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Session 2793

TELLEGEN’S THEOREM APPLIED TO MECHANICAL, FLUID AND THERMAL SYSTEMS

Ravi P. Ramachandran1 and V. Ramachandran2 1. Department of Electrical and Computer Engineering, Rowan University, Glassboro, New Jersey 08028 2. Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada H3G 1M8

Introduction Tellegen’s theorem [1][2] has been applied to several electrical systems that are linear or nonlinear, reciprocal or nonreciprocal, time-variant or time-invariant, and so forth. Tellegen’s theorem states that the total power delivered to all the components of an electrical network is zero [1][2]. This result has profound consequences in that the sum of the products of voltages and currents should be zero. If the voltage and current variables of a circuit are interchanged, we get an equivalent circuit with the same total delivered power. The two circuits are equivalent in terms of Kirchoff’s Laws and topological equivalence [1][2]. However, there is no dependence on the components of the circuit. For example, one may be a nonlinear resistive circuit and the other may be a linear circuit. The significant implication of Tellegen’s theorem comes from the fact that two or more circuits with the same power constraints can be configured with no restrictions on linearity, time-invariance and method of analysis. The practical implication comes in the design process where students can exmine several equivalent networks and use for example, the simpler one in part of a design. So far, the discussion has centered about analog electrical networks only. Tellegen’s theorem has been extended to discrete systems used in discrete signal processing [3]. This provides the derivation of different structures and a desirable one is chosen to suit the other properties required for a design. In this paper, we show that Tellegen’s theorem can be extended to other types of systems. We consider mechanical, fluid and thermal systems. Across and Through Variables It is known that these four systems (electrical, mechanical, fluid and thermal) can be given a unified treatment by the use of across-variabes {av(t)} and through-variables {tv(t)} [4].

“Proceedings of the 2001 American Society for1Engineering Education Annual Conference & Exposition Copyright  2001, American Society for Engineering Education”

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Ramachandran, V., & Ramachandran, R. (2001, June), Tellegen's Theorem Applied To Mechanical, Fluid And Thermal Systems Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9896