Why is this pattern different from the sin² θ “doughnut” of a short dipole?

The short dipole assumes a uniform current over a length much smaller than λ. A half-wave dipole has a nearly sinusoidal current distribution along the wire, which changes the far-field integral and replaces the simple sin θ factor with cos(½π cos θ)/sin θ in the E-plane. The overall shape is still a figure-of-eight in that plane, but the lobes are slightly “slimmer” near broadside, giving a bit higher directivity.

What does “dBi” mean here?

dBi expresses gain or directivity relative to an ideal isotropic radiator (uniform in all directions). For a lossless antenna, maximum directivity in dBi is 10 log₁₀(D). The simulator quotes D ≈ 1.64 for an ideal thin λ/2 dipole, i.e. about 2.15 dBi.

Does this simulator include a ground plane or a coax feed?

No. It shows the classical free-space element pattern. Real installations (vertical over ground, inverted-V, proximity to mast or roof) change impedance, efficiency, and the full 3D pattern; those require numerical modeling or measurements beyond this pedagogical plot.

How should I orient a half-wave dipole for best FM or VHF reception?

For linearly polarized broadcast signals, the broadside direction (perpendicular to the wire) is strongest. In the E-plane, the pattern has nulls along the wire axis, so pointing the wire toward a distant transmitter (end-fire toward the tower) is usually the weakest orientation; broadside alignment toward the horizon is the usual rule of thumb for a horizontal dipole.

Half-Wave Dipole Antenna Pattern

Far-field E-plane pattern of a thin λ/2 wire: power ∝ [cos(½π cos θ)/sin θ]², directivity D ≈ 1.64 (~2.15 dBi); optional sin² θ overlay vs a short dipole.

About this model

A center-fed half-wave dipole (a straight conductor about λ/2 long) is one of the most common reference antennas in RF engineering and amateur radio. Unlike the ideal Hertzian (infinitesimal) dipole, whose far-field pattern follows sin θ in the electric field and sin² θ in time-averaged power, a thin λ/2 wire in free space has a slightly different angular dependence derived from the sinusoidal standing-wave current along the wire. In the E-plane containing the dipole axis, the magnitude of the far-zone electric field is proportional to F(θ) = cos(½π cos θ)/sin θ, where θ is measured from the wire axis. The corresponding radiated power pattern is proportional to F²(θ). Nulls remain along the wire axis (θ = 0 and π), while maximum radiation occurs broadside (θ = π/2). The directivity relative to an isotropic radiator is approximately D ≈ 1.64 (about 2.15 dBi) for a lossless half-wave dipole—slightly higher than the short-dipole limit because the same total power is concentrated into a marginally narrower main lobe. This interactive page plots the normalized power pattern in polar form, optionally overlays the normalized sin² θ short-dipole pattern for comparison, and reports numeric half-power beamwidth (HPBW) in the E-plane. The model assumes a thin wire in free space, neglects ohmic loss, feed geometry, and ground effects, and does not include the H-plane pattern differences that appear for finite wire thickness or non-ideal feeds—those refinements matter for precision antenna design but not for the textbook λ/2 element pattern used in array theory.

Who it's for: Students and instructors in electromagnetics, RF systems, and antenna courses; hobbyists learning dipole orientation and pattern vocabulary before Yagi–Uda or phased-array topics.

Key terms

half-wave dipole
antenna radiation pattern
λ/2 dipole
cos(½π cos θ)/sin θ
directivity
dBi
E-plane
far field
Hertzian dipole comparison
HPBW

How it works

Far-field E-plane pattern of a thin center-fed half-wave dipole: normalized radiated power ∝ [cos(½π cos θ) / sin θ]², with θ measured from the wire axis. Directivity D ≈ 1.64 (~2.15 dBi) over an isotropic radiator. Compare the dashed Hertzian (short) dipole sin² θ overlay — shapes are similar but not identical.

Key equations

F(θ) = cos(½π cos θ) / sin θ (|E_θ| factor)

⟨P⟩ ∝ |F|² ; D ≈ 1.64 ( 10 log₁₀ D ≈ 2.15 dBi )

Frequently asked questions

Why is this pattern different from the sin² θ “doughnut” of a short dipole?: The short dipole assumes a uniform current over a length much smaller than λ. A half-wave dipole has a nearly sinusoidal current distribution along the wire, which changes the far-field integral and replaces the simple sin θ factor with cos(½π cos θ)/sin θ in the E-plane. The overall shape is still a figure-of-eight in that plane, but the lobes are slightly “slimmer” near broadside, giving a bit higher directivity.
What does “dBi” mean here?: dBi expresses gain or directivity relative to an ideal isotropic radiator (uniform in all directions). For a lossless antenna, maximum directivity in dBi is 10 log₁₀(D). The simulator quotes D ≈ 1.64 for an ideal thin λ/2 dipole, i.e. about 2.15 dBi.
Does this simulator include a ground plane or a coax feed?: No. It shows the classical free-space element pattern. Real installations (vertical over ground, inverted-V, proximity to mast or roof) change impedance, efficiency, and the full 3D pattern; those require numerical modeling or measurements beyond this pedagogical plot.
How should I orient a half-wave dipole for best FM or VHF reception?: For linearly polarized broadcast signals, the broadside direction (perpendicular to the wire) is strongest. In the E-plane, the pattern has nulls along the wire axis, so pointing the wire toward a distant transmitter (end-fire toward the tower) is usually the weakest orientation; broadside alignment toward the horizon is the usual rule of thumb for a horizontal dipole.

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Half-Wave Dipole Antenna Pattern

About this model

How it works

Key equations

Frequently asked questions

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Key equations

Frequently asked questions