Question

Which factor determines the range resolution of a radar?

• A. Size of the antenna
• B. Power radiated from the antenna
• C. Aperture of the antenna
• D. Bandwidth of the transmitted pulse

Hint:

Range Resolution \(\Delta R = c\tau/2\), where \(\tau\) is the pulse width.
Pulse bandwidth \(B \approx 1/\tau\).
Therefore, \(\Delta R \approx c/(2B)\).
Better range resolution (smaller \(\Delta R\)) is achieved with shorter pulses or, equivalently, wider bandwidths.
Angular resolution depends on antenna beamwidth, which is related to antenna size and wavelength.

Answer 1

The Correct Option is D

Range resolution (\(\Delta R\)) of a radar is its ability to distinguish between two closely spaced targets along the same line of sight (i.e., at slightly different ranges). For a simple pulse radar, the range resolution is determined by the pulse width (\(\tau\)) of the transmitted pulse: \[ \Delta R = \frac{c\tau}{2} \] where \(c\) is the speed of light. A shorter pulse width leads to better (smaller) range resolution. The bandwidth (\(B\)) of a pulse is inversely proportional to its pulse width. For a rectangular pulse of width \(\tau\), the approximate bandwidth is \(B \approx 1/\tau\). Substituting \(\tau \approx 1/B\) into the range resolution formula: \[ \Delta R \approx \frac{c(1/B)}{2} = \frac{c}{2B} \] This shows that range resolution is inversely proportional to the bandwidth of the transmitted pulse. A wider bandwidth allows for better range resolution. Let's consider the options: (a) Size of the antenna: Antenna size primarily affects angular resolution (beamwidth) and gain, not directly range resolution. (b) Power radiated from the antenna: Radiated power affects the maximum detection range and signal-to-noise ratio, but not directly the range resolution. (c) Aperture of the antenna: Similar to antenna size, relates to gain and angular resolution. (d) Bandwidth of the transmitted pulse: As shown above, range resolution is directly determined by (inversely proportional to) the bandwidth of the transmitted pulse. Wider bandwidth \(\implies\) shorter effective pulse \(\implies\) better range resolution. \[ \boxed{\text{Bandwidth of the transmitted pulse}} \]