[Suggestion] Low frequency loudspeaker impedance magnitude fit

[estearg]

To test if you consider it worthwhile. A simplified model of impedance magnitude and a function to fit the model parameters to measured data. The fit seems to be not excellent but good enough to get usable Thiele-Small parameters.

function [mag] = impedance_speaker_model (f,params)

Rdc=params(1); f0=params(2); Qe=params(3); Qm=params(4); Le=params(5);

w0 = 2pif0; w = 2pif;

% low-frequency impedance (resonance peak, LCR part): Res = Rdc*Qm/Qe; Ces = Qe/w0/Rdc; Les = 1/w0^2/Ces;

ZCes = 1./(iwCes); ZLes = iwLes; Zlow = 1 ./ ( 1/Res + 1./ZCes + 1./ZLes );

% total impedance: Z = Rdc + w * Le + Zlow; mag = abs (Z);

endfunction

function [Rdc,f0,Qe,Qm,Le] = impedance_fit_speaker (f,mag)

% guess starting value for Rdc: Rdc = min (mag);

% guess starting values for f0: u = diff (mag); F = ( f(1:end-1) + f(2:end))/2; [u1,k1] = max (u); [u2,k2] = min (u); if ~exist ('f0','var') f0 = (F(k1)+F(k2))/2; endif clear F

% estimate impedance at f0: [u,k] = min(abs(f-f0)); Rmax = mag(k); clear u clear k

% estimate f1 and f2: k = find(f<f0); [u,k] = min(abs(mag(k)-sqrt(Rmax*Rdc))); f1 = f(k); clear u clear k f2 = f0^2/f1;

% guess starting values for Qe and Qm: Qm = f0/(f2-f1)*sqrt(Rmax/Rdc); Qe = Qm / (Rmax/Rdc-1);

% starting value for Le Le = 0;

clear f1 clear f2

inputparams = [Rdc,f0,Qe,Qm,Le]; [f,p,cvg,iter,corp,covp]=leasqr(f,mag,inputparams,"impedance_speaker_model"); Rdc=p(1); f0=p(2); Qe=p(3); Qm=p(4); Le=p(5);

endfunction

[mbrennwa]

Thanks for this, and sorry I have missed this until now. Somehow it seems I never received a notice.

[mbrennwa]

Can you provide some example / test to demonstrate your suggested method?