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Doppler Radar Online Simulator


Advanced Doppler Simulator

Doppler Radar Simulator







Simulation Workflow & Mathematics

Simulation Workflow

  1. User Input: User enters transmit frequency (GHz), target velocity (km/h), and direction.
  2. Unit Conversion:
    • Frequency: GHz → Hz
    • Velocity: km/h → m/s
  3. Doppler Calculation: System computes Doppler shift using radar equation.
  4. Direction Handling:
    • Approaching target → Positive frequency shift
    • Receding target → Negative frequency shift
  5. Visualization:
    • Graph updates (frequency vs velocity)
    • Radar animation shows moving target
  6. Audio Simulation:
    • Doppler shift modifies sound frequency
    • User hears pitch change

Mathematical Model

Doppler Frequency Formula (Radar):

fd = (2 × v × f) / c
  • fd = Doppler frequency shift (Hz)
  • v = Target velocity (m/s)
  • f = Transmitted frequency (Hz)
  • c = Speed of light = 3 × 10⁸ m/s

The “2” appears because radar measures Doppler shift over a round trip (to target + back)

Unit Conversions

Velocity conversion:
v (m/s) = v (km/h) × (1000 / 3600)

Frequency conversion:
f (Hz) = f (GHz) × 10⁹

Direction Effect

If target is approaching:
fd = + (2vf / c)

If target is receding:
fd = − (2vf / c)

Graph Relationship

The Doppler shift is directly proportional to velocity:

fd ∝ v

This results in a straight-line graph between velocity and Doppler frequency.

Audio Mapping

To simulate sound:

faudio = fbase + fd
  • Base frequency ≈ 440 Hz
  • Doppler shift modifies pitch

Example Calculation

  • f = 5 GHz = 5 × 10⁹ Hz
  • v = 100 km/h = 27.78 m/s
fd = (2 × 27.78 × 5 × 10⁹) / (3 × 10⁸)

Result ≈ 927 Hz

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