# Project Description

## Physical bounds in antenna theory

### 2003-01-01 -> 2008-12-31

### Project Description

In this project, we analyze physical bounds (physical limitations) on antennas, ie we investigate questions as:

How do size and geometry affect the performance of an antenna?

or

What characterizes the best antenna that can be built within a given geometry?

### Our approach (see also research)

- Uses an identity (sum rule) that relates the extinction cross section of a scatterer with the polarizability of the object.
- The effective antenna aperture (equals the absorption cross section for lossless antennas) is bounded by the extinction cross section.
- Rewrite as an antenna identity that relates the realized gain with the polarizability.
- Use that the polarizability is monotonic to express the result in an arbitrary circumscribing geometry.
- Estimate the integral to obtain the final bounds.

### Results

- The new bounds are valid for arbitrary circumscribing geometries.
- They resemble the Chu (and Thal) bound for spherical geometries.
- They separate electric and magnetic material properties.
- They provide a dependence of the polarization.

- M. Gustafsson, C. Sohl, G. Kristensson:

**Physical limitations on antennas of arbitrary shape**

Proc. Roy. Soc. A, Vol. 463, No. 2086, pp. 2589-2607, 2007. TEAT-7153 - C. Sohl, M. Gustafsson:

**A priori estimates on the partial realized gain of ultra-wideband (UWB) antennas**

Quart. J. Mech. Appl. Math.,Vol. 61,No. 3, pp. 415-430, 2008. TEAT-7160 - M. Gustafsson, C. Sohl, G. Kristensson:

**Illustrations of new physical bounds on linearly polarized antennas**

IEEE Trans. Antennas Propagat.,Vol. 57,No. 5, pp. 1319-1327, 2009. - A. Derneryd, M. Gustafsson, G. Kristensson, C. Sohl:

**Application of gain-bandwidth bounds on loaded dipole antennas** - M. Gustafsson, C. Sohl:

**New physical bounds on elliptically polarized antennas**

European Conference on Antennas and Propagation, Berlin, Germany, pp. 1-3, 2009-03-23.

### Background

The investigations of this problem go back to Wheeler (1947) and Chu (1948). Some references are given below. Note that the list isn't complete.

- H.A. Wheeler 1947, 1959, 1975: Lumped element models.
- L.J. Chu, 1948:

- Computes a lower bound of the antenna radiation
*Q*and an upper bound on*D*/*Q*. - Circumscribe the antenna with a sphere (radius
*a*) and expand the EM-field in partial waves. - Use recurence relations for the partial waves and a circuit representation to determine the stored energy and the radiated power.
- The results are
*Q*_{1}≥1/(*ka*)^{3}+1/*ka*and*D*/*Q*≤3/2*Q*_{1}, where*k*denotes the resonance wavenumber. - Chu also discusses the possibility to use Fano's bounds on broadband matching and he gives an approximate formula for
*Q*for higher order modes._{n}

- Computes a lower bound of the antenna radiation
- The approach by Chu have been extended in several steps,
*eg*

- R.F. Harrington, 1958, 1960, 1961; bounds on
*G*and*D*. Disuss the combination of TE and TM modes, has a typo in the problem. - R.E. Collin and S. Rothschild, 1964: closed form expressions for
*Q*for_{n}*n*=1,2,.. and extend the analyze to cylinder waves. - R.L. Fante 1969, 1992: Q, D/Q, G/Q for combinations of TE and TM modes
- J.S. McLean 1996:
*Q*_{1 }using explicit formulas for the modes and combined TE and TM modes. - J.C-E. Sten
*etal*2001: Q for antennas close to a conducting plane. - W. Geyi 2003: Q and G/Q for combined TE and TM modes.
- A. Karlsson 2004: Q and G for antennas in a lossy medium.
- D.H. Kwon 2005: G and Q for combined TE and TM modes.
- H.L. Thal 2006: Excludes the interiour of the sphere.

- R.F. Harrington, 1958, 1960, 1961; bounds on
- Some extensions of the bounds to spheroidals are reported.
- H.D. Foltz and J.S. McLean 1999:
- J.C-E. Sten etal 2001:

- Relationships between radiation
*Q*and bandwidth are eg discussed by- W. Geyi etal 2000:
- A.D. Yaghjian and S.R. Best 2005:
- A. Hujanen etal 2005:
- M. Gustafsson and S. Nordebo 2006, 2007:
- R.C. Hansen 2006, 2008:
- H. Stuart
*etal*. 2007:

- The bounds for combined TE and TM modes are criticized in
- Grimes
*etal*1995, 1997, 2000

- Grimes

##### References

- H. A. Wheeler, Fundamental limitations of small antennas, Proc. IRE, vol. 35, no. 12, pp. 1479-1484, 1947.
- L. J. Chu, Physical limitations of omni-directional antennas, Appl. Phys., vol. 19, pp. 1163-1175, 1948.
- R. Harrington, On the gain and beamwidth of directional antennas," IEEE Trans. Antennas Propagat., vol. 6, no. 3, pp. 219-225, 1958.
- H. Wheeler, The radiansphere around a small antenna, Proceedings of the IRE, vol. 47, no. 8, pp. 1325-1331, 1959.
- R. F. Harrington, Effect of antenna size on gain, bandwidth and effciency, Journal of Research of the National Bureau of Standards - D. Radio Propagation, vol. 64D, pp. 1-12, January - February 1960.
- R. F. Harrington, Time Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961.

R. E. Collin and S. Rothschild, Evaluation of antenna Q, IEEE Trans. Antennas Propagat., vol. 12, pp. 23-27, Jan. 1964. - R. L. Fante, Quality factor of general antennas, IEEE Trans. Antennas Propagat., vol. 17, no. 2, pp. 151-155, Mar. 1969.
- R. C. Hansen, Fundamental limitations in antennas," Proc. IEEE, vol. 69, no. 2, pp. 170-182, 1981.
- D. Grimes and C. Grimes, Bandwidth and Q of antennas radiating TE and TM modes, IEEE Trans. Electromagn. Compatibility, vol. 37, no. 2, pp. 217-226, 1995.
- J. S. McLean, A re-examination of the fundamental limits on the radiation Q of electrically small antennas, IEEE Trans. Antennas Propagat., vol. 44, no. 5, pp. 672-676, May 1996.
- D. Grimes and C. Grimes, Minimum Q of electrically small antennas: A critical review, Electron Lett, vol. 33, no. 433, p. 434, 1997.
- R. E. Collin, Minimum Q of small antennas, J. Electro. Waves Applic., vol. 12, pp. 1369-1393, 1998.
- W. Geyi, P. Jarmuszewski, and Y. Qi, The Foster reactance theorem for antennas and radiation Q, IEEE Trans. Antennas Propagat., vol. 48, no. 3, pp. 401-408, Mar. 2000.
- C. Grimes, G. Liu, D. Grimes, and K. Ong, Characterization of a wideband, low-Q, electrically small antenna, Microwave and Optical Technology Letters, vol. 27, no. 1, pp. 53-58, 2000.
- J. C.-E. Sten, P. K. Koivisto, and A. Hujanen, Limitations for the radiation Q of a small antenna enclosed in a spheroidal volume: axial polarisation, AEÜ Int. J. Electron. Commun., vol. 55, no. 3, pp. 198-204, 2001.
- W. Geyi, Physical limitations of antenna," IEEE Trans. Antennas Propagat., vol. 51, no. 8, pp. 2116-2123, Aug. 2003.
- A. Karlsson, Physical limitations of antennas in a lossy medium, IEEE Trans. Antennas Propagat., vol. 52, pp. 2027-2033, 2004.
- A. D. Yaghjian and S. R. Best, Impedance, bandwidth, and Q of antennas, IEEE Trans. Antennas Propagat., vol. 53, no. 4, pp. 1298-1324, 2005.
- R. C. Hansen, Electrically small, superdirective, and superconductive antennas. New Jersey: John Wiley & Sons, 2006.
- M. Gustafsson and S. Nordebo, Bandwidth, Q factor, and resonance models of antennas, Progress in Electromagnetics Research, vol. 62, pp. 1-20, 2006.
- H. L. Thal, New radiation Q limits for spherical wire antennas," IEEE Trans. Antennas Propagat., vol. 54, no. 10, pp. 2757-2763, Oct. 2006.
- M. Gustafsson and S. Nordebo, On the spectral effciency of a sphere, Progress in Electromagnetics Research, vol. 67, pp. 275-296, 2007.
- H. Stuart, S. Best, and A. Yaghjian, Limitations in relating quality factor to bandwidth in a double resonance small antenna, Antennas and Wireless Propagation Letters, vol. 6, 2007.
- R.C. Hansen, Bode and Fano impedance matching, Microwave and Optical Technology Letters, vol. 50, no. 4, pp. 875-877, 2008.