ESA Antenna Pattern Calculator: How to Use It

The ESA Antenna Pattern Calculator is a free online tool that computes the far-field radiation pattern of a parabolic reflector antenna from its diameter, frequency, and feed illumination taper. You enter the antenna size, operating frequency, and edge taper, and it returns the gain, beamwidth, and sidelobe levels in a plotted pattern.

Formula

The calculator uses the standard aperture efficiency model for a uniformly illuminated circular aperture, modified by the edge taper. The gain is given by:

G = 20 log₁₀(π D / λ) + 20 log₁₀(cos(θ_e/2))

where:

• D = antenna diameter (m)
• λ = wavelength = c / f (m), with c = 299,792,458 m/s
• f = frequency (Hz)
• θ_e = edge taper angle = asin(10^(t/20)), where t is the edge taper in dB (negative value)

The half-power beamwidth (HPBW) is approximated by HPBW ≈ 70° / (D/λ), and the first sidelobe level is estimated from the edge taper using a linear fit: SLL ≈ -17.6 + 2.5·t dB.

Worked Example

Using the default values: D = 2.4 m, f = 10 GHz, t = -10 dB.

1. Compute wavelength: λ = 299,792,458 / 10,000,000,000 = 0.02998 m
2. Compute D/λ = 2.4 / 0.02998 ≈ 80.05
3. Compute edge taper angle: θ_e = asin(10^(-10/20)) = asin(0.3162) ≈ 18.43°
4. Compute gain: G = 20 log₁₀(π × 80.05) + 20 log₁₀(cos(9.215°)) = 48.01 + (-0.12) ≈ 47.89 dBi
5. Compute beamwidth: HPBW = 70 / 80.05 ≈ 0.874°
6. Compute sidelobe level: SLL = -17.6 + 2.5×(-10) = -42.6 dB

The calculator returns gain ≈ 47.89 dBi, beamwidth ≈ 0.87°, and first sidelobe level ≈ -42.6 dB.

What the Calculator Tells You

The output gives three key figures for a parabolic dish antenna:

• Gain (in dBi) – the maximum directive gain relative to an isotropic radiator. Higher gain means a stronger signal in the main beam direction.
• Half-power beamwidth (in degrees) – the angular width of the main beam where power drops to half (-3 dB). A narrower beamwidth means a more focused beam.
• First sidelobe level (in dB) – the level of the largest sidelobe relative to the main beam peak. Lower (more negative) is better for reducing interference.

These numbers help you evaluate link budgets, interference, and coverage for satellite communications, radar, or radio astronomy.

How to Choose Inputs

Pick realistic values for your antenna system:

• Diameter – use the physical diameter of the reflector in meters. Common sizes: 0.6 m for VSAT, 1.2 m for TVRO, 3.7 m for teleport.
• Frequency – enter the operating frequency in GHz. Common bands: C-band (4–8 GHz), Ku-band (12–18 GHz), Ka-band (26–40 GHz).
• Edge taper – typically -10 dB to -15 dB for a feed that illuminates the dish edge less than the center. A deeper taper (more negative) reduces sidelobes but also reduces aperture efficiency and gain.

For a real antenna, the actual edge taper depends on the feed horn pattern and the f/D ratio. If you don’t know it, use -10 dB as a typical default.

Common Mistakes and Limitations

The model assumes a perfect parabolic reflector with a rotationally symmetric feed pattern. Real antennas have:

• Blockage from the feed and support struts, which reduces gain and raises sidelobes.
• Surface errors that cause gain loss, especially at higher frequencies.
• Non-ideal feed patterns that are not perfectly symmetric.

Common mistakes when using the calculator:

• Entering frequency in MHz instead of GHz – always convert to GHz.
• Using diameter in feet – convert to meters (1 ft = 0.3048 m).
• Forgetting that the edge taper is negative – the calculator expects a negative dB value.

The beamwidth formula is an approximation that works well for D/λ > 10. For smaller antennas, the pattern is wider and the formula underestimates the beamwidth.

Comparison with Other Tools

There are several antenna pattern calculators online, but they differ in features:

• Some only compute gain and beamwidth, not sidelobes.
• Some allow you to input the feed pattern explicitly, which gives more accurate results but requires more data.
• Some are designed for specific applications like satellite dishes or radar.

This calculator is a quick estimate that is accurate enough for initial link budget calculations. For final design, you would use a full electromagnetic simulation tool like GRASP or FEKO.

Frequently Asked Questions

What is an antenna pattern?

An antenna pattern (or radiation pattern) is a graph that shows how the antenna radiates energy in different directions. It typically has a main lobe (the direction of maximum radiation) and sidelobes (smaller lobes in other directions). The pattern is usually plotted in polar coordinates.

What is edge taper and why does it matter?

Edge taper is the reduction in illumination at the edge of the reflector compared to the center, expressed in dB. A deeper taper (more negative) reduces sidelobes and spillover but also reduces the effective aperture and gain. A typical value is -10 to -15 dB for a compromise between gain and sidelobe performance.

Can I use this calculator for a horn antenna?

No, this calculator is specifically for parabolic reflector antennas. Horn antennas have different radiation patterns and require different formulas. For a horn, you would need to calculate the pattern based on the aperture dimensions and the mode of propagation.

How accurate is the gain calculation?

The gain formula assumes 100% aperture efficiency, which is never achieved in practice. Real antennas have efficiencies of 50–70% due to spillover, blockage, and surface errors. To get a more realistic gain, you can multiply the result by the efficiency factor (e.g., 0.6 for 60% efficiency). The calculator does not include this factor, so the gain is an upper bound.

What is the difference between dBi and dBd?

dBi is gain relative to an isotropic radiator (a theoretical point source that radiates equally in all directions). dBd is gain relative to a half-wave dipole antenna. Since a dipole has 2.15 dBi gain, dBi = dBd + 2.15. This calculator outputs dBi, which is the standard for most applications.

Why does the beamwidth formula use 70 as a constant?

The constant 70 is an approximation that works for a uniformly illuminated circular aperture. The exact beamwidth depends on the illumination taper and the aperture shape. For a typical parabolic antenna with a -10 dB edge taper, the constant is close to 70. For deeper tapers, the beamwidth is slightly wider.

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in d | Antenna Diameter | m | 2.4 | 0
in f | Frequency | GHz | 10 | 0
in t | Edge Taper | dB | -10 | 0
out gain | Antenna Gain | dBi | 20*log10(pi*d*(f*1e9/299792458)) + 20*log10(cos(0.5*asin(10^(t/20)))) | 2
out beamwidth | Half-Power Beamwidth | deg | 70*(299792458/(f*1e9))/d | 2
out sll | First Sidelobe Level | dB | -17.6 + 2.5*t | 2