Radar Range Resolution Formula : Calculating Target Separation

This page explains Radar crucial parameters such as radar range resolution, PRF and radar range with their formula, calculations and basic concepts.

Radar PRF

PRF is pulse repetition frequency. PRF determination depends on maximum range at which target is expected to be detected. Echo signals received after PRF period is referred as multiple time around echoes. Figure depicts B and C signals in this category. These echoes cause erroneous calculation of radar range for the target referred as ambiguous range.

Radar Range

As shown in the figure, target A is within the maximum unambiguous radar range R_unamb. Target B and C falls outside this. Range measured for target A is only correct while range measured for target B and C is ambiguous.

Unambiguous radar range is expressed as below:
R_unamb = c/(2*PRF)
Where, c is the velocity of light 3 x 10⁸ m/s
PRF is the pulse repetition frequency in Hz

Operating radar with varying PRF will help distinguish multiple timearound echoes from unambiguous echoes. This way, echo from unambiguous target (Here A) will appear at the same place while echoes from multiple time around echoes spread across the finite range as shown in the figure (Signal B and C).

Radar range resolution

Radar range resolution is the capability of the radar to distinguish or resolve nearby adjacent targets in the range. Search radars usually will have poor resolution and will distinguish two targets at about 100 meters apart.

The radar range resolution mainly depends upon following parameters/factors:
•  transmitted pulse width
•  beamwidth
•  type of target
•  size of target
•  radar receiver efficiency
•  resolution of the radar display unit

Formula #1

Range resolution as a distance can be calculated as follows:
R_res = c * τ /2 ... equation-1
Where, τ is the transmitted pulse width and c is the velocity of light in the free space.
• Narrower beamwidth is very useful to distinguish two adjacent targets.

Formula #2

The radar range resolution formula is typically expressed as follows.
➨R_res = c/(2*B) ... equation-2
Where,
R_res = Range resolution
c = speed of light (approx. 3 x 10^8 m/s)
B = Bandwidth of radar signal

The equation-2 shows that higher bandwidth results in better range resolution, making it possible to distinguish targets that are closer together. Factors such as pulse width and signal processing techniques also influence range resolution.

Conclusion

Understanding the radar range resolution formula helps in optimizing radar performance for various applications, from air traffic control to military surveillance, by enabling accurate target identification.

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