Measuring Fc and Qtc of a closed-box system

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C

cT equals piD

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Joined 2012
#1
In several places I've seen the method described for measuring/ calculating free air resonance Fs and Qts of a loudspeaker driver. For example, see Section 1.1 of this article by Rod Elliott-

http://www.sound-au.com/tsp.htm

So my question is, can this methodology be successfully applied to a closed-box loudspeaker system? After building a closed-box system, I wanted to check that Fc and Qtc actually are what I intended them to be. I imagine this is something that quite a few other builders would like to do.

Thanks if you know,
Pete
 
#3
Thanks Marcel. I measured the box resonant frequency and it was according to design. Then based on Ro equal to Zmax / Re, I found f1 and f2. However then based on those measurements and calculations, Qmc is less than Qms given in the driver specifications. Also Qtc works out to half of what it should be.

My speaker system is a bit unusual, so that might be why I'm not getting the measured values that I expected. My system has six woofers, three of two woofers wired in-series, and the three pairs of woofers connected in parallel to the output terminals of a passive low-pass filter.
 
#4
All six woofers are back loaded by a common closed box. This evening, I looked at near-field sound pressure versus frequency around the resonance frequency on an oscilloscope and the response corresponds to measured Qtc equal to 1.1. Based on the idea of the six woofers acting like one driver back-loaded by a volume of air six times that for one driver, I had calculated Qtc equal to 2.0.
 
#5
Any damping material in the box will lower the Q. Typically designers target a Qb, Qtc in the box, of around 0.707 for the best low end extension with a relatively flat response. With a Q of 2 there would be a pretty large peak in the bass and a higher cuttoff frequency of the bass.
 
#6
Actually there is very little damping in the box and I think that the lack of damping might be the problem, just a guess. The box is very elongated which as I understand it can result in interior standing waves. The inside volume measures 6 inches (15 cm) wide by 4 inches (10 cm) deep by 45.5 inches (116 cm) high. It would be a lengthy explanation as to why I chose Qtc = 2, but that is definitely what I was aiming for. Also I should add that the six woofers are identical and relatively small diameter, 5.25 inch (13 cm).
 
#7
If you have a PC, I highly recommend you download the free software package Arta. It includes a program Limp that combine with a very simple single 100 Ohm resistor and a few connections to the PC audio inputs and output let you make excellent impedance sweep measurements. With the whole sweep you can see any resonances. It also calculates the full TS parameters for a driver. The software manual has diagrams for the measurement setup schematic and excellent instructions for making all sorts of audio measurements.
 
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#8
The six woofers are connected 3 times a pair of woofers in-series. Then the three pairs are connected in parallel to the output terminals of the low-pass filter. The mistake that I made in calculating Qtc was assigning twice Qts to the speaker-pairs connected in-series. Actually some years ago I knew better, but I had forgotten that connecting 2 speakers in series (or parallel) has Qts of the single speaker driver.

Calculating Qtc = sqrt(alpha + 1) * Qts (of the spec sheet) then gives me a Qtc that agrees with what I derived by measuring.
 
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