FMCW radar altimeter · interactive technical study
120 m above ground → 0.80 µs round-trip delay → 800 kHz beat frequency.
The transmitter continuously sweeps its frequency upward. The received ground echo is a delayed copy, so it has a lower instantaneous frequency during the same upward ramp. Mixing the echo with the current transmit signal and low-pass filtering produces a tone whose frequency gives the height.
Equations, assumptions and source
S = B/T · τ = 2h/c · fᵦ = Sτ · h = cfᵦ/(2S)
Illustrative sweep: B = 100 MHz, T = 100 µs, S = 1 MHz/µs. The graph shows only the first 8 µs of the linear ramp, with frequency measured above its starting frequency; the RF carrier is omitted. The beat trace shows a 5 µs window from the valid transmit/echo overlap, with arbitrary phase and normalized amplitude. The initial interval before the echo arrives is excluded. Calculations use c ≈ 3 × 10⁸ m/s.
The model assumes a level aircraft over flat ground, vertical incidence, negligible antenna separation and Doppler omitted. Height is above ground (AGL), not altitude above sea level. Real altimeters must handle Doppler, terrain spread, antenna footprint, noise and leakage. Flow markers illustrate continuous propagation and are not transmitted pulses. Aircraft geometry and propagation speed are schematic. Automatic height cycles smoothly between 60 and 180 m over 24 seconds. The equations update as a sequence of instantaneous stationary cases; climb/descent Doppler is intentionally omitted. Dragging the height slider holds a chosen height; turn Auto height back on to resume the cycle.
Underlying FMCW delay and beat-frequency relationship: Texas Instruments — FMCW system model, slides 4–8.