What is antenna reciprocity?

The reciprocity theorem (Lorentz reciprocity) states that, in linear, passive and isotropic media, the response at port B to a source at port A equals the response at A to the same source at B. As a consequence an antenna’s transmit and receive patterns, gain and input impedance are identical.^[1][2]

What does reciprocity imply in practice?

• Patterns may be measured in either mode, whichever is more convenient.^[3]
• Mutual impedance Z₁₂ = Z₂₁ and S₂₁ = S₁₂ between antennas.
• The relation A_e = λ²G/4π holds for every reciprocal antenna.

When does reciprocity fail?

Reciprocity fails with non-reciprocal media or devices: magnetized ferrites (circulators, isolators), magnetized plasma such as the ionosphere (Faraday rotation reverses differently in each direction), and active circuits such as amplifiers in active antennas or active phased arrays with separate transmit and receive chains.^[2]

Is the received noise reciprocal?

No. Received signal follows reciprocity, but noise environments differ: at HF a receiving antenna is often limited by atmospheric and man-made noise, so a small inefficient receive antenna can perform as well as a large one, while it would be a poor transmitter.^[4]

Frequently asked questions

See also

• Gain
• Effective aperture
• Measurement overview
• Massive MIMO

References

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

1. “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
2. “Antennas and Radiowave Propagation”. R. E. Collin, McGraw-Hill. 1985.
3. “IEEE Recommended Practice for Antenna Measurements (IEEE Std 149-2021)”. IEEE Antennas and Propagation Society. 2022.
4. “Recommendation ITU-R P.372: Radio noise”. ITU-R. current edition.