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Speaker simulation model for open source project

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gnuarm:
I need to design a driver for a speaker to sound an alarm on an open source project.  The drive is from a PWM modulated 32.768 kHz waveform.  I'm not worried so much about the 33 kHz drive, but I would be interested in seeing how the circuit handles that.  If nothing else the speaker and the ear should integrate the 33 kHz. 

I'm interested in seeing the frequency response of the in series cap with the speaker characteristics as well as the resulting current through a sense resistor used to detect a speaker failure.  Yeah, I know, this sounds a bit extreme.  It's for a ventilator where the alarm circuit has requirements regarding this.

I've found a number of web pages that show a 5 element equivalent circuit, LR(LCR) where the parentheses enclose components in parallel and everything else is in series.  What they don't show is how to obtain the parameters for the speaker. 

I've written to the speaker maker to see if they can provide the parameters for simulation.  One of the web pages for the model show how to calculate the simulation parameters from other, equally hard to get parameters such as Mechanical Q factor, Electrical Q factor and other Thiele Parameters.  I'm pretty sure I'm not going to get Thiele Parameters for a 2" speaker (although BMS has them for some of their 500 watt products which would be about perfect other than the price).  I'm not sure I'll be able to get the passive model data either. 

The speaker I'm using has a resonance of 300 Hz and a response range of 150 Hz to 12500 Hz, impedance 50 ohms.  I could come up with values for a three element model, but that doesn't seem it would be as effective as the five element model.  Any suggestions?  I suppose without more data there's no way to come up with a fuller simulation model. 

One effect I'd like to get right is the DC response.  I would expect the DC resistance to be a lot different from the stated impedance but I have no way of estimating that.

Ian.M:
Your GoogleFu is lacking! Try https://www.google.com/search?q=measuring+thiele+small+parameters
This result looked interesting and relatively simple to implement
https://audiojudgement.com/measure-thiele-small-parameters-using-free-software/

Hint: simply measure the DC resistance, preferably using a meter that supports four wire measurement.

Of course if you haven't got the speaker yet, you'll be a bit stuck . . . .

Circlotron:
T&S parameters are pretty straightforward to measure. Here's my tried and true spreadsheet that does it all for you.

https://www.diyaudio.com/forums/multi-way/24864-parameter-spreadsheet-post353269.html

Ian.M:
@Circlotron,
diyAudio attachments are members only. :( Any chance you can repost your spreadsheet here?

Circlotron:
Here you go.

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