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1. Kim, Noori. Analysis and measurement of anti-reciprocal systems.

Degree: PhD, 1200, 2015, University of Illinois – Urbana-Champaign

Loudspeakers, mastoid bone-drivers, hearing-aid receivers, hybrid cars, and more – these “anti-reciprocal” systems are commonly found in our daily lives. However, the depth of understanding about the systems has not been well addressed since McMillan in 1946. The goal of this study is to provide an intuitive and clear understanding of the systems, beginning from modeling one of the most popular hearing-aid receivers, a balanced armature receiver (BAR). Models for acoustic transducers are critical in many acoustic applications. This study analyzes a widely used commercial hearing-aid receiver, manufactured by Knowles Electronics, Inc (ED27045). 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, while the gyrator accounts for the anti-reciprocity characteristic of Lenz’s law. Aside from the work of Hunt, to our knowledge no publications have included the gyrator element in their electromagnetic transducer models. The most prevalent method of transducer modeling evokes the mobility method, an ideal transformer alternative to a gyrator followed by the dual of the mechanical circuit. The mobility approach greatly complicates the analysis. The present study proposes a novel, simplified, and rigorous receiver model. Hunt’s two-port parameters as well as the electrical impedance Ze(s), acoustic impedance Za(s), and electroacoustic transduction coefficient Ta(s) are calculated using transmission and impedance matrix methods. 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. As a utilization of this model, we study the motional impedance (Zmot) that was introduced by Kennelly and Pierce in 1912 and highlighted by many researchers early in the 20th century. Our goal for this part of the study is to search for the theoretical explanation of the negative real part (resistance) observed in Zmot in an electromechanical system, as it breaks the positive-real (PR) property of Brune’s impedance, as well as the conservation of energy law. Specifically, we specify conditions that cause negative resistance in the motional impedance using simple electromechanical network models. Using Hunt’s two-port system parameters (a simplified version of an electroacoustic system), Zmot is defined as −TemTme Zm, where the subscript m stands for mechanic, Tem and Tme are transfer impedances, and Zm is the mechanical impedance of the system. Based on the simplified electromechanical model simulation, we demonstrate that Zmot(s) is a minimum-phase function, but does not have to be a positive-real (PR) function. Any electromechanical network with shunt losses in the electrical side (including a semi-inductor and a resistor) sees… Advisors/Committee Members: Allen, Jont B. (advisor), Allen, Jont B. (Committee Chair), Boppart, Stephen A. (committee member), Franke, Steven J. (committee member), Oelze, Michael (committee member).

Subjects/Keywords: anti-reciprocal systems; acoustic transducer models; balanced armature receivers

…one of the most important and complex hearingaid components, the balanced armature receiver… …Figure 1.1: The balanced armature receiver (BAR) circuit as a model (Kim and… …x5D; in size. These receivers consist of a coil, an armature, two magnets, and a diaphragm… …the types of ring armature receivers adapted from Mott and Miner (1951). The other… …electric loudspeaker by A. G. Bell in 1876. Attraction and release of the armature are under the… 

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APA (6th Edition):

Kim, N. (2015). Analysis and measurement of anti-reciprocal systems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from

Chicago Manual of Style (16th Edition):

Kim, Noori. “Analysis and measurement of anti-reciprocal systems.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed November 14, 2019.

MLA Handbook (7th Edition):

Kim, Noori. “Analysis and measurement of anti-reciprocal systems.” 2015. Web. 14 Nov 2019.


Kim N. Analysis and measurement of anti-reciprocal systems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2019 Nov 14]. Available from:

Council of Science Editors:

Kim N. Analysis and measurement of anti-reciprocal systems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: