# Antenna Pattern Calculator - Dipole, Phased Array, Link Budget, Antenna Length

> Exact dipole/monopole patterns, directivity and radiation resistance; phased-array steering with Chebyshev tapers; Friis link budget; antenna length by band.

- URL: https://qilingtools.com/en/physics/antenna
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Drag the dipole length L/λ to see the exact E-plane and H-plane patterns of a centre-fed thin-wire dipole in dB or linear scale, with directivity, half-power beamwidth and radiation resistance from numerical integration: about 73 Ω and 2.15 dBi for a half-wave dipole. The array page sets the number of elements, spacing, steering angle and uniform, cosine or Chebyshev tapers, showing the pattern, sidelobe level, grating-lobe warning and a live wave field. There is also a Friis link budget with Fresnel-zone and Earth-curvature checks, and an antenna length reference by band.

## How to use

1. On the dipole tab drag the length or tap a preset, switch between dipole and monopole, and read the pattern and radiation resistance
2. On the linear array tab set N, spacing d/λ, steering angle and taper, and watch the main lobe, sidelobes and grating lobes
3. Turn on the sweep animation or wave field to see a phased array steer by phase alone
4. On the link budget tab enter transmit power, gains, frequency and distance to get received power, margin and Fresnel clearance
5. On the antenna length tab enter a frequency or tap a band for half-wave dipole, quarter-wave monopole and coax stub lengths

## Features

- Exact thin-wire dipole far field, E-plane and H-plane polar plots in dB or linear
- Numerical directivity, half-power beamwidth, radiation resistance and feed-point resistance
- Linear arrays with uniform, cosine, Hann, binomial and Dolph–Chebyshev tapers and sidelobe level
- Beam-steering animation, grating-lobe warning and instantaneous wave-field heat map
- Friis link budget: EIRP, path loss, received power, margin, max range, Fresnel zone and Earth bulge
- Band reference for FM, Wi-Fi, LoRa, ham radio, GPS and more

## FAQ

### Why is a half-wave dipole 73 Ω and 2.15 dBi?

A centre-fed thin dipole carries an approximately sinusoidal current, giving the far field E_θ ∝ [cos(kL/2·cosθ) − cos(kL/2)]/sinθ. Integrating the radiated power over the sphere for L = λ/2 gives a radiation resistance R = (η₀/2π)∫F² sinθ dθ ≈ 73.1 Ω. Peak intensity over the average is the directivity D ≈ 1.64, or 10 log 1.64 ≈ 2.15 dBi. The tool runs the same integration for any length.

### How does a monopole relate to a dipole?

By image theory a monopole standing on a perfect ground plane behaves like a dipole of twice its length that radiates only above ground. All the power goes into half the space, so the directivity doubles (about 5.15 dBi for λ/4) and the radiation resistance halves (about 36.5 Ω). Real car roofs and radials are not infinite perfect conductors, so measured values differ somewhat.

### How does a phased array steer its beam?

A linear array’s pattern is the element pattern times the array factor AF = Σ a_n e^{jn(kd sinφ + β)}. Giving successive elements a phase step β = −kd sin θs makes all signals add in phase in direction θs, so the main lobe points there while the array itself stays still. The larger the scan angle, the smaller the effective aperture and the wider the beam.

### What are grating lobes and how do I avoid them?

If the elements are too far apart, a second beam as strong as the main lobe appears in visible space: a grating lobe. It happens when d/λ ≥ 1/(1 + |sin θs|), so a broadside array needs d < λ and an array scanning to ±90° needs d < λ/2. That is why phased arrays usually use about λ/2 spacing. The tool warns you when the condition is met.

### Why does the link budget check the Fresnel zone?

Radio waves do not travel along a single line; obstacles anywhere inside the first Fresnel zone, a long ellipsoid between the antennas, affect the signal. Its radius at midpoint is r = √(λd₁d₂/(d₁+d₂)). Keeping at least 60% of that radius clear is the usual rule; otherwise the loss is noticeably worse than the Friis free-space result. Long links also have to clear the Earth’s bulge at midpoint.

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