Antennas — Half-Wave Dipole + N-Element Linear Array

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Two classic GATE topics in one workbench. Tab 1: half-wave dipole — drag the length to see the radiation pattern evolve from a short dipole (capacitive, low R_rad) through the half-wave resonance (R_rad = 73 Ω) to a full-wave (anti-resonance). Tab 2: N-element linear array — set N, spacing d, and progressive phase β; see the element pattern, the array factor, and the total pattern with pattern multiplication. Grating lobes are flagged when d/λ > 0.5.

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Dipole

Length L/λ: 0.500

Frequency f: MHz

L is the total dipole length in wavelengths. f sets the absolute length for the KV panel.

Presets

① Radiation pattern |E_θ(θ)| (E-plane cross-section)

The 2D polar plot is a cross-section of the 3D pattern. The half-wave dipole is omnidirectional in the H-plane (φ); in the E-plane (θ) the pattern is a figure-8 with maxima at θ = 90° and nulls at θ = 0°, 180°.

linear |F(θ)| 20 log₁₀ |F(θ)| (dB)

② Current distribution I(z) = I₀ sin(k(L/2 − |z|))

The standing-wave current on a thin center-fed dipole is sinusoidal. At half-wave (L = 0.5λ), the maximum is at the center; at full-wave (L = 1λ) there's a null at the center and two lobes.

③ Input impedance Z_in(L/λ)

R_in peaks at L = 0.5λ (half-wave, R_rad = 73 Ω) and again near L = 1.5λ. X_in is negative (capacitive) for L < 0.5λ, positive (inductive) for 0.5λ < L < 1λ, and goes to ±∞ at L = 1λ (anti-resonance).

Geometry

L (length)

— m

L/λ

—

Input impedance

R_in

— Ω

X_in

— Ω

|Z_in|

— Ω

Resonance

—

Pattern metrics

Directivity D

— (linear)

D (dBi)

—

HPBW (E-plane)

— °

Array

N (elements): 4

d/λ (spacing): 0.50

β (phase): 0°

Beam direction:

Element length L/λ: 0.50

Presets

① Array factor alone |AF(θ)|

The array factor depends only on N, d/λ, and β — not on the element. The main beam direction is at cos θ₀ = −β / (kd). For β = 0 (broadside), the beam is at θ = 90°; for β = −kd (end-fire), at θ = 0°.

② Total pattern |F_element(θ) · AF(θ)| (pattern multiplication)

The total radiation pattern is the product of the element pattern and the array factor. Where the element pattern is small (e.g. near θ = 0 for a half-wave dipole), the array factor lobes are suppressed — even if they would otherwise be there.

element pattern AF total (element × AF)

Array geometry

N (elements)

—

d/λ (spacing)

—

β (progressive phase)

— °

Total length (N−1)·d

— λ

Beam

Main beam θ₀

— °

HPBW (approx)

— °

Directivity D

—

D (dBi)

—

Grating lobes

d/λ ≤ 0.5?

no grating lobes