An S-band radar transmitting at 3 GHz radiates 200 kW of power. Determine the signal power density at a range of 100 ...

Q. An S-band radar transmitting at 3 GHz radiates 200 kW of power. Determine the signal power density at a range of 100 nautical miles if the effective area of the radar antenna is 9 m².

Solution

Given,

• Transmitted power: P_t = 200 kW = 200,000 W
• Frequency: f = 3 GHz = 3 × 10⁹ Hz
• Range: R = 100 nautical miles
• Effective antenna area: A_e = 9 m²
• Speed of light: c = 3 × 10⁸ m/s

Step 1: Convert Nautical Miles to Meters

One nautical mile equals 1852 meters.

R = 100 × 1852 = 185200 m

Step 2: Calculate the Wavelength

The wavelength is calculated using the relationship between the speed of light and frequency:

λ = c / f

λ = (3 × 10⁸) / (3 × 10⁹)

λ = 0.1 m

Step 3: Calculate the Antenna Gain

The relationship between effective aperture and antenna gain is:

G = (4πAₑ) / λ²

G = (4π × 9) / (0.1)²

G ≈ 11309.73

Antenna gain is dimensionless when expressed as a linear ratio.

Step 4: Calculate the Signal Power Density

In the far field, the power density at a distance R from a transmitting antenna is:

S = (PₜG) / (4πR²)

Substituting the antenna gain formula gives a simpler expression:

S = (PₜAₑ) / (λ²R²)

S = (200000 × 9) / [(0.1)² × (185200)²]

S ≈ 0.005248 W/m²

Step 5: Convert to Milliwatts per Square Meter

Since 1 W = 1000 mW:

S = 0.005248 × 1000

S = 5.248 mW/m²

Final Answer: Option 4

5.248 mW/m²