Compare Woofer in Bass Reflex- and Closed Speakers


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In the early seventies, A.N.Thiele and Richard H. Small devised a set of formulas to predict how a driver would perform in any given box. Thiele was the senior engineer of design and development for the Australian Broadcasting Commission and was responsible at the time for the Federal Engineering Laboratory, as well as for analyzing the design of equipment and systems for sound and vision broadcasting. Small was, at the time, a Commonwealth Post-graduate Research Student in the School of Electrical Engineering at the University of Sydney.

Thiele and Small devoted considerable effort to show how the following parameters define the relationship between a speaker and a particular enclosure. However, they can be invaluable in making choices because they tell you far more about the transducer's real performance.

Efficiency Bandwidth Product (EBP) is a number which shows the trade-off between efficiency and bandwidth of a driver. It is useful in determining if a driver is suited for a sealed or vented box and is also used to determine suitability for horn loading.

  1. Enter the Thiele-Small parameters of the Woofer and calculate the Frequency Response
  2. Vb, Fb, F3, Lp and Pmin are calculated for Reflex Loudspeaker.
  3. Vb, Fb and F3 are calculated for the Closed Loudspeaker
  4. EBP - The efficiency bandwidth product, a rough indicator measure is calculated.
    A common rule of thumb indicates that for EBP > 100, a driver is perhaps best used in a reflex enclosure,
    while EBP < 50 indicates a clsed enclosure. For 50 < EBP < 100, either enclosure may be used effectively.
  5. Both frequency curves ( Reflex and Closed ) are displayed for comparison.

  • Vas - Volume of air equal to the speaker's spring characteristics
  • Qts - Total Q of driver
  • Qes - Electrical Q factor
  • Fs - Free air resonance of speaker
  • Sd - Effective piston area
  • Xmax - Driver excursion

  • Vb - The airspace volume of the box. The volume of the driver and any building material needs to be added to this value.
  • F3 - lower -3db frequency
  • Fb = Box frequency
  • EBP = Efficiency Bandwidth Product
  • Qtc of 0.707 is optimal damped

Thiele-Small Parameters :

Bass Reflex Box :

Closed Box :

Vas [liters] : Vb [liters] : Vb [liters]
Qes : F3 [Hz] : F3 [Hz] :
Qts : Fb [Hz] : Fb [Hz] :
Fs [Hz] : Lp [cm] :
Sd [cm2] : Pmin [cm] :
Xmax [mm] :
EBP of woofer :

Vent parameters :

Damping :

# of Ports : Qtc :
Port diameter [cm] :


Frequency Response




Last UpDate: April, 11 2020

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