Calculating the Gain of a Parabolic Dish Antenna:

To calculate the gain of a parabolic dish antenna, we need to consider the diameter of the dish, the frequency of operation, and the efficiency of the antenna.

Given Information:
- Diameter of the parabolic dish antenna: 1 metre
- Frequency of operation: 20 GHz
- Efficiency of the antenna: 70%

Formula for Antenna Gain:
The formula for the gain of a parabolic dish antenna is given by:

G = (4πAη) / λ²

where,
G is the gain of the antenna,
A is the effective aperture area of the antenna,
η is the efficiency of the antenna, and
λ is the wavelength of the electromagnetic wave.

Calculating the Wavelength:
The wavelength (λ) can be calculated using the formula:

λ = c / f

where,
λ is the wavelength,
c is the speed of light (3 x 10^8 m/s), and
f is the frequency.

Substituting the given frequency into the formula, we can find the wavelength:

λ = (3 x 10^8 m/s) / (20 x 10^9 Hz) = 0.015 meters

Calculating the Effective Aperture Area:
The effective aperture area (A) of the antenna can be calculated using the formula:

A = πr²

where,
A is the effective aperture area, and
r is the radius of the dish.

Given the diameter of the dish is 1 meter, the radius (r) can be calculated as:

r = 1 / 2 = 0.5 meters

Substituting this value into the formula, we can find the effective aperture area:

A = π(0.5)² = 0.785 square meters

Calculating the Gain:
Substituting the values of A, η, and λ into the gain formula, we can calculate the gain of the antenna:

G = (4π(0.785)(0.7)) / (0.015)² = 45

Therefore, the approximate gain of the parabolic dish antenna at 20 GHz is 45.00 (rounded to two decimal places).

Λ = c/f = (3 x 10⁸)/(20 x 10⁹) = 3/200