker's suspension. Stiff speakers have lower Vas and tend to use small enclosures. Speakers with loose suspension have a higher Vas and use larger enclosures.

Qes:
Qes is the electrical Q of the speaker and only takes the electrical properties into consideration.

Qms:
Qms is the mechanical Q of the speaker and only takes the speaker's mechanical properties into consideration.

Qts:
Qts is the total Q of the speaker. It is defined as 1/Qts = 1/Qes + 1/Qms.

Qtc:
Qtc is the total Q of the speaker in an enclosure including all system resistances. A Qtc of .707 is the most common and generally produces the flattest frequency response with approximately a 12dB/octave rolloff. Higher values of Qtc will give a peak in the output with a sharper rolloff. A lower Qtc will start to roll off earlier and will roll off at a slower rate. If you don't know what Qtc you need, start with a Qtc of .707.

Violet = Qtc: 0.9; Green = Qtc: 0.8; Red = Qtc: 0.7; Yellow = Qtc: 0.6; Cyan = Qtc: 0.5;

Qtc Curves

Vb:
Vb is the net internal volume of the speaker enclosure

EBP:
EBP is the efficiency bandwidth product. It is used as a guide to determine whether a speaker will work better in a ported or sealed enclosure. It is defined as Fs/Qes.

no:
no is the reference efficiency of a driver.


  • This calculator will tell you:
  • Whether the speaker is better suited for a sealed or ported enclosure
  • The 3dB down point of the speaker in either enclosure
  • The recommended volume for sealed and ported enclosures
  • The resonant frequency of both enclosures
  • The port length for ported enclosures
  • The reference efficiency in both % and decibels at one watt
  • If any of the fields return 'NAN' or 'infinity', you did not fill one of the fields required to make the calculations.

Please keep in mind that the data produced by this calculator is simply a guideline. If the manufacturer suggests a particular enclosure, use their recommended design.

  • Notes:
  • The output response curve for the sealed enclosure is determined by the Qtc that you enter.
  • The output response curve for the ported enclosure is going to be a maximally flat design.

Use this program to calculate Qts if you only have Qms and Qes.
Data Input:
Qms?
Qes?
Data Output:
Qts:

Data Input:
Speaker's Resonant Frequency (fs)? Hertz
Qes?  
Qts?  
Qtc?  
Port diameter for ported enclosures? Inches
Vas? Ft3
Data Output:

Sealed Enclosure
3dB Down Point (f3) Hertz
Resonant Frequency (fc) Hertz
Enclosure Volume (Vb) Ft3
   
Ported Enclosure
3dB Down Point (f3) Hertz
Resonant Frequency (fb) Hertz
Enclosure Volume (Vb) Ft3
Proper Port Length Inches
Reference Efficiency %
Reference Efficiency Decibels
(Efficiency is at 1 watt input when measured at a distance of 1 meter)
EBP =  


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