What is a Hertzian dipole?
A Hertzian dipole is an idealized current element of length l ≪ λ carrying uniform current. Its far-field pattern is proportional to sin θ, its directivity is 1.5 (1.76 dBi), its half-power beamwidth is 90°, and its radiation resistance is Rr = 80π²(l/λ)² Ω.[1] Every wire antenna can be analyzed as a superposition of such elements.
What are the fields of a Hertzian dipole?
For a z-directed element with current I0, the far-zone fields are Eθ ≈ jηkI0l·sinθ·e−jkr/(4πr) and Hφ = Eθ/η.[1] Closer in, terms in 1/r² and 1/r³ dominate; they store reactive energy and define the near field. The boundary where the three terms have equal magnitude is r = λ/2π, the “radiansphere” of Wheeler.[2]
What are its radiation resistance and directivity?
Integrating the Poynting vector gives Prad = η(π/3)|I0l/λ|², hence Rr = (2π/3)η(l/λ)² ≈ 80π²(l/λ)² Ω.[1] The radiation intensity is proportional to sin²θ, so D = 1.5 (1.76 dBi) and the half-power points are at θ = 45° and 135°, a 90° beamwidth.
How does a short dipole differ?
A real short dipole fed at its center has a current that tapers roughly linearly to zero at the ends. Its average current is half the feed current, so its radiation resistance is one quarter of the Hertzian value, Rr ≈ 20π²(l/λ)², while its directivity remains 1.5.[1] Top loading (capacitance hats) flattens the current and raises Rr toward the Hertzian value.
Frequently asked questions
Why is the Hertzian dipole useful if it cannot be built?
It is the Green’s-function building block: any current distribution is a sum of infinitesimal dipoles.
What is the directivity of any very small antenna?
Close to 1.5 for electric or magnetic dipole-like small antennas.
What is the radiation resistance of a λ/10 short dipole?
About 2 Ω with a triangular current, versus about 7.9 Ω for a uniform-current element of the same length.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
- “The Radiansphere Around a Small Antenna”. H. A. Wheeler, Proceedings of the IRE, vol. 47, no. 8, pp. 1325-1331. August 1959.