====== Find Thiele and Small parameters from an unknown speaker ======

^           Parameter name           ^               Significance                ^
|  F<sub>s</sub> (=2πω<sub>s</sub>)  | Resonance frequency (Hz)                  |
|           R<sub>e</sub>            | Electrical resistance (ω=0) (Ω)           |
|           L<sub>e</sub>            | Electrical inductance (ω>>ω<sub>s</sub>)  |
|           B<sub>l</sub>            | Force factor (N/A)                        |
|           M<sub>ms</sub>           | Mobile mass (Kg)                          |
|           C<sub>ms</sub>           | Suspension swiftness                      |
|           R<sub>ms</sub>           | Mecanical losses                          |
|           S<sub>d</sub>            | Mobile area (m²)                          |
|                VAS                 | equivalent of C<sub>ms</sub>              |
|           Q<sub>es</sub>           | Electrical quality factor                 |
|           Q<sub>ms</sub>           | Mecanical quality factor                  |
|           Q<sub>ts</sub>           | Total quality factor                      |



===== Re =====

Re is the continuous current impedance (**not the average impedance**).

==== 1st solution ====

Use a precise multimeter, a good one, 20,000 pts or so.

==== 2nd solution ====

Put a high (relative to measured value) value resistor in series with the voicecoil, power the thing from a big 12V battery (so that the voltage does not drop during measure).

<m>R_e = R_b * {V_e / V_b}</m>

Ex: Re is arround 10Ω, we choose a 100Ω 1% resistor as burden resistor (>=5W).

===== Sd =====

Sd is the pushing area, that is the area of the mobile part.

Measure mobile part diameter, including half the suspension suround.

<m>S_d = pi * {D^2 / 4}</m>

===== Impedance =====

The impedance curve is constructed on log scale using a probed test amp and a fequency generator.

===== Le =====

Extracted from <m>delim{|}{Z_e(omega)}{|}_{omega>>omega_s} = sqrt({R_e}^2 + (L_e * omega)^2)</m> where <m>delim{|}{Z_e(omega)}{|}_{omega>>omega_s}</m> is the measured impedance.

===== Bl =====

Put a coin on the mobie apparatus (or a precisely known mass). For a fixed frequency increase the applied voltage, catch its value when the mass starts to "take off".

<m>B_l = omega * {{U_hp - {R_e} * i} / g}</m>, where g = 9.81m/s² (at this moment the mobile part speed is <m>v = g * omega</m>

The speaker MUST be even. The "take off" can be detected using a microphone, looking at the moment when the sinus signal starts to deteriorate.

===== Mms =====

This parameter is measured using a known mass placed on the mobile part, the applied signal is small enough to avoid the mass takin off.

The resonant frequency is measured without (<m>f_s</m>) and with (<m>f_s''</m>) the mass.

<m>M_ms = {m_add / {(f_s / {f_s''})^2 - 1}} - {{8/{3 * pi}} * rho * a * S_d}</m>, where <m>rho</m> = 1.2 Kg/m^3 and a = ???

===== Cms =====

<m>C_ms = 1 / {{omega_s}^2 * M_ms}</m>

===== Rms =====

<m>R_ms = {{B_l}^2 / {Z_e(omega_s) - R_e}} - ({{pi * a^4^}/{S_d}} * rho * omega_s)</m>

<m>Z_e(omega_s) = R_e + {B_l}^2 / R_tms</m>