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The active area of an X-band marine radar antenna is rectangular with a width of 1 m and a height of 0.15 m. Estimate the far-field distance in free space at 10 GHz. Will this antenna produce a fan-beam or a pencil-beam pattern? Explain based on the antenna dimensions.

User Jbcaveman
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Final answer:

The far-field distance of the antenna is estimated to be 66.7 meters at 10 GHz. Based on the dimensions of the antenna, it will produce a fan-beam pattern rather than a pencil-beam pattern.

Step-by-step explanation:

The far-field distance of an antenna is calculated using the formula:

d = 2D^2 / λ

Where d is the far-field distance, D is the largest dimension of the antenna (in this case, the width which is 1m), and λ is the wavelength of the signal.

At 10 GHz, the wavelength is given by the formula: λ = c / f,

where c is the speed of light (3 x 10^8 m/s) and f is the frequency (10 GHz = 10^10 Hz).

Plugging in the values, we have: λ = 3 x 10^8 m/s / 10^10 Hz = 0.03 m.

Substituting the values of D and λ into the formula for d, we get:

d = 2(1)^2 / 0.03 = 66.7 m.

Therefore, the far-field distance in free space at 10 GHz is estimated to be 66.7 meters.

Based on the dimensions of the antenna (1m x 0.15m), it is a rectangular shape. Rectangular antennas tend to produce a fan-beam pattern rather than a pencil-beam pattern. A fan-beam pattern spreads out in a wider angle compared to a pencil-beam pattern, which concentrates the radiation in a narrow angle.