Pole-Zero Fitting for Transfer Function of Hearing-Aid Receiver: Evidence-Based Review

The hearing-aid transducer is ubiquitous in the hearing-aid industry. For example, the balanced armature receiver (BAR), first invented by A.G. Bell, has been used in all telephone earphones because it has the highest output and best frequency response. Nevertheless, previous electro-mechanical studies on these miniature speakers are quite primitive, given the price of the transducers. Thus, more detailed analysis is critically important for the field of hearing science. This review study was motivated by Hunt’s parameter calibration (1954), a widely used commercial hearing-aid receiver (ED series, manufactured by Knowles Electronics, Inc.). In the body of the study, the transfer function of the BAR system (i.e., pressure over voltage) was calculated from Hunt’s parameters, solely from the electrical terminals of the device. The computed transfer function was then further investigated by comparing to the pole-zero fitting method using the methods of Gustavsen and Semlyen (1999) and Prony (1975). Based on our short experiment, the better fitting result was achieved with Gustavsen and Semlyen’s method. By decomposing results of the transfer function fitting into all-pass and minimum-phase parts, the system was confirmed as a delay system. We conclude that the BAR system is linear, time-invariant, stable, and causal while providing an evidence-based understanding of the hearing-aid receiver system.