Table of Contents

Find Thiele and Small parameters from an unknown speaker

Parameter name Significance
Fs (=2πωs) Resonance frequency (Hz)
Re Electrical resistance (ω=0) (Ω)
Le Electrical inductance (ω»ωs)
Bl Force factor (N/A)
Mms Mobile mass (Kg)
Cms Suspension swiftness
Rms Mecanical losses
Sd Mobile area (m²)
VAS equivalent of Cms
Qes Electrical quality factor
Qms Mecanical quality factor
Qts 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).

R_e = R_b * {V_e / V_b}

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.

S_d = pi * {D^2 / 4}

Impedance

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

Le

Extracted from delim{|}{Z_e(omega)}{|}_{omega>>omega_s} = sqrt({R_e}^2 + (L_e * omega)^2) where delim{|}{Z_e(omega)}{|}_{omega>>omega_s} 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”.

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

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 (f_s) and with (f_s'') the mass.

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

Cms

C_ms = 1 / {{omega_s}^2 * M_ms}

Rms

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

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