REW Beta Release Problems with Thiele-Small parameter estimation from free-air impedance curve

[witwald]

I have been attempting to determine Thiele-Small parameters for the B&C Speakers 18SW115-8 18-inch woofer, whose data can be found here. The impedance .ZMA file was obtained by using VituixCAD's curve tracing feature, with minimum-phase phase response determination. The .ZMA file has been truncated to only include impedance data that covers the range from 20 Hz to 20 kHz, as shown on the impedance plot published by B&C Speakers.

For reference, the key Thiele-Small parameters published by B&C Speakers are as follows:

Fs  = 32 Hz
Qms = 5.6
Qes = 0.32
Qts = 0.3
Re  = 5.3 Ω
Sd  = 1210 cm²
Mms = 275 g
Vas = 187 dm³
Le  = 1.9 mH
η0  = 1.9 %
Bl  = 30.3 Tm

After reading in the .ZMA file (attached as 18SW115-8.zma.txt), I used REW V5.40 Beta 112 to perform the Thiele-Small parameter and extended impedance parameter estimation using Tools ► Thiele-Small parameters.

In the input screen, I set the value of the Voice Coil DC Resistance to be 5.3 Ω, and the Effective area of the diaphragm to be 1210 cm².

After clicking Calculate parameters I get the following results:

In general, the curve-fit that has been determined seems to be quite good, especially in the way it has captured the behaviour around the free-air impedance peak.

Below is the Thiele-Small parameters dialog box with the results:

It is clear from the above that the value of QTS = 0.175 is much less than that from the data sheet. Also, the value of RE is 3.393 Ω, which is much less than the voice coil DC resistance. The value of dR = −1.907 Ω.

As RE = RVC + dR, the negative value of dR has clearly produced the invalid value of RE.

From the above, it would appear that the Thiele-Small parameter estimation process is failing on this particular impedance curve. If the impedance values below 25 Hz are removed from the .ZMA file, the resulting Thiele-Small parameters are much closer to the data sheet values, and the value of dR is now much smaller, but still negative.

If I understand the formulation correctly, dR ≥ 0. Would it be possible to constrain the value of dR to meet this requirement? This could improve the reliability of the Thiele-Small parameter estimation process. The constraint could be easily accomplished by using x = ln(dR) in the estimation process, whereby if x was a larger negative number, it would simply convert to a small positive value of dR, thus ensuring that dR > 0.

I would be grateful for some help with this particular curve-fitting problem.

 

[John Mulcahy]

You need more low frequency data for a better fit.

 

[witwald]

Actually that's not entirely the case, as I can get a better and more realistic fit by removing all data below 25 Hz!

In any case, that's all the data that I have to work with (20Hz to 20kHz), as that's all that was provided in the datasheet by the manufacturer.

I completely recognize that the data provided is not ideal, but would it have been expected that the T-S parameter estimator would do a little bit better than it has, would it not? The very high quality of the curve-fit itself seems to indicate that it can.

 

[John Mulcahy]

I completely recognize that the data provided is not ideal, but would it have been expected that the T-S parameter estimator would do a little bit better than it has, would it not? The very high quality of the curve-fit itself seems to indicate that it can.

The curve fit is poor, here's an example of a more typical fit:

REW can measure impedance, that would give better data.