What limits the performance of electrically small antennas?

Q: What is ka?

Wavenumber times the radius of the smallest sphere enclosing the antenna.

Q: Can metamaterials beat the Chu limit?

Passive linear antennas cannot; claims should be examined for loss or measurement errors.

Q: Why do phone antennas need tuners?

They must cover many bands with limited volume.

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

An antenna is electrically small when it fits inside a sphere of radius a with ka < 1 (k = 2π/λ). Wheeler (1947) and Chu (1948) showed that such antennas have a minimum radiation Q, so bandwidth shrinks with size. McLean’s form for a linearly polarized antenna is Q_min = 1/(ka)³ + 1/(ka).^[1]^[2]^[3]

What does the limit mean in practice?

Fractional bandwidth is roughly inversely proportional to Q (for a given VSWR criterion), so halving the size of a small antenna reduces achievable bandwidth by roughly 8×. Adding loss lowers Q and widens bandwidth but reduces efficiency. Real antennas generally have Q well above the bound.^[3]

How do designers cope?

Use the whole device ground plane as part of the radiator.
Use tunable matching (aperture or impedance tuners) to cover bands sequentially.
Accept lower efficiency where link budget allows.
Use fill-the-sphere 3D geometries that approach the bound more closely.

What about matching networks?

Matching a high-Q antenna is also constrained by the Bode–Fano limit; lossless networks cannot overcome the Chu bound for bandwidth, only redistribute it.^[4]

Frequently asked questions

What is ka?

Wavenumber times the radius of the smallest sphere enclosing the antenna.

Can metamaterials beat the Chu limit?

Passive linear antennas cannot; claims should be examined for loss or measurement errors.

Why do phone antennas need tuners?

They must cover many bands with limited volume.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Fundamental Limitations of Small Antennas”. H. A. Wheeler, Proceedings of the IRE, vol. 35, no. 12, pp. 1479-1484. December 1947.
“Physical Limitations of Omni-Directional Antennas”. L. J. Chu, Journal of Applied Physics, vol. 19, pp. 1163-1175. December 1948.
“A Re-Examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas”. J. S. McLean, IEEE Transactions on Antennas and Propagation, vol. 44, no. 5, pp. 672-676. May 1996.
“Theoretical Limitations on the Broadband Matching of Arbitrary Impedances”. R. M. Fano, Journal of the Franklin Institute, vol. 249. 1950.

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