Question

The maximum range, \( d_{\text{max}} \), of radar is:

• A. Proportional to the cube root of the peak transmitted power
• B. Proportional to the fourth root of the peak transmitted power
• C. Proportional to the square root of the peak transmitted power
• D. Not related to the peak transmitted power at all

Hint:

Radar range is related to the power of transmission, and the maximum range increases with the fourth root of the transmitted power.

Answer 1

The Correct Option is B

Step 1: Understanding the radar range equation
The maximum range of a radar system depends on several factors such as transmitted power, antenna gain, wavelength, radar cross-section, and minimum detectable signal. These quantities are related through the radar range equation:

\( d_{\text{max}} = \left( \frac{P_t \cdot G^2 \cdot \lambda^2 \cdot \sigma} {(4\pi)^3 \cdot S_{\text{min}}} \right)^{1/4} \)

Step 2: Identifying dependence on transmitted power
From the above expression, all quantities except transmitted power \(P_t\) are constants for a given radar system and target conditions. Therefore, we can write:

\( d_{\text{max}} \propto (P_t)^{1/4} \)

Step 3: Physical meaning of the relation
This relationship shows that the maximum detectable range increases with transmitted power, but only as the fourth root. This implies that even a large increase in transmitted power leads to a relatively small increase in range.

Step 4: Final conclusion
Thus, the maximum range of radar is proportional to the fourth root of the peak transmitted power.