Question

Consider an X-band (10GHz ) radar on an aircraft traveling at 100 m/s. Assume the 3-dB azimuth beamwidth of the antenna is 3∘. Compute the Doppler shift F0​ of a scatterer on the antenna boresight and the Doppler bandwidth {30 across the beam for squint angles of 0∘,30∘,60∘, and 90∘.

Please answer all parts of question completely, showing formulas and worked out equations. Please show worked out equation for doppler bandwidth!

Answer 1

The Doppler shift and bandwidth for an aircraft's radar at 10 GHz can be calculated using the velocity of the aircraft, the radar frequency, and the speed of light, along with the beamwidth and squint angles.

Step-by-step explanation:

To compute the Doppler shift (F0) and the Doppler bandwidth across the azimuth beamwidth of an aircraft antenna operating at an X-band frequency of 10 GHz, we must apply the Doppler effect formula for radar systems. The Doppler shift for a radar system is given by F0 = 2 * V * Fc / c, where V is the velocity of the aircraft, Fc is the carrier frequency of the radar, and c is the speed of light.

For a squint angle (θ) of 0°, the Doppler shift can be calculated using the formula above:

F0 = 2 * (100 m/s) * (10 GHz) / (3*108 m/s)

The Doppler bandwidth (Δf) across the beam for different squint angles can be computed using the beamwidth and the relation Δf = F0 * sin(θ).

For squint angles of 0°, 30°, 60°, and 90°, we calculate:

• Δf0° = F0 * sin(0°)
• Δf30° = F0 * sin(30°)
• Δf60° = F0 * sin(60°)
• Δf90° = F0 * sin(90°)

This will give us the Doppler bandwidth at different angles across the antenna beamwidth.