A Direct Method of Determining the Natural Frequency and Dimensionless Damping Coefficient of any Second-order Circuit

James A. Kearns; Jennifer Owrutsky

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Conference: 2021 ASEE Virtual Annual Conference Content Access
Location: Virtual Conference
Publication Date: July 26, 2021
Start Date: July 26, 2021
End Date: July 19, 2022
Conference Session: Electrical and Computer Division Technical Session 7
Tagged Division: Electrical and Computer
Page Count: 11
DOI: 10.18260/1-2--36576
Permanent URL: https://strategy.asee.org/36576
Download Count: 469

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Paper Authors

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James A. Kearns York College of Pennsylvania

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Jim Kearns is an Associate Professor of Electrical & Computer Engineering at York College of Pennsylvania. He received a B.S. in Mechanical Engineering (SEAS) and a B.S. in Economics (Wharton) from the University of Pennsylvania in 1982. Subsequently, he received his M.E. from Carnegie-Mellon University in 1984, and his Ph.D. from the Georgia Institute of Technology in 1990, both in Mechanical Engineering. While at Georgia Tech he was the recipient of a Presidential Fellowship. Subsequently, he worked as a Postdoctoral Fellow at the Applied Research Laboratory of the University of Texas-Austin. Dr. Kearns has spent the past 24 years at York College of Pennsylvania developing new programs in mechanical, electrical, and computer engineering. He recently co-authored another edition of Principles and Applications of Electrical Engineering with Dr. Giorgio Rizzoni of The Ohio State University.

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Jennifer Owrutsky

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Abstract

All electrical and computer engineering students, and those from many other engineering disciplines, learn to generate first- and second-order ordinary linear differential equations and subsequent solutions for circuit variables from circuit diagrams by applying basic analytic methods and laws, such as Kirchhoff's laws and Ohm's law. These differential equations and their solutions are expressed in terms of key characteristic parameters: a time constant for first-order circuits and a dimensionless damping coefficient and natural frequency for second-order circuits. Unfortunately, methods of designing a circuit subject to other constraints to also achieve given values for these parameters are generally not taught and consequently are less well understood.

A method is presented in this paper that facilitates the design of a second-order circuit with prescribed characteristics. The method extends a fundamental result of The'venin's theorem to relate four time constants to the dimensionless damping coefficient and natural frequency. These time constants are readily associated with simple first-order circuit structures that act as guides in the construction of a circuit with desired characteristics. This method has the added pedagogical advantage of offering students an alternate and potentially appealing means of generating these characteristic parameters from direct observation of a second-order circuit.

Preliminary assessment data suggests improved problem solving for both first- and second-order circuit analysis. Across 4 different problems there were 28 cases in which students were unable to correctly solve a second-order problem using traditional methods, 17 were able to do so using the approach outlined in this paper. There were no instances in which a student was successful using the traditional approach but unsuccessful using this new approach. All students received full instruction in both methods.

Citation
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Kearns, J. A., & Owrutsky, J. (2021, July), A Direct Method of Determining the Natural Frequency and Dimensionless Damping Coefficient of any Second-order Circuit Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. 10.18260/1-2--36576