Projects per year

### Abstract

The fundamental limitations in performance of electrically small antennas (ESAs) - and how far these may be approached - have been of great interest for over a century. Particularly over the past few decades, it has become increasingly relevant and important, to approach these limits in view of the emerging and huge demand for an increasing number of ever smaller mobile communication devices. The classical investigations of fundamental ESA performance limitations are usually formulated in terms of a lower bound upon the radiation quality factor Q, because for ESAs, Q is directly related to the important antenna parameters of radiation efficiency e and impedance bandwidth. For single-mode antennas the fundamental minimum Q is the Chu lower bound.

In this Ph.D. dissertation, the topic is miniaturization of spherical antennas loaded by an internal magnetodielectric core. The goal is to determine, quantify, and assess the effects of an internal material loading upon antenna performance, including its potentials towards miniaturization. Emphasis have been upon performing an exhaustive and exact analysis of rigorous validity covering a large class of spherical antennas. In the context of this study, spherical antenna(s) are defined as; A spherical solid, simple, linear, lossless or lossy magnetodielectric core with an impressed surface current density exciting spherical transverse electric (TE) or transverse magnetic (TM) modes of arbitrary order. For such antennas, closed-form expressions have been derived for several important antenna performance parameters - of these, particularly the following are important; Stored electric/magnetic energies (both external and internal to the current), the radiation efficiency e, and the radiation quality factor Q. These expressions are all exact, and valid for; Arbitrary order of the spherical wave, arbitrary radius of the spherical antenna, as well as arbitrarily large core permeability and/or permittivity, given an inversely proportional frequency variation of the imaginary part(s) and an arbitrary dispersion of the real part(s) - thus describing both lossless and lossy cores. Such rigorously valid expressions are not previously published. The rigorous validity of the found expressions, allows investigations of both electrically small as well as larger antennas.

For antennas with a lossless core, increasing antenna radius, core relative permeability, and/or permittivity are shown to introduce cavity resonances producing internal energy balance but zero radiation, reducing the antenna to a non-radiating resonator. Cavity resonances thus pose restrictions upon antenna performance. For electrically small antennas, asymptotic results are presented, supplemented by detailed theoretical predictions, demonstrating how the internal stored energy and thus Q depend upon the core parameters. Dependent on the antenna electrical size, the minimum single-mode Q is obtained for either an air-core electric dipole antenna or a magnetic-core magnetic dipole antenna with a large optimum relative permeability.

For antennas with a lossy core, it is shown how a sufficiently large loss tangent reduces the internal fields, internal stored energy, and Q/e well below that which is attainable with a lossless core of the same radius. This mitigates the harmful effect of cavity resonances upon Q/e, at the expense of a reduced efficiency. In the limit of a perfect magnetic conducting core, Q/e reaches the Chu lower bound with an efficiency of unity for dipole antennas, but also for more moderate magnetic loss tangents, very low Q/e values are attainable with a decent to good efficiency. For example, a specific magnetic-core magnetic dipole antenna with a magnetic loss tangent of 10 and relative permeability of 32 yield Q/e equal 100.2% of the Chu lower bound, with e equal 83%.

Exciting both of the two dipole modes, the relative mode excitation provides an extra degree of freedom to the antenna designer. Closed-form expressions for the relative mode excitation have been derived yielding self-resonant or circular polarized operation. Furthermore, an even lower Q is attainable when combining the two dipole modes. For example for a specific self-resonant dual-dipole antenna, a magnetic core with a magnetic loss tangent of 1 and relative permeability of 300 yield Q/e equal 65% of the Chu lower bound, with a simultaneous e of 71%.

In this Ph.D. dissertation, the topic is miniaturization of spherical antennas loaded by an internal magnetodielectric core. The goal is to determine, quantify, and assess the effects of an internal material loading upon antenna performance, including its potentials towards miniaturization. Emphasis have been upon performing an exhaustive and exact analysis of rigorous validity covering a large class of spherical antennas. In the context of this study, spherical antenna(s) are defined as; A spherical solid, simple, linear, lossless or lossy magnetodielectric core with an impressed surface current density exciting spherical transverse electric (TE) or transverse magnetic (TM) modes of arbitrary order. For such antennas, closed-form expressions have been derived for several important antenna performance parameters - of these, particularly the following are important; Stored electric/magnetic energies (both external and internal to the current), the radiation efficiency e, and the radiation quality factor Q. These expressions are all exact, and valid for; Arbitrary order of the spherical wave, arbitrary radius of the spherical antenna, as well as arbitrarily large core permeability and/or permittivity, given an inversely proportional frequency variation of the imaginary part(s) and an arbitrary dispersion of the real part(s) - thus describing both lossless and lossy cores. Such rigorously valid expressions are not previously published. The rigorous validity of the found expressions, allows investigations of both electrically small as well as larger antennas.

For antennas with a lossless core, increasing antenna radius, core relative permeability, and/or permittivity are shown to introduce cavity resonances producing internal energy balance but zero radiation, reducing the antenna to a non-radiating resonator. Cavity resonances thus pose restrictions upon antenna performance. For electrically small antennas, asymptotic results are presented, supplemented by detailed theoretical predictions, demonstrating how the internal stored energy and thus Q depend upon the core parameters. Dependent on the antenna electrical size, the minimum single-mode Q is obtained for either an air-core electric dipole antenna or a magnetic-core magnetic dipole antenna with a large optimum relative permeability.

For antennas with a lossy core, it is shown how a sufficiently large loss tangent reduces the internal fields, internal stored energy, and Q/e well below that which is attainable with a lossless core of the same radius. This mitigates the harmful effect of cavity resonances upon Q/e, at the expense of a reduced efficiency. In the limit of a perfect magnetic conducting core, Q/e reaches the Chu lower bound with an efficiency of unity for dipole antennas, but also for more moderate magnetic loss tangents, very low Q/e values are attainable with a decent to good efficiency. For example, a specific magnetic-core magnetic dipole antenna with a magnetic loss tangent of 10 and relative permeability of 32 yield Q/e equal 100.2% of the Chu lower bound, with e equal 83%.

Exciting both of the two dipole modes, the relative mode excitation provides an extra degree of freedom to the antenna designer. Closed-form expressions for the relative mode excitation have been derived yielding self-resonant or circular polarized operation. Furthermore, an even lower Q is attainable when combining the two dipole modes. For example for a specific self-resonant dual-dipole antenna, a magnetic core with a magnetic loss tangent of 1 and relative permeability of 300 yield Q/e equal 65% of the Chu lower bound, with a simultaneous e of 71%.

Original language | English |
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Place of Publication | Kgs. Lyngby |
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Publisher | Technical University of Denmark |

Number of pages | 153 |

Publication status | Published - 2013 |

## Projects

- 1 Finished

## Metamaterial Homogenization and Antenna Miniaturization

Hansen, T. V., Breinbjerg, O., Arslanagic, S., Kim, O. S., Mørk, J., Gustafsson, M. & Yaghjian, A. D.

01/04/2010 → 15/01/2014

Project: PhD

## Cite this

Hansen, T. V. (2013).

*Miniaturization of Spherical Magnetodielectric Antennas*. Technical University of Denmark.