Electro-mechanical formulas ( Thiele / Small )

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Posted by Wayne Parham [ 70.128.110.173 ] on January 04, 2009 at 19:31:33:

In Reply to: Re: Vad calculator posted by hitsware on January 04, 2009 at 11:03:26:


I stopped maintaining the VadCalc applet. It was written in a weird little language called CA Realizer (Computer Associates), which I also used to write tubing movement programs for the oil and gas industry. I do most of my programming in C++, but that language was easier to use for some things, so I gave it a go for a while.

I assume you want to use it because you don't want to build a box to find Vas with the sealed box method. If that's the case, I suggest the added mass method. Then again, I understand the desire to have a method that works without two impedance sweeps. The VadCalc process was simple to do, and provided a pretty good estimate of Vas.

Here's a formula that you can use to calculate Vas, knowing efficiency n0, Qes and fs:

More woofers specs list the SPL output at 1W/1M than reference efficiency, so here's a converter:

These days, I use Keith Larson's Woofer Tester and Speaker Tester products. They really make life easier. It has evolved a long way since the original Woofer Tester that he used to sell through Parts Express. You can use it to do acoustic measurements and make a digital crossover using Spice models to simulate passive crossovers. It's a great tool. And it still does the T/S measurements.

If you want to find T/S specs making measurements manually, or if you want to calculate values from other known values, here's a list of formulas that can be used to solve pretty much whatever you want to find:

Speaker system total Q at fc

α constant

Speaker total Q at fs

Efficiency/bandwidth product

Resonant frequency

Electrical Q

System resonant frequency

System total Q at fc

Resonant frequency

Speaker total Q at fs

Half power frequency (-3dB point)

System resonant frequency

Internal box volume

Compliance

Free air reference efficiency

Speaker resonant frequency

Compliance

Speaker electrical Q

Sound pressure level

Free air reference efficiency

Maximum air volume displaced by cone excursion

Peak linear displacement

Diaphragm radiating area

Volume displaced at Xmax

Diaphragm effective radiating diameter

Diaphragm radiating area

K1 constant

Air density

System resonant frequency

Volume displaced at Xmax

Speed of sound

K2 constant

K1 constant

Amax constant

Maximum displacement limited power output

K1 constant

Amax constant

Required electrical input to achieve Par

Maximum displacement limited power output

Free air reference efficiency

Peak sound pressure level

Maximum power input




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