Force Factor Modulation in Electro Dynamic Loudspeakers

The relationship between the non-linear phenomenon of ’reluctance force’ and the position dependency of the voice coil inductance was established in 1949 by Cunningham, who called it ’magnetic attraction force’. This paper revisits Cunningham’s analysis and expands it into a generalised form that includes the frequency dependency and applies to coils with non-inductive (lossy) blocked impedance. The paper also demonstrates that Cunningham’s force can be explained physically as a modulation of the force factor which again is directly linked to modulation of the flux of the coil. A verification based on both experiments and simulations is presented along discussions of the impact of force factor modulation for various motor topologies. Finally, it is shown that the popular L2R2 coil impedance model does not correctly predict the force unless the new analysis is applied.