volume | PIER Journals

2006-05-28

Bandwidth, q Factor, and Resonance Models of Antennas

Mats Gustafsson,

Dr. Mats Gustafsson

Department of Electroscience

Lund Institute of Technology

Sweden

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Sven Nordebo

Dr. Sven Nordebo

School of Mathematics and System Engineering

Vaxjo University

Sweden

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Progress In Electromagnetics Research, Vol. 62, 1-20, 2006

doi:10.2528/PIER06033003

Abstract

In this paper, we introduce a first order accurate resonance model based on a second order Padé approximation of the reflection coefficient of a narrowband antenna. The resonance model is characterized by its Q factor, given by the frequency derivative of the reflection coefficient. The Bode-Fano matching theory is used to determine the bandwidth of the resonance model and it is shown that it also determines the bandwidth of the antenna for sufficiently narrow bandwidths. The bandwidth is expressed in the Q factor of the resonance model and the threshold limit on the reflection coefficient. Spherical vector modes are used to illustrate the results. Finally, we demonstrate the fundamental difficulty of finding a simple relation between the Q of the resonance model, and the classical Q defined as the quotient between the stored and radiated energies, even though there is usually a close resemblance between these entities for many real antennas.

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Mats Gustafsson, and Sven Nordebo, "Bandwidth, q Factor, and Resonance Models of Antennas," Progress In Electromagnetics Research, Vol. 62, 1-20, 2006.
doi:10.2528/PIER06033003

References

1. Arfken, G., Mathematical Methods for Physicists, third ed., 1985.

2. Chu, L. J., "Physical limitations of omni-directional antennas," Appl. Phys., Vol. 19, 1163-1175, 1948.
doi:10.1063/1.1715038

3. Collin, R. E. and S. Rothschild, "Evaluation of antenna Q," IEEE Trans. Antennas Propagat., Vol. 12, No. 1, 23-27, 1964.
doi:10.1109/TAP.1964.1138151

4. Fano, R. M., "Theoretical limitations on the broadband matching of arbitrary impedances," Journal of the Franklin Institute, Vol. 249, 57-83, 1950.
doi:10.1016/0016-0032(50)90006-8

5. Gustafsson, M. and S. Nordebo, "On the spectral efficiency of a sphere," Tech.Rep.LUTEDX/(TEAT-7127)/1-24/(2004), 1-24, 2004.

6. Hansen, R. C., "Fundamental limitations in antennas," Proc. IEEE, Vol. 69, No. 2, 170-182, 1981.

7. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill, 1961.

8. Jackson, J. D., Classical Electrodynamics, second ed., 1975.

9. Newton, R. G., Scattering Theory of Waves and Particles, second ed., 2002.

10. Petersan, P. J. and S. M. Anlage, "Measurement of resonant frequency and quality factor of microwave resonators: Comparison of methods," Appl. Phys., Vol. 84, No. 6, 3392-3402, 1998.
doi:10.1063/1.368498

11. Pozar, D. M., Microwave Engineering, John Wiley & Sons, 1998.

12. Vassiliadis, A. and R. L. Tanner, "Evaluating the impedance broadbanding potential of antennas," IRE Trans. on Antennas and Propagation, Vol. 6, No. 3, 226-231, 1958.
doi:10.1109/TAP.1958.1144593

13. Willson, A. N. and H. J. Orchard, "Insights into digital fillters made as the sum of two allpass functions," IEEE Trans. on Circuits and Systems I: Fundamental theory and applications, Vol. 42, No. 3, 129-137, 1995.
doi:10.1109/81.376877

14. Yaghjian, A. D. and S. R. Best, "Impedance, bandwidth, and Q of antennas," IEEE Trans. Antennas Propagat., Vol. 53, No. 4, 1298-1324, 2005.
doi:10.1109/TAP.2005.844443