Nov
19
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 reasonably low distortion
(<1%), as flat frequency response as possible, and good, stable frequency.
You’ll need an AC voltmeter that is also flat over the indented range and
has the needed sensitivity. 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 resistance as 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.
Here’s 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:o---- 1kOhm -----+<-------+ | | | Sine gen. 8 ohms AC voltmeter | | | o----------------+<-------+This circuit is called an impedometer,
where the voltage across the load is proportional to the impedance of the
load. The 1 kohm resistor turns the oscillator into a pretty good
approximation of 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!
- 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:
Fs sqrt(Rc) Qms = ----------- f2 - f1 [in the example, it will be: 32 sqrt(6.46) 32 * 2.54 81.3 Qms = ------------- = ----------- = ---- = 3.58 45.3 - 22.6 22.7 22.7 - Calculate Qes as:
Qms Qes = -------- (Rc - 1) [in this example, it will be: 3.58 3.58 Qes = --------- = ------ = 0.66 6.46 - 1 5.46 - Calculate Qts as:
Qes * Qms Qts = --------- Qes + Qms [here, it would be: 0.66 * 3.58 2.36 Qts = ----------- = ------ = 0.56 0.66 + 3.58 4.24
So, you have derived Fs, Res, Qms, Qes, Qts for the driver.
- Repeat the measurements in a sealed, leak-free, unlined test box, and
determine the equivalent values of Fc, Qmc, Qec, and Qtc (use a box
whose volume, Vb, is close to the expected Vas for maximum accuracy).
[In our example, Vb = 20L, Fc = 80 Hz, Qec = 0.95] - calculate Vas as follows:
Fc Qec Vas = Vb [ -------- - 1 ] Fs Qes [In our example: 80 * 0.95 76 Vas = 20 [ ----------- - 1 ] = 20 [ ---- - 1 ] = 20 * 2.62 = 52L 32 * 0.66 21 Our Vas is 52 liters].
You now have Fs, Re, Qms, Qes, Qts and Vas.
Information sources
The information in this article is mainly based on news articles from Dick
Pierce posted to rec.audio.pro newsgroup at 1998.
Comments
Leave a Reply
You must be logged in to post a comment.