It's possible to get most of the Thiele-Small parameters from a loudspeaker by
just accurately measuring the impedance versus frequency. If this is done
twice, one with the driver in open air and one with an added (known) mass it
should be fairly easy to calculate the fs, Vas and Qt.
What you need:
is a sine wave generator with good, stable frequency. You'll need an AC
voltmeter that is also flat over the indented range (15..200Hz) and has the
needed sensitivity. A amplifier is useful.
A frequency counter is also useful, since the frequency calibration of most
oscillators is pretty awful. You'll need an accurate means of measuring DC
resistanceas well. Add to that a precision 8-10 ohm resistor for calibration
purposes, and a 1 kOhm resistor to turn your frequency generator into a virtual
current source.
How to proceed:
Using either an 8 ohm precision resistor (or accurately measuring the
resistance of the "calibration" resistor), turn your generator/AC voltmeter
into an impedometer by driving the calibrated resistor from the generator
through the 1 kOhm resistor, and adjust the output of the generator until you
get a convenient voltage across the resistor. For example, if the calibration
resistor is 8 ohms, you might adjust the output so that you measure 8 mV across
it. Basically you make the current 1 mA so that on the mV scale on your
voltmeter the reading is effectively both mV and Ohms.
Your setup will look like this:
The 1 kohm resistor turns the oscillator into a constant-current source.
Measure the DC resistance of the driver to test. This gives you Re. [Let's say
it's 6.5 ohms]
Replace the calibration resistor with the driver to test.
Do not change the voltage from the generator or
amplifier!
Adjust the frequency in the region of the specified resonance until the voltage
across the driver is at a MAXIMUM. Record the frequency. This is Fs, the
resonant frequency [let's say it's 32 Hz].
Also, measure the voltage across the driver. This is defined by Re+Res. [let's
say voltage is 42 mV which means Re+Res is 42 ohms]. (using an oscilloscope set
for phase measurement, Fs will also be where the phase is 0).
Calculate the ratio between the DC resistance (Re) and the maximum impedance
(Re+Res), call it Rc. [In this case, it will be 42/6.5 or 6.46] Find the two
frequencies on either side of the resonant frequency f1 and f2 where the
impedance is Re * sqrt(Rc) [in this example, that impedance will be 6.5 *
sqrt(6.46) = 16.5 ohms, and let's say that occurs at f1 = 22.6 Hz and f2 = 45.3
Hz].
Calculate Qms as:
Qms = Fs sqrt(Rc) / f2 - f1
in the example, it will be:
Qms = 32 * sqrt(6.46) / 45.3 - 22.6 = 32 * 2.54 / 22.7 = 81.3 / 22.7 = 3.58
Calculate Qes as:
Qes = Qms / (Rc -1)
in this example, it will be: Qes = 3.58 / 6.46 -1 = 3.48 / 5.46 = 0.66
Calculate Qts as:
Qts = Qes * Qms / Qes / Qms
here, it would be: Qts = 0.66 * 3.58 / 0.66 + 3.58 = 2.36 / 4.24 = 0.56
So, now you have Fs, Res, Qms, Qes, Qts for the driver.
Calculate Vas with Mass:
With the speaker facing upward, place small weights evenly around the dust cap
in the center. With the added mass on the speaker, find the shifted resonant
frequency using the same method you used before to determine the free air
resonant frequency.
The formule is: Vas = 1.42 * 105 x Sd2 * Cms
Sd = Conearea
In our example, Mass = 30 grams, shifted resonant frequency = 13 Hz, VAS is 58.5 Liter.
Now you have Fs, Re, Qms, Qes, Qts and Vas.
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Measuring Loudspeakers (analog)