Calculating Radar Distance from Signal Travel Time
This question asks us to determine the distance to a target based on the time it takes for a radar signal to travel to the target and return.
Understanding Radar Principles
Radar systems work by sending out electromagnetic waves (like radio waves or microwaves) and detecting the waves that are reflected back after hitting an object. The time it takes for the signal to complete this round trip (to the target and back) can be used to calculate the distance to the target.
Key principles involved:
- Speed of Signal: Radar signals travel at the speed of light ($c$).
- Travel Time: The time measured is for the signal to go to the target and return (round trip).
- Distance Formula: The fundamental relationship between distance, speed, and time is: $ \text{Distance} = \text{Speed} \times \text{Time} $
Step-by-Step Calculation
- Identify Given Values:
- Round-trip travel time ($t$) = $1 \text{ µs}$
- Speed of light ($c$) ≈ $3 \times 10^8 \text{ m/s}$
- Convert Time to Standard Units: The time is given in microseconds (µs). We need to convert this to seconds (s) for consistency with the speed of light unit (m/s). $ 1 \text{ µs} = 1 \times 10^{-6} \text{ s} $ So, $t = 1 \times 10^{-6} \text{ s}$.
- Calculate Total Round-Trip Distance: Using the distance formula, we can find the total distance the radar signal traveled. $ d_{\text{round trip}} = c \times t $ $ d_{\text{round trip}} = (3 \times 10^8 \text{ m/s}) \times (1 \times 10^{-6} \text{ s}) $ $ d_{\text{round trip}} = 3 \times 10^{(8 - 6)} \text{ m} $ $ d_{\text{round trip}} = 3 \times 10^2 \text{ m} $ $ d_{\text{round trip}} = 300 \text{ m} $
- Calculate One-Way Distance to Target: The calculated distance of 300 meters represents the path to the target and back. To find the actual distance from the radar to the target, we need to divide the round-trip distance by 2. $ d_{\text{target}} = \frac{d_{\text{round trip}}}{2} $ $ d_{\text{target}} = \frac{300 \text{ m}}{2} $ $ d_{\text{target}} = 150 \text{ m} $
Conclusion
Therefore, a round-trip travel time of $1 \text{ µs}$ for a radar signal corresponds to a distance of 150 meters to the target.
Important Questions from Antennas
- The configuration of a PIN diode operating at microwave frequencies is given by ____________.
If the effective area of an antenna becomes \(\frac{2A}{3}\) from its initial value of 'A', while keeping its operating frequency same. Then, the antenna gain becomes \(\left(\frac{2x+4}{15}\right)\) times of its initial value. The value of x will be:
Match List I with List II
LIST I (Type of Aperture Antenna) LIST II (Beam widtd half power points) A. Uniformly illuminated linear Array I. \(\frac{58}{D_\lambda}\) B. Uniformly illuminated circular aperture II. \(\frac{56}{a_{E\lambda}}\) C. Optimum E-plane rectangular horn III. \(\frac{67}{a_{E\lambda}}\) D. Optimum H-plane rectangular horn IV. \(\frac{51}{L_\lambda}\) Choose the correct answer from the options given below:
Match the following lists in terms of radiation resistances of various antennas :
List – I List – II a. Short vertical monopole i. \(31200\left(\dfrac{\text{Area of Loop}}{\lambda^{2}}\right)^{2}\) b. Small loop antenna ii. \(80\pi^{2}\left(\dfrac{L}{\lambda}\right)^{2}\) c. Dipole antenna iii. 73 ohms d. Radiation resistance of half wave dipole iv. \(400\left(\dfrac{\text{Physical height}}{\lambda}\right)^{2}\) Choose the correct answer from the codes given below:
Following statements are given :
(a) Beam width between first nulls for a broadside long array is given by \(\dfrac{2\lambda}{nd}\).
(b) Beam width between first nulls for an end fire long array is given by \(2\sqrt{\dfrac{2\lambda}{nd}}\).
(c) Beam width between first nulls for a broadside long array is given by \(\dfrac{\lambda}{nd}\).
(d) Beam width between first nulls for an end fire long array is given by \(\dfrac{\lambda}{nd}\).
Which of the above statements are correct ?
