**7. References**


Johnson, K. L. (1985). *Contact Mechanics*, Cambridge University Press, ISBN: 978-0521347969, Cambridge, United Kingdom.

**Section 2** 

**Electromagnetics and Microelectronics** 


**Electromagnetics and Microelectronics** 

154 Numerical Simulation – From Theory to Industry

Cambridge, United Kingdom.

Johnson, K. L. (1985). *Contact Mechanics*, Cambridge University Press, ISBN: 978-0521347969,

Kalker, J. J., & van Randen, Y. A. (1972). A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-Space Contact Problems. *Journal of* 

Liu, S. B., & Wang, Q. (2002). Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm. *ASME Journal of* 

Liu, S. B., Wang, Q., & Liu, G. (2000). A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses. *Wear*, Vol. 243, No. 1-2, pp. 101–111, ISSN: 0043-1648. Mindlin, R. D. (1949). Compliance of Elastic Bodies in Contact. *ASME Journal of Applied* 

Polonsky, I. A., & Keer, L. M. (1999). A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient

Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). *Numerical Recipes in C – The Art of Scientific Computing – Second Edition*, Cambridge University Press, ISBN: 0-

Renouf, M., Massi, F., Fillot, N., & Saulot, A. (2011). Numerical Tribology of a Dry Contact.

Shewchuk, J. R., (1994). *An Introduction to the Conjugate Gradient Method without the Agonizing Pain*, School of Computer Science, Carnegie Mellon University, Retrieved from

Spinu, S., & Diaconescu, E., (2008). Numerical Simulation of Elastic Conforming Contacts under Eccentric Loading. *Proceedings of the STLE/ASME International Joint Tribology Conference IJTC2008*, ISBN: 978-0-7918-3837-2, October 20-22, Miami, Florida, USA, pp.

Spinu, S., & Frunza, G. (2011). A Numerical Approach to the Cattaneo-Mindlin Problem. *Proceedings of VI International Conference Balttrib'2011*, Kaunas, Lithuania, November 17-

Spinu, S., & Frunza, G. (2011). Numerical Analysis of Elastic Contact Considering Tangential Friction. *Proceedings of VI International Conference Balttrib'2011*, Kaunas, Lithuania,

Wang, Z. J., Meng, F. M., Xiao, J. X., & Wang, W. Z. (2011). Numerical Analysis of Partial Slip Contact under a Tangential Force and a Twisting Moment. *Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology*, Vol. 225, No. 2,

Wang, Z. J., Wang, W. Z., Wang, H., Zhu, H., & Hu, Y. Z. (2010). Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half Space. *ASME Journal of Tribology*,

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http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf.

**Chapter 8** 

© 2012 Yurtsev and Ptashinsky, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Numerical Simulations** 

**of Dipole and LOOP Antennas** 

Oleg A. Yurtsev and Grigory V. Ptashinsky

Additional information is available at the end of the chapter

well known. The length of a loop perimeter is *L*

example, in the form of a cylindrical helix with a radius *A*

loop antenna. The following is related to these problems:

antennas with series excitation are described briefly [Rothammels, 1995].

http://dx.doi.org/10.5772/47760

**1. Introduction** 

*Ao* 

**of Radiation and Scattering Characteristics** 

Dipole and loop antennas are used in communication lines, in radar and navigation systems, TV and other fields of radio-engineering. Structures of antennas depend on their bandwidth. In VHF, UHF, L and S ranges, these antennas are made, as a rule, of conductors with a radius

Dipole and monopole antennas [Balanis, 1997; Markov, 1960], a Yagi-Uda antenna [Volakis, 2007; Aisenberg, Jampolsky and Terjoshin, 1977), bicone and discone antennas [Drabkin and Zuzenko, 1961], loop antennas consisting of one or two loops located in one plane [Rothammels, 1995] are

resonance (a reactive part of input resistance is 0) *Xr* . To reduce sizes of dipole antennas, conductor with surface reactive resistance is used. Such a conductor can be implemented, for

1974]. To tune antennas in resonance, reactive resistances are used. Linear arrays of dipole

In communication nodes and antenna arrays, dipole and loop antennas function in the conditions of strong coupling. Therefore, one of the problems of numerical simulation is the

Scattering characteristics of antennas are a strong factor that facilitates radar reconnaissance. These characteristics of loop and dipole antennas have hardly been studied in the literature. In the literature, there is no enough information or there is no information at all about a number of questions related to research into and the versions of construction of dipole and

and reproduction in any medium, provided the original work is properly cited.

research into the influence of interaction on the electrical characteristics of antennas.

(λ – wavelength in the air). Further, we will study wire dipole and loop antennas.

. This ensures tuning of the antenna in

[Yurtsev, Runov and Kazarin,

Oleg A. Yurtsev and Grigory V. Ptashinsky

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/47760
