Doppler effect

A Doppler radar is a specialized radar that makes use of the Doppler effect to produce velocity data about objects at a distance. It does this by beaming a microwave signal towards a desired target and listening for its reflection, then analyzing how the frequency of the returned signal has been altered by the object's motion. This variation gives direct and highly accurate measurements of the radial component of a target's velocity relative to the radar. Doppler radars are used in aviation, sounding satellites, meteorology, police speed guns,[1], radiology, and bistatic radar (surface to air missile).

Partly because of its extremely common use by television meteorologists in on-air weather reporting, the specific term "Doppler Radar" has erroneously become popularly synonymous with the type of radar used in meteorology. Most modern weather radars use the pulse-doppler technique to examine the motion of precipitation, but it is only a part of the processing of their data. So, while these radars use a highly specialized form of doppler radar, the term is much broader in its meaning and its applications.

## Concept

### Doppler effect

The emitted signal toward the car is reflected back with a variation of frequency that depend on the speed away/toward the radar (160 km/h). This is only a component of the real speed (170 km/h).

The Doppler effect (or Doppler shift), named after Austrian physicist Christian Doppler who proposed it in 1842, is the change in frequency of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is increased (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is decreased during the recession. This variation of frequency also depends on the direction the wave source is moving with respect to the observer; it is maximum when the source is moving directly toward or away from the observer, and diminishes with increasing angle between the direction of motion and the direction of the waves, until when the source is moving at right angles to the observer, there is no shift.

An analogy would be pitcher throwing one ball every second in a person's direction (a frequency of 1 ball per second). Assuming that the balls travel at a constant velocity, if the pitcher is stationary, the man will catch one ball every second. However, if the pitcher is jogging towards the man, he will catch balls more frequently because the balls will be less spaced out (the frequency increases). The inverse is true if the pitcher is moving away from the man; he will catch balls less frequently because of the pitcher's backward motion (the frequency decreases). If the pitcher were to move at an angle but with the same speed, the variation of the frequency at which the receiver would catch the ball would be less as the distance between the two would change more slowly.

Note that, from the point of view of the pitcher, the frequency remains constant (whether he's throwing balls or transmitting microwaves). Since with electromagnetic radiation like microwaves frequency is inversely proportional to wavelength, the wavelength of the waves is also affected. Thus, the relative difference in velocity between a source and an observer is what gives rise to the doppler effect.[2]

### Frequency variation

The exact formula for radar doppler shift is the same as that for reflection of light by a moving mirror.[3] There is no need to invoke Einsteins' theory of special relativity, because all observations are made in the same frame of reference.[4] The exact result derived with c as the speed of light and v as the target velocity gives the shifted frequency (Fr) as a function of the original frequency (Ft) :

$F_r = F_t (\frac{1+v/c}{1-v/c})$

The exact "beat frequency", aka Doppler Frequency (Fd), is thus[5]:

$F_d = F_r-F_t = 2v \frac {F_t}{(c-v)}$

Since for most all practical applications of radar, $v \ll c$ , so $\left(c-v\right) \rightarrow c$. We can then write:

$F_d \approx 2v \frac {F_t}{c}$

### Technology

U.S. Army soldier using a radar gun, an application of Doppler radar, to catch speeding violators.

There are four ways of producing the Doppler effect. Radars may be Coherent pulsed (CP), pulse-doppler radar, Continuous wave (CW), or Frequency modulated (FM). CW doppler radar only provides a velocity output as the received signal from the target is compared in frequency with the original signal. Early doppler radars were CW, but these quickly led to the development of frequency modulated continuous wave(FM-CW) radar, which sweeps the transmitter frequency to encode and determine range.

The CW and FM-CW radars can normally only process one target, which limits their use. With the advent of digital techniques, Pulse-Doppler radars (PD) were introduced, and doppler processors for coherent pulse radars were developed at the same time. The advantage of combining doppler processing with pulse radars is to provide accurate velocity information. This velocity is called Range-Rate. It describes the rate that a target moves towards or away from the radar. A target with no range-rate reflects a frequency near the transmitter frequency, and cannot be detected. The classic zero doppler target is one which is on a heading that is tangential to the radar antenna beam. Basically, any target that is heading 90 degrees in relation to the antenna beam cannot be detected by its velocity (only by its conventional reflectivity).

## History

FM radar was highly developed during World War II for the use by US Navy aircraft. Most used the UHF spectrum, and had a transmit yagi antenna on the port wing, and a receiver yagi antenna on the starboard wing. This allowed bombers to fly an optimum speed when approaching ship targets. Later when magnetrons and microwaves became available, the use of FM radar fell into disuse.

When the digital Fast Fourier transform became available, it was immediately connected to Coherent Pulsed radars, where velocity information was extracted. This quickly proved useful in both weather and air traffic control radars. The velocity information provided another input to the software tracker, and improved computer tracking. Because of the low pulse repetition frequency (PRF) of most coherent pulsed radars, which maximizes the coverage in range, the amount of doppler processing is limited. The doppler processor can only process velocities up to ±1/2 the PRF of the radar. This was not a problem for weather radars.

Specialized radars quickly were mechanized when digital techniques became affordable. Pulse-Doppler radars combine all the benefits of long range, and high velocity capability. Pulse-Doppler radars use a medium to high PRF (on the order of 3 to 30 kHz). This medium PRF allows for the detection of either high speed targets, or high resolution velocity measurements. Normally it is one or the other, that is, a radar designed for detecting targets from zero to Mach 2, does not have a high resolution in speed, while a radar designed for high resolution velocity measurements does not have a wide range of speeds. Weather radars are high resolution velocity radars, while air defense radars have a large range of velocity detection, but the accuracy in velocity is in the 10's of knots.

Antenna designs for the CW and FM-CW started out as separate transmit and receive antennas before the advent of affordable microwave designs. In the late 1960s traffic radars began being produced which used a single antenna. This was made possible by the use of circular polarization, and a multi-port waveguide section operating at X band. By the late 1970s this changed to linear polarization and the use of ferrite circulators at both X and K bands. PD radars operate at too high a PRF to use a Transmit-Receive gas filled switch, and most use solid-state devices to protect the receiver Low Noise Amplifier when the transmitter is fired.

## References

1. ^ CopRadar.com -- subsidiary of Sawicki Enterprises (1999-2000). "Police Traffic Radars". CopRadar.com -- subsidiary of Sawicki Enterprises. Retrieved July 17, 2009.
2. ^ CopRadar.com -- subsidiary of Sawicki Enterprises (1999-2000). "Doppler Principles (Police Traffic Radar Handbook)". CopRadar.com -- subsidiary of Sawicki Enterprises. Retrieved July 17, 2009.
3. ^ Ditchburn, R.W. "Light", 1961, 1991. Dover publications Inc., pp331-333
4. ^ Jaffe, Bernard M., "Forward Reflection of Light by a Moving Mirror," American Journal of Physics, Vol. 41, April 1973, p577-578
5. ^ Ridenour, "Radar System Engineering", MIT Radiation Lab series, vol 1, year 1947, page 629

• Luck, David G. C. (1949). Frequency Modulated Radar. New York: McGraw-Hill.

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