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Mathematical Problems in Engineering
Volume 2015, Article ID 951718, 9 pages
Research Article

Propagation Modeling of Point Source Excited Magnetoinductive Waves Based on a New Plane Wave Expansion Approach

1Beijing Engineering Research Center of Optoelectronic Information and Instrument, Beijing Key Laboratory of Optoelectronic Measurement Technology, Beijing Information Science & Technology University, Beijing 100192, China
2Department of Biomedical Engineering, Oregon Health and Science University, Beaverton, OR 97006, USA
3School of Mechanical Engineering, University of Science & Technology, Beijing 100083, China

Received 12 June 2014; Revised 7 October 2014; Accepted 11 October 2014

Academic Editor: Hsuan-Ling Kao

Copyright © 2015 Feng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The signal fading in wireless underground sensor networks (WUSNs), which is caused by lossy media such as soil and sand, can be reduced by applying technology of magnetoinductive (MI) propagation. This technology can effectively establish a communication at very low frequency (VLF). In contrast to the previous studies in the literature, which mostly focus on the propagation of plane waves, we propose a new approach based on the plane wave expansion (PWE) to model the near field MI waves. The proposed approach is based on excitation of a point source, which is a common case in a practical WUSN. The frequent usage of square lattice MI structure is investigated. To verify the mathematical derivation, the simulation of time domain based on the fourth-order Runge-Kutta (RK) method is carried out. Simulation results show that the new model can provide a precise prediction to the MI wave’s propagation, with the computation load being one-tenth of that of the time domain simulation. The characteristics of the propagation of the MI waves are presented and discussed. Finally, the reflection on the edge of the MI structure is reduced by analysing the terminal matching conditions and calculating a method for matching impedances.