Two-port network analysis and modeling of a balanced armature receiver

Models for acoustic transducers, such as loudspeakers, mastoid bone-drivers, hearing-aid receivers, etc., are critical elements in many acoustic applications. Acoustic transducers employ two-port models to convert between acoustic and electromagnetic signals. This study analyzes a widely-used commercial hearing-aid receiver ED series, manufactured by Knowles Electronics, Inc. Electromagnetic transducer modeling must consider two key elements: a semi-inductor and a gyrator. The semi-inductor accounts for electromagnetic eddy-currents, the 'skin effect' of a conductor (Vanderkooy, 1989), while the gyrator (McMillan, 1946; Tellegen, 1948) accounts for the anti-reciprocity characteristic [Lenz's law (Hunt, 1954, p. 113)]. Aside from Hunt (1954), no publications we know of have included the gyrator element in their electromagnetic transducer models. The most prevalent method of transducer modeling evokes the mobility method, an ideal transformer instead of a gyrator followed by the dual of the mechanical circuit (Beranek, 1954). The mobility approach greatly complicates the analysis. The present study proposes a novel, simplified and rigorous receiver model. Hunt's two-port parameters, the electrical impedance Ze(s), acoustic impedance Za(s) and electro-acoustic transduction coefficient Ta(s), are calculated using ABCD and impedance matrix methods (Van Valkenburg, 1964). The results from electrical input impedance measurements Zin(s), which vary with given acoustical loads, are used in the calculation (Weece and Allen, 2010). The hearing-aid receiver transducer model is designed based on energy transformation flow [electric→ mechanic→ acoustic]. The model has been verified with electrical input impedance, diaphragm velocity in vacuo, and output pressure measurements. This receiver model is suitable for designing most electromagnetic transducers and it can ultimately improve the design of hearing-aid devices by providing a simplified yet accurate, physically motivated analysis. This article is part of a special issue entitled "MEMRO 2012".