Build of Loudspeaker Enclosures

Arches National Park, Utah USA (Photo by Yuichi)

Characteristics of a loudspeaker driver are explained by the Thiele Small parameters (often called TS Parameters).
We can calculate major TS values by using following procedure with very simple manner and conventional tools. In this page, KMS (Kilo, Meters, Seconds) system is used. To design speaker enclosures, Fs, Qts and Vas are needed at minimum. If those are listed in the catologue, you can use those numbers. However, if you like to measure your own driver(s), you can do it by yourself.

Finding out Fs and Qts

Speaker driver construction is shown below. The diaphragm has its own resonance frequency.
When mass of the movement is given as M(Kg) and suspension stiffness as K(N/m), then resonance frequency f(Hz) is generated as equation [1]. However, we can measure f(Hz) quite easily.
The procedure to find out TS parameters are as follows.
(A): First, measure the voice coil resistance (Re) by the circuit meter.

(B): Find out (f) or (Fs) by changing the generator frequency. Find out the highest impedance point which is the lowest voltage in the system diagram. This point is (Fs).

(C):Obtain (Rmax) at Fs.

(D): Calculate (ro) by equation [2]

(E): Calculate (Rx) by equation [3].

(F): Find out (f1) and (f2) by changing the generator frequency.

(G):Now, we can calculate Qms by equation [4].

(H): Then, calculate Qes and finally Qt

(System diagram)
The signal generator may be a audio signal generator or PC based software generator.
When the generator has less power, a power amp should be used.

Finding out Vas by "added air load" method

Single impedance curve generates Fs, Qts and other parameters. However we have to have second impedance curve to get (Vas). There are two practical ways to get Vas.

One is to add air load onto the diaphragm. We have to provide closed box. There is no acoustic treatment inside. Recommended box size are...
10cm driver : 5 liters / 20cm driver : 10 liters / 30cm driver : 20 liters
In this case, new Fs gets higher than Fs because suspension gets strong.

The procedure to find out Vas parameter is as follows. We setup the same measurement diagram as used in the previous measurements.
After adding air load in front of the diaphragm, we do the same measurements. In this case I rename (Rmaxc) instead of (Rmax), (Rxc) instead of (Rx) and so on. Just added small "c" to identify added air load case.
[I] : Perform the same measurements from procedure [A] through [H].
Then, we can find out Fsc, Qesc. Vb is added air load (cubic meters)

[J] : Then, calculate (Vas) by equation [11]

Finding out Vas by "added mechanical mass" method

One other way to measure Vas is added mass method which is to add known mass (kg) on the diaphragm. In this case new Fs gets lower than Fs because diaphragm total mass gets heavier..
[I] : First, measure the effective diameter (meter) of the diaphragm.

[J] : Then, measure new resonance frequency which is (Fsm) in this case. Those are all we do.

[K] : Then, calculate Vas by equation [13]

Above are the procedure how to measure key TS parameters. Some other parameters are also generated through the process. Followings are some notes to perform.

1): Remember that values are all described in the MKS system. Therefore, all units must be Kilogram, Meter, Square meter, Cubic meter, Second. If calculation does not much to expected value or the catalogue spec, please verify.

2): To get Vas, we add air load or mechanical mass. The new Fs' may be high or low. To have better accuracy, the ratio of Fs and Fs' is around 2 or 0.5. Which means if Fs is 80Hz, then Fs' may be around 40Hz or 160Hz depending upon the methods.

3): Repetitive calculations bother us. So, we can build up spreadsheet such as MS Excel. A sample of the spreadsheet can be downloaded from the download page.

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