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What is the Q factor of an antenna?

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The quality factor Q of an antenna is ω times the time-averaged non-propagating stored energy divided by the power accepted, Q = 2ω·max(We, Wm)/PA.[1] High Q means narrow bandwidth; for a tuned antenna the VSWR-s bandwidth is FBW ≈ (s−1)/(Q√s).[1] Electrically small antennas have unavoidably high Q.[2]

How is Q estimated from impedance?

Yaghjian and Best derived Q(ω) ≈ ω|Z′0(ω)|/(2R0(ω)), where Z′0 is the frequency derivative of the input impedance after tuning to resonance with a series reactance. This lets Q be computed from simulated or measured impedance at a single frequency and agrees well with field-based Q when Q is not too low.[1]

What is the lower bound on Q?

For an antenna enclosed in a sphere of radius a, the minimum radiation Q of a single TM or TE mode is Q ≥ 1/(ka)³ + 1/(ka) (McLean’s exact form of Chu’s bound), and roughly half that for an antenna exciting both TM01 and TE01 modes equally.[3][2] Losses lower the measured Q but at the expense of efficiency; the relevant bound scales with efficiency.

Why does low Q not always mean wide bandwidth?

The Q–bandwidth relation holds for single-resonance antennas. Multi-resonant designs and matching networks can exceed the single-tuned bandwidth, up to a factor bounded by the Bode–Fano limit (for a 2:1 VSWR, an ideal infinite-order network gives roughly four times the single-tuned bandwidth). Lossy loading lowers Q and widens bandwidth by wasting power.[1][4]

Frequently asked questions

What Q does a λ/10-radius antenna have?

ka = 0.628 gives a Chu–McLean minimum Q of about 5.6.

Is high Q bad?

It narrows bandwidth and increases sensitivity to detuning and loss; it is inherent to small antennas.

Can Q be measured?

Yes, from the impedance bandwidth or from the Yaghjian–Best derivative formula.

References

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

  1. “Impedance, Bandwidth, and Q of Antennas”. A. D. Yaghjian and S. R. Best, IEEE Transactions on Antennas and Propagation, vol. 53, no. 4, pp. 1298-1324. April 2005.
  2. “Physical Limitations of Omni-Directional Antennas”. L. J. Chu, Journal of Applied Physics, vol. 19, pp. 1163-1175. December 1948.
  3. “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.
  4. “Theoretical Limitations on the Broadband Matching of Arbitrary Impedances”. R. M. Fano, Journal of the Franklin Institute, vol. 249, pp. 57-83 and 139-154. 1950.
Categories: Fundamentals