1. Doppler effect, Doppler radar

2. Doppler effect

4. Stationary sound source Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c (assuming speed of sound, c = 330 m/s), which is the speed of sound in the medium. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f 0

5. Moving source The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed υ s = 0.7 c (Mach 0.7). The wave-fronts are produced with the same frequency as before. However, since the source is moving, the centre of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency and an observer behind the source will hear a lower frequency

6. Moving source Now the source is moving at the speed of sound in the medium (υ s = c, or Mach 1). assuming the speed of sound in air at sea level is about 330 m/s. The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives where. An observer behind of the source

7. Moving source The sound source has now broken through the sound speed barrier, and is traveling at 1.4 times the speed of sound, c (Mach 1.4). Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer actually hears the sound it creates. As a result, an observer in front of the source will detect and an observer behind the source

8. The Doppler Radar When radio-frequency energy transmitted from a fixed point continuously strikes an object that is either moving toward or away from the source of the energy, the frequency of the reflected energy is changed. This shift in frequency is known as the DOPPLER EFFECT. The difference in frequency between the transmitted and reflected energy indicates both the presence and the speed of a moving target. In radar technology the Doppler Effect is using for two tasks: Speed measuring and MTI (Moving Target Indication).

9. Frequency variation

10. The Doppler effect The Doppler- Effect is the apparent change in frequency or pitch when a sound source moves either toward or away from the listener, or when the listener moves either toward or away from the sound source. This principle, discovered by the German physicist Christian Doppler, applies to all wave motion. The apparent change in frequency between the source of a wave and the receiver of the wave is because of relative motion between the source and the receiver.

11. The Doppler frequency The Doppler ferquency is given by: f D = (2*V)/λ where f D = Doppler Frequency [Hz] λ = wavelength [m] v = speed of the wave-source [m/s] This equation is valid, if the speed if the source of a wave is like the radial speed. But the airplane usually flies in another direction than the direction towards to the radar. Only the radial speed is then also measured. However, this is different from the aim speed so that the following equation is valid: f D = (2*V*cos α)/λ v = speed of the aircraft [m/s]. α = angle between the direction of the transmitted/reflected signal and the direction of flight of the target λ. When α=0 the doppler frequency is maximum. The doppler is zero when the trajectory is perpendicular to the radar line of sight (0 = 90°).

12. The Doppler frequency f D = (2*V)/λ = (2*v r *f 0 )/c

13. Derivation of the Doppler-frequency formula The phase shifting φ of an electromagnetic wave from the radar antenna to the aim and back results from the ratio of the covered distance and the wavelength of the transmitted energy multiplied with the scale of the full circle (2·π): φ = (2r*2π)/λ φ = phase-difference between the transmitted and the received signal 2r = the distance: the way and the way back 2π = 360°: the period of an oscillation λ = wavelength of the transmitted energy If the aim has the radial speed then: v r = d(r) /dt then the value of the phase changes to d(φ)/dt = (- 4π · v r )/ λ

14. Derivation of the Doppler-frequency formula This is equivalent to the Doppler- frequency f D according to: f D = d(φ) / (2π dt) = (1 /2π)* (- 4π·v r / λ) Then: | f D | = (2 · v r )/ λ = (2 · v r · f tx )/ c 0 where: f tx = is the transmitters frequency c 0 = is the speed of the light v r = is the radial speed of the aim This means that In practice the Doppler- frequency occurs twice at a radar: Once on the way from the radar to the aim, and then for the reflected (and already afflicted by a Doppler-shift) energy on the way back.

15. Doppler use in radar system To distinguish a moving target of a fixed object with help of the Doppler frequency, at least two periods of the deflection must be compared with each other. Since the Doppler- frequency (few Hertz) is small relatively to the transmitted frequency (much Mega-Hertz), therefore a phase comparison is more easily to carry out than a direct frequency comparison technically. Well, a fixed target suppression happens by the phase comparison of the echoes received by several pulse periods (pulse- pair processing). If the phase relationship is always equal, then there isn't any phase difference and the target will be suppressed. If the target has moved, the phase difference is unequally zero and the target will be shown on the screen. To get the necessary frequency-reference for the phase-detector, a high correct coherent oscillator (called: “Coho”) is synchronized with the down converted on the IF- frequency transmitting pulse.

16. EEE381B Radar range equation calculation The US Navy AN/SPS-48 Air Search Radar is a medium-range, three-dimensional (height, range, and bearing) air search radar. Published technical specifications include: – Operating frequency 2900-3100 MHz – Transmitter peak power 60-2200 kW – PRF 161-1366 Hz, and pulse widths of 9 / 3 μsec – Phased array antenna with a gain of 38.5 dB 1) For its published maximum range of 250 miles for a nominal target such as the F-18, what is the receiver chain sensitivity in bBm? 2) a plane is flying making 45° with the line of sight of this radar calculate the corresponding Doppler frequency captured if it has a velocity of 800 Km/h.

17. Doppler radar A Doppler radar is controlling vehicles speed at a of frequency F = 24.125 GHz (K band Mesta 208) emits wave trains with a PRF (Pulse Repetition Frequency) F 0 = 30kHz. The Doppler angle α between the axis of the radar beam and the axis of movement of vehicles measured is 25 °. a) What is the wavelength of the signal? b) What is the maximum speed |V Max |measured by radar? c) What is the Doppler frequency ∆F corresponding to a measured vehicle speed of 130km / h? d) The calculation speed is achieved using an FFT algorithm on a number N = 256 points. How accurate dv on measuring the speed?

18. Doppler radar An air Doppler radar control approach emits a EMW with a frequency F = 3GHz. The pulse duration τ emitted is equal to 1 μs and the repetition period T 0 is 100 μs. a) What is the wavelength of the signal? What is the PRF? b) What is the speed |V Max | measurable by this radar? c) What is the maximum range R max of this radar? d) What is the blind zone of the radar? e) Two planes during landing, follow with a spacing of 120m. What does the air traffic controller on the radar screen? Why?

19. Doppler radar A vehicle is traveling in urban area (speed limited to 50km / h) is controlled by a Doppler radar of the gendarmerie type Mesta 208, K-band (F = 24.125 GHz). In passing vehicle wave frequency response is F '= F + 2500Hz. The viewing angle is equal to α = 25 °.This car is it offending?

20. Doppler use in radar system

21. The echo signal of a moving target at the output of the phase-detector changes it's value and also the polarity in every pulse period. A fixed clutter signal will keep it's value and polarity in every pulse period. A pulse period is stored in a memory. This memory stage has got a memory-cell for each range-cell and delays the whole scan for one pulse period (PRT). Both periods, the actually period and its predator, are led to an extractor. The output of this stage is the difference of both input- signals. Clutter with a constant amplitude will be eleminated. Moving targets pass this stage. On this way the moving target produce an output signal and the fixed clutter don't do this.

22. Doppler use in radar system The purpose of the Doppler amplifier is to eliminate echoes from stationary targets and to amplify the Doppler echo signal to a level where it can operate an indicating device. It might have a frequency-response characteristic similar to that shown in figure below. The low-frequency cutoff must be high enough to reject the d-c component caused by stationary targets, but yet it must be low enough to pass the smallest Doppler frequency expected. Sometimes both conditions cannot be met simultaneously and a compromise is necessary. The upper cutoff frequency is selected to pass the highest Doppler frequency expected.