Abstract

The ratio of Bessel functions J1(z)/J0(z) often occurs in the calculation of impedance of lossy components in electroacoustic devices. In particular, the electric impedance of hearing aid receivers or loudspeakers has a term proportional to a Bessel function ratio of this form when losses due to eddy currents are taken into account. This so-called semi-inductance has been notoriously difficult to model in simple lumped-parameter circuit calculation tools such as SPICE. This paper presents a simple ladder network derived from the Bessel function ratio expressed as a continuous fraction. The same transformation has been used to model the acoustic impedance of small cavities with losses at the thermal boundary layer.

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