Radar Target Range Calculation Explained

A pulsed radar system determines the distance to a target by transmitting short electromagnetic pulses and measuring the time it takes for the echo of these pulses to return. This fundamental principle is known as the time-of-flight method.

Understanding Pulsed Radar Operation

A pulsed radar sends out brief bursts of electromagnetic energy. When these pulses hit an object (the target), a small portion of the energy is reflected back towards the radar receiver. By precisely measuring the time elapsed between sending the pulse and receiving its echo, the radar can calculate the distance to the target.

• The radar transmits a pulse.
• The pulse travels through space at the speed of light.
• It strikes a target and reflects back as an echo.
• The radar receiver detects the echo.
• The time taken for this round trip is measured.

Key Principle: Time of Flight

The speed of electromagnetic waves in free space is constant and equal to the speed of light, denoted by \(c\). Since the radar signal travels from the radar to the target and then back to the radar, the total distance covered by the pulse is twice the range (distance) to the target.

Radar Range Formula

The relationship between the range to the target, the speed of light, and the total time taken for the pulse to travel to the target and return is given by the following formula:

\[ \text{Range (R)} = \frac{\text{Speed of Light (c)} \times \text{Total Time Delay (t)}}{2} \]

Where:

• \(R\) is the approximate range of the target in meters (m).
• \(c\) is the speed of electromagnetic waves (speed of light) in free space, approximately \(3 \times 10^8\) meters per second (m/s).
• \(t\) is the total time elapsed from the transmission of the pulse until the reception of the echo, in seconds (s). The division by 2 accounts for the round trip travel of the signal.

Applying the Radar Range Formula

From the given question, we have the following parameters for the pulsed radar system:

• Speed of Light (\(c\)) = \(3 \times 10^8\) m/s (standard value).
• Time taken to receive the echo (\(t\)) = 10 μsec.

First, we need to convert the echo reception time from microseconds (μsec) to seconds (s):

\[ 1 \, \mu\text{sec} = 1 \times 10^{-6} \, \text{s} \]

So, \(t = 10 \, \mu\text{sec} = 10 \times 10^{-6} \, \text{s} = 1 \times 10^{-5} \, \text{s}\)

The operating frequency (3 GHz) and pulse width (2 μsec) are characteristics of the radar system but are not directly required for calculating the target range given the echo reception time.

Calculating Target Range Step-by-Step

Now, we substitute the values into the radar range formula:

\[ R = \frac{c \times t}{2} \]

\[ R = \frac{(3 \times 10^8 \, \text{m/s}) \times (1 \times 10^{-5} \, \text{s})}{2} \]

Perform the multiplication in the numerator:

\[ R = \frac{3 \times 10^{(8-5)} \, \text{m}}{2} \]

\[ R = \frac{3 \times 10^3 \, \text{m}}{2} \]

\[ R = \frac{3000 \, \text{m}}{2} \]

Finally, calculate the approximate range of the target:

\[ R = 1500 \, \text{m} \]

Therefore, the approximate range of the target from the pulsed radar is 1500 meters.