Understanding Radar Range Calculation

The maximum radar range is determined by the radar equation:

\[R_{\text{max}} = \left( \frac{P_t \cdot G^2 \cdot \sigma}{(4\pi)^3 \cdot P_{\text{min}}} \right)^{1/4}\]

Where:

• R_max: Maximum radar range (meters)
• P_t: Transmitter power (W)
• G: Antenna gain
• σ: Radar cross section of the target (m²)
• P_min: Minimum detectable power (W)

Example Calculations

Example 1: Air Traffic Control Radar

• Transmitter Power (\(P_t\)): 1000 W
• Antenna Gain (\(G\)): 10000 (40 dB)
• Radar Cross Section (\(σ\)): 1 m²
• Minimum Detectable Power (\(P_{\text{min}}\)): \(10^{-13}\) W

Steps:

1. Using the radar range equation:
   \[R_{\text{max}} = \left( \frac{1000 \cdot (10000)^2 \cdot 1}{(4\pi)^3 \cdot 10^{-13}} \right)^{1/4}\]
2. Simplify:
   \[R_{\text{max}} = \left( \frac{10^{11}}{6.3617 \cdot 10^{-9}} \right)^{1/4} \approx 240,000 \, \text{m}\]

Result: The maximum radar range is approximately 240 km.

Example 2: Long-Range Radar

• Transmitter Power (\(P_t\)): 5000 W
• Antenna Gain (\(G\)): 20000 (43 dB)
• Radar Cross Section (\(σ\)): 5 m²
• Minimum Detectable Power (\(P_{\text{min}}\)): \(10^{-14}\) W

Steps:

1. Using the radar range equation:
   \[R_{\text{max}} = \left( \frac{5000 \cdot (20000)^2 \cdot 5}{(4\pi)^3 \cdot 10^{-14}} \right)^{1/4}\]
2. Simplify:
   \[R_{\text{max}} = \left( \frac{2 \cdot 10^{14}}{6.3617 \cdot 10^{-9}} \right)^{1/4} \approx 562,000 \, \text{m}\]

Result: The maximum radar range is approximately 562 km.

Factors Affecting Radar Range

• Transmitter Power: Higher transmitter power increases the range.
• Antenna Gain: Better focusing of energy through higher gain extends range.
• Target Radar Cross Section (RCS): Larger targets reflect more energy and are detectable at greater distances.
• Receiver Sensitivity: A lower minimum detectable power (P_min) allows detection of weaker signals, improving range.