Horn Antenna Gain Calculator

The gain of a Horn antenna depends on its frequency of operation, aperture and its efficiency.

Formula

Gain = (4π A e_A)/λ²

where

A is Area of Aperture
e_A or η is Aperture Efficiency
λ (=c/f) is the wavelength

Background

Horn antennas are widely used in applications like radar, satellite communication, and testing due to their high gain and directional properties. Gain of a horn antenna is an important parameter. It determines performance in transmitting or receiving electromagnetic waves.

The picture below shows a horn antenna

What Is Antenna Gain?

Antenna gain represents the ability of an antenna to focus energy in a specific direction, compared to an ideal isotropic antenna that radiates equally in all directions. For horn antennas, gain depends on several factors, including the size of the aperture, operating frequency, and efficiency.

Gain is typically expressed in decibels (dB) and calculated as:

G = Power Radiated in Desired Direction/Power Radiated by Isotropic

Key Parameters for Horn Antennas

Aperture Area (A): The physical opening of the horn.

A = (π/4)⋅a⋅b

where,

a: Width of the aperture.

b: Height of the aperture.

Wavelength (λ): Related to the operating frequency

λ = c/f

where,

c: Speed of light = 3×10⁸ m/s

f: Operating frequency (in Hz).

Efficiency (η): Accounts for losses due to imperfections, typically between 0.5 and 0.9.

Gain Formula for a Horn Antenna

The gain (G) of a horn antenna can be calculated using the following formula:

G=η⋅(4π⋅A)/λ²

Where:

G: Gain (linear scale, convert to dB later)
η: Efficiency
A: Aperture area (m²)
λ: Wavelength (m)

Step-by-Step Calculation

1. Calculate the Aperture Area

Measure the width (a) and height (b) of the horn’s aperture.
Use the formula: A = (π/4)⋅a⋅b

2. Determine the Wavelength

Use the formula: λ = c/f
Example: For a frequency of 10 GHz, λ = 3×10⁸ / 10×10⁹ = 0.03 m

3. Apply Efficiency

Choose an efficiency value (η) based on the antenna design (e.g., 0.8 for a well-designed horn).

4. Calculate Gain in Linear Scale

Plug values into the gain formula: G = η⋅(4πA)/λ²

5. Convert to Decibels (dB)

Convert linear gain to dB using: GdB = 10⋅Log⁡₁₀(G)

Example Calculation

Given:

Aperture dimensions: a=0.2, b=0.1
Operating frequency: 10 GHz
Efficiency: 0.80

Use the Calculator to find:

G = 175.9
G (dB) = 22.44 dB