# How to calculate the Antenna gain?

Antenna gain is defined as 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, that is, with superior performance in one direction than in others. The antenna gain is denoted by the symbol G_{dB,} and its unit of measurement is decibels (dB). It is directly proportional to the aperture area, efficiency, and wavelength of the signal.

### Antenna gain Formula

G_{dB}= 10 log_{10}(4πηA/λ^{2})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

A = 20

λ = 2

Using the formula we get,

G

_{dB}= 10 log_{10}(4πηA/λ^{2})= 10 log

_{10}((4 × 3.14 × 80 × 20)/4)= 10 (3.7012)

= 37.012 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

A = 4

λ = 0.01

Using the formula we get,

G

_{dB}= 10 log_{10}((4 × 3.14 × 40 × 4)/0.0001)= 10 (7.303)

= 73.03 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

A = 10

λ = 3

Using the formula we get,

G

_{dB}= 10 log_{10}((4 × 3.14 × 95 × 10)/9)= 10 (3.12)

= 31.2 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

G = 20

λ = 6

Using the formula we get,

20 = 10 log

_{10}((4 × 3.14 × 10 × A)/36)=> 125.6 A/36 = 0.303

=> A = 2.11 m

^{2}

**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

G = 80

λ = 1

Using the formula we get,

80 = 10 log

_{10}((4 × 3.14 × 80 × A)/1)=> 1004.8 A = 0.903

=> A = 3.38 m

^{2}

**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 log

_{10}((4 × 3.14 × η × 50)/25)=> 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 log

_{10}((4 × 3.14 × η × 80)/100)=> 10.048 η = 0.477

=> η = 1.99%