How to Calculate the Antenna Gain?

The ability of an antenna to focus radio frequency (RF) energy, either sent or received, in a specific direction relative to an ideal isotropic radiator is known as antenna gain.

Antenna Gain is calculated by using the formula energy:

Antenna Gain = 10 × log₁₀ (P_out/P_in)

where,

• P_out is the radiated power in a specific direction (usually in watts)
• P_in ​ is the power supplied to the antenna (also in watts).

Determine the energy emitted by the antenna in the direction of interest. This can be done experimentally using specialized equipment such as a power meter or by simulation using antenna modelling software. The calculation result will give us the gain in decibels relative to an isotropic radiator (dBi).

What is Antenna Gain?

Antenna gain is the degree of directivity of the antenna's radiation pattern. It is equal to the product of the antenna's electrical efficiency and directivity. In other words, it is a passive phenomenon in which the antenna simply redistributes power to produce more radiated power in a specific direction than an isotropic antenna would broadcast.

A transmitting antenna can acquire antenna gain by making an antenna directional emitted, with superior performance in one direction than in others. The symbol GdB denotes the antenna gain_, and its unit of measurement is decibels (dB). It is directly proportional to the aperture area, efficiency, and inversely proportional to the squar of signal wavelength.

Antenna Gain Formula

G_dB  = 10 log₁₀ (4πηA/λ²)

Where,

• G_dB is the Antenna Gain
• η is the Efficiency
• A is the Physical Aperture Area
• λ is the Wavelength of the Signal

Sample Problems

Problem 1: Calculate the antenna gain if the aperture area is 20 sq. m, the wavelength is 2 m, and the efficiency is 80%.

Solution:

We have,

η = 80% = 0.80

A = 20

λ = 2

Using the formula we get,

G_dB  = 10 log₁₀ (4πηA/λ²)

= 10 log₁₀ ((4 × 3.14 × 0.80 × 20)/4)

= 10 (3.7012)

= 17.01 dB

Problem 2: Calculate the antenna gain if the aperture area is 4 sq. m, the wavelength is 0.01 m, and the efficiency is 40%.

Solution:

We have,

η = 40% = 0.40

A = 4

λ = 0.01

Using the formula we get,

G_dB = 10 log₁₀ ((4 × 3.14 × 0.40 × 4)/0.0001)

= 10 (7.303)

= 53.03 dB

Problem 3: Calculate the antenna gain if the aperture area is 10 sq. m, the wavelength is 3 m, and efficiency is 95%.

Solution:

We have,

η = 95℅ = 0.95

A = 10

λ = 3

Using the formula we get,

G_dB = 10 log₁₀ ((4 × 3.14 × 0.95 × 10)/9)

= 10 (3.12)

= 11.22 dB

Problem 4: Calculate the aperture area if antenna gain is 20 dB, the wavelength is 6 m, and efficiency is 10%.

Solution:

We have,

η = 10% = 0.10

G = 20 

λ = 6

Using the formula we get,

20 = 10 log₁₀ ((4 × 3.14 × 0.10 × A)/36)

⇒ 1.256 A/36 = 100

⇒A = 2866.24 m² 

Problem 5: Calculate the aperture area if antenna gain is 80 dB, the wavelength is 1 m, and efficiency is 70%.

Solution:

We have,

η = 70% = 0.70

G = 80

λ = 1

Using the formula we get,

80 = 10 log₁₀ ((4 × 3.14 × 0.70 × A)/1)

⇒ 8.792 A = 100000000

⇒ A = 11373976.34 m²

Problem 6: Calculate the efficiency if the antenna gain is 47 dB, the wavelength is 5 m, and the aperture area is 50 sq. m.

Solution:

We have,

A = 50

G = 47

λ = 5

Using the formula we get,

47 = 10 log₁₀ ((4 × 3.14 × η × 50)/5)

⇒ 25.12 η = 0.672

⇒ η = 4.37%

Problem 7: Calculate the efficiency if antenna gain is 30 dB, the wavelength is 10 m, and aperture area is 80 sq. m.

Solution:

We have,

A = 80

G = 30

λ = 10

Using the formula we get,

30 = 10 log₁₀ ((4 × 3.14 × η × 80)/100)

⇒ 10.048 η = 0.477

⇒ η = 1.99%

Practice Problems

P1. An antenna has an efficiency (η) of 0.9, a physical area (A) of 1 square meter, and operates at a wavelength (λ) of 0.2 meters. What is the gain in decibels (dB)?

P2. An antenna with an efficiency (η) of 0.75 and a physical area (A) of 0.8 square meters operates at a wavelength (λ) of 0.15 meters. Calculate the gain in decibels (dB).

P3. Calculate the gain in decibels (dB) for an antenna with an efficiency (η) of 0.5, a physical area (A) of 1.2 square meters, and a wavelength (λ) of 0.3 meters.