Radar Range Resolution Formula: Target Separation Explained

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

Radar PRF

PRF stands for Pulse Repetition Frequency. The determination of PRF depends on the maximum range at which a target is expected to be detected. Echo signals received after the PRF period are referred to as “multiple time around echoes,” as shown by signals B and C in the figure below. These echoes can cause erroneous calculation of the radar range for the target, which is referred to as ambiguous range.

Radar Range

Radar Range

As shown in the figure, target A is within the maximum unambiguous radar range ($R_{unamb}$). Targets B and C fall outside this range. The range measured for target A is correct, while the range measured for targets B and C is ambiguous. The unambiguous radar range is expressed as:

$R_{unamb} = \frac{c}{2 \cdot PRF}$

Where:

• $c$ is the velocity of light ($3 \times 10^8$ m/s)
• $PRF$ is the pulse repetition frequency in Hz

Operating the radar with varying PRF will help distinguish multiple time-around echoes from unambiguous echoes. This way, the echo from an unambiguous target (here, A) will appear at the same place, while echoes from multiple time around echoes spread across the finite range (signals B and C).

Radar Range Resolution

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

$R_{res} = \frac{c \cdot \tau}{2}$ … equation-1

Where:

• $\tau$ is the transmitted pulse width
• $c$ is the velocity of light in free space

A narrower beamwidth is very useful to distinguish two adjacent targets.

Formula #2

The radar range resolution formula is typically expressed as follows:

$R_{res} = \frac{c}{2 \cdot B}$ … equation-2

Where:

• $R_{res}$ = Range resolution
• $c$ = speed of light (approx. $3 \times 10^8$ m/s)
• $B$ = Bandwidth of radar signal

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.