The Doppler Principle

Chapter 2.1
• Doppler Examples
• Stationary Radar Doppler
  Figure 2.1-1 -- Radar Signal
  Figure 2.1-2 -- Stationary Radar Spectrum
• Moving Radar Doppler
  Figure 2.1-3 -- Moving Mode Spectrum Opposite Direction Target
  Figure 2.1-4 -- Moving Mode Spectrum Same-lane Target Front Antenna
  Figure 2.1-5 -- Moving Mode Spectrum Same-lane Target Rear Antenna

Doppler Examples
Everyday life has multiple examples of the Doppler phenomenon with sound; the whistle from a moving train is a good example. As the train approaches a stationary listener, the pitch (frequency) of the whistle sounds higher than when the train passes by, at which time the pitch sounds the same as if the train were stationary. As the train recedes from the listener, the pitch decreases. Car horns exhibit the same phenomenon, as does all sound. Note that in the above example if a car horn is stationary and a listener is on the train, the Doppler principle still applies. As the listener on the train approaches the stationary horn, the pitch of the horn sounds higher; as the train recedes from the stationary horn the pitch sounds lower (to anyone on the train).

Electromagnetic waves radiated by traffic radar, as well as sound waves, obey the Doppler principal, although electromagnetic waves travel at the speed of light and audio waves travel at the speed of sound. The Doppler effect is a frequency shift that results from relative motion between a frequency source and a listener. If both source and listener are not moving with respect to each other (although both may be moving at the same speed in the same direction), no Doppler shift will take place. If the source and listener are moving closer to each other, the listener will perceive a higher frequency -- the faster the source or receiver is approaching the higher the Doppler shift. If the source and listener are getting farther apart, the listener will perceive a lower frequency -- the faster the source or receiver is moving away the lower the frequency. The Doppler shift is directly proportional to speed between source and listener, frequency of the source, and the speed the wave travels (speed of light for electromagnetic waves).

Stationary Radar Doppler
Police traffic radar emits an unmodulated continuous wave (CW) and measures' reflections (echoes). Reflections are frequency shifted (Doppler shift) if the target is moving; the faster the target is traveling, the more the frequency shifts. A target traveling toward the radar shifts the frequency higher while a target traveling away from the radar shifts the frequency lower (compared to transmit frequency). The radar, by design, simultaneously transmits a continuous signal while receiving continuous signal echoes.

Target echo frequency (f_t) is a function of radar transmit frequency (f_o) and radar Doppler shift (f_d). A Doppler shift occurs only if the target is moving. f_d is positive (+) for approaching targets and negative (-) for receding targets.

Radar Doppler shift frequency is a function of radar transmit frequency (f_o), speed of wave (c = speed of light), and target velocity (v_t). Note, v_t is positive (+) for approaching targets and negative (-) for receding targets.

Approaching (on-coming) targets have a positive Doppler shift (target echo higher frequency than transmit); receding (going away) targets have a negative Doppler shift (target echo lower frequency than transmit). If the velocity term v_t is positive (+) target is approaching the radar; if the velocity term v_t is negative (-) target is receding (going away from) the radar.

Ground echoes are usually the strongest signal return, but since the ground is not moving these echoes are not Doppler shifted (ground returns are at frequency f_o) and may be drowned out by transmitter leakage. With moving-mode radar the ground echo is frequency shifted by the speed of the patrol car.

Moving-mode Radar Doppler
Moving-mode radar is slightly more complicated. The target echo frequency is shifted by the relative speed between the target and radar. Target relative speed (to radar) is the sum of target and patrol car speed for opposite direction targets. For same-lane (direction) targets relative target speed is the difference between target and patrol car speed.

Ground echoes are Doppler shifted by the patrol car velocity. The radar tracks the ground echo to determine patrol car (radar) velocity. The radar uses patrol car velocity and relative (to radar) target speed (target echo) to calculate actual target speed.

Note that on-coming (opposite direction) targets have a negative speed (compared to same-lane targets). This type of radar can (if built-in) distinguish between same-lane targets and opposite direction targets.

Figure 2.1-5 -- Moving Mode Spectrum
Same Direction (lane) Target
Rear Antenna

Target Relative Speed to Radar is V_relative = V_t - V_p

V_t = V_relative + V_p

Note that receding (opposite direction) targets have a negative speed (compared to same-lane targets). This type of radar can (if built-in) distingush between same-lane targets and opposite direction targets.