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Title:Analysis and measurement of anti-reciprocal systems
Author(s):Kim, Noori
Director of Research:Allen, Jont B.
Doctoral Committee Chair(s):Allen, Jont B.
Doctoral Committee Member(s):Boppart, Stephen A.; Franke, Steven J.; Oelze, Michael
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):anti-reciprocal systems
acoustic transducer models
balanced armature receivers
Abstract: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 a negative real part in Zmot, which may arise when there are frequency-dependent real parts. In conclusion, Zmot is not a PR impedance because of the phase lag. Several significant topics will be discussed in addition to these two larger issues (modeling the balanced armature receiver and investigating Zmot). We generalize the gyrator with the non-ideal gyrator, analogous to the ideal vs. non-ideal transformer cases. This formula is reinterpreted via electromagnetic fundamentals. This work helps to transparently explain the anti-reciprocal property embedded in a gyrator. Explaining the matrix composition method is another contribution, which is characterized by the M¨obius transformation. This is a significant generalization of the transmission matrix cascading method. Systems where the quasi-static approximation fails will also be considered (i.e., derivation of Kirchhoff’s circuit laws from Maxwell’s equations). This leads us to the definition of “wave impedance,” which is distinct from the traditional Brune impedance, discussed in modern network theory by Vanderkooy. The Brune impedance is defined by a reflectance that is minimum phase, which is a significant limitation on this classical form of impedance. The typical example of a non-Brune impedance is a transmission line. This non-Brune distinction is important, and we believe it to be a novel topic of research.
Issue Date:2015-01-21
Rights Information:Copyright 2014 Noori Kim
Date Available in IDEALS:2015-01-21
Date Deposited:2014-12

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