A ladder network impedance model for lossy wave phenomena

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.

A method for calibration of bone driver transducers to measure the mastoid impedance

“…This model contains four parameters: the DC resistance R o , an inductance L o , the resistance factor R, and shunt inductance factor L. The ladder network parameters R and L are functions of physical properties of the transducer. From Warren and LoPresti (2006) and Vanderkooy (1989),…”

“…This model accounts for the effect of eddy currents in the driver magnet, which reduce the inductive impedance at the expense of loss at high frequencies due to magnetic flux diffusion, leading to a ffiffiffiffiffiffi jx p behavior. As shown by Warren and LoPresti (2006), the Bessel function ratio in Vanderkooy's model can be expanded as a diffusion ladder network, such that the electrical impedance can be represented by the circuit shown in Fig. 8.…”

“…7. The effect of using more terms is negligible for the frequency range of interest (Warren and LoPresti, 2006). The DC resistance R o was read directly from Z d .…”

High strain-rate magnetoelasticity in Galfenol

“…To the authors' knowledge, the above approach has previously been used to model cylindrical acoustic systems 56 and only once to describe piezomagnetic eddy currents. 18 The parameters used in the analytical model are as follows.…”

Analog model for thermoviscous propagation in a cylindrical tube

“…Acoustic propagation modeling in cylindrical tubes continues to be an active area of investigation, for example for the study of absorbing materials, 6 for propagation in small tubes such as in hearing aids, 7,8 for propagation at very low frequencies, 9,10 for thermoacoustics, 11 and for modeling of wind musical instruments. 5 In many of these applications, the systems are sufficiently linear that a frequency domain analysis provides the required accuracy.…”