Calculation of the Bass Reflex Box losses using the Impedance Plot

That a loudspeaker housing is airtight - of course with the exception of the bass reflex opening - promises the theory, but can hardly keep the practice. The lack of sealing strips when installing the loudspeaker chassis, for example, is devastating.

And finally, even with 100% airtight housings, losses are possible because the housing walls vibrate.

The housing losses can be quantified by the quality factor QL, which flows into the dimensioning of the housing volume.
The lowest possible housing losses enable a smaller housing and at the same time a deeper bass reproduction.

When constructing a box, you will have to take account the box losses (QL).
Consider that the box will have a normal amount of leakage, which is QL = 7. After you have completed the box, you will have to measure the box losses and see if the value is between 5 and 20.

  • Discovering that QL is too low (QL < 5), means you will have to make the box bigger.
  • If QL too high ((QL > 20)), then you will have to make the box smaller.
The impedance curve of the bass reflex speaker must measured without a crossover.

The point between the peaks which has the lowest impedance, marks the
resonant frequency ( fb ) of the box.
Depending on how the 2 peaks compare to each other, in terms of height, we can consider
3 particular cases :

  1. The two peaks match in height. This means that the resonant frequency of the driver in free air (fs) matches the resonant frequency of the box (fb).
  2. The first peak is higher than the second. This means that fb > fs.
  3. The second peak is higher than the first peak. This means that fb < fs.

Impedance Curve

Speaker Parameter

Re: Ohms ( D.C. resistance of speaker )
fs: Hz ( Resonance frequency )
Qms: unitless ( Mechanical Q factor )
Qes: unitless ( Electrical Q factor )
Qts: unitless ( Total Q factor )

Enclosure Parameter

Fl: Hz ( impedance peak at low frequency )
Fh: Hz ( impedance peak at high frequency )
fb: Hz ( resonant frequency of the box )
Ro: Ohms ( the lowest impedance between the two peaks is Ro )

Please enter measured values with a minimum of two digits after the decimal point!

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