Introduction : The Doppler radar system is a cornerstone of modern radar technology, utilizing the principles of the Doppler effect to measure the frequency shifts of waves reflected off moving objects. This technology is pivotal in various applications, from weather forecasting to air traffic control, and is particularly renowned for its use in police radar to measure vehicle speed. By understanding the underlying principles, frequency equations, and practical applications of the Doppler radar system, we can appreciate its role in enhancing safety, security, and efficiency in numerous fields.

The doppler radars are very simple and utilize continuous wave for the transmission. Hence doppler radar is also referred as CW radar. Doppler radar systems typically operate at microwave frequencies in the range of a few gigahertz (GHz). This radar is based on the following functional principle. The frequency of the returned signal i.e. echo from the fixed target remains same as the transmitted wave while frequency of the returned signal from moving target will be shifted based on doppler frequency. By measuring difference between transmitted and reflected received frequency radar extracts relative velocity of the target.

Let us assume that target is moving towards the radar. In this case, distance between radar and target is decreasing and it depends upon the magnitude of the velocity of the moving target. Radar experiences apparent shift in frequency of the returned reflected wave referred as doppler shift. This doppler shift is approximately about order of 1KHz when transmitted wave is in GHz. Based on this change in frequency velocity of the target is determined and its moving direction can also be found. This has been described below with doppler radar equation.

## Doppler shift equation

fd = 2* f0 /c = dR/dt = 2*(dR/dt)/λ0 = 2*v*cosθ/λ0
Where,
fd is Doppler Frequency Shift
v is the relative velocity of the target making angle θ with respect to position vector (R).
λ0 = c/f0
f0 is the frequency of transmitted radar signal
"c" is the speed of light 3 x 108 m/sec

When target is moving in the direction of radar, angle θ will be between 0 to 90 degree and signal frequency f0 will increase by the amount fd. When target is moving away from radar, θ will be between 90 to 180 degree and f0 will decrease by fd. When velocity is perpendicular, there will be no change in f0 and fd is zero.

In doppler radar, range rate can be determined by measuring doppler frequency shift and polarity.

Because of continuous form of the CW emission, basic doppler radar is not useful for range measurement. This concept is used in the police radar described below for tracking the velocity of the fast moving vehicles. It is used for rate of climb meter and also to measure velocity of the aircraft.

## What is Radar doppler effect ?

As described, doppler effect in radar is a phenomenon where there is a change in frequency of radar signal when it is reflected off a moving target. This effect is named after Austrian physicist Christian Doppler. The change in frequency is proportional to velocity of the target and wavelength of the radar signal.

Doppler effect has several functions or applications or uses which include speed measurement, weather radar, air traffic control and military applications. The doppler radar works based on the principle of doppler effect.

Doppler effect in radar is dependent on the motion of the target relative to the radar system. There are three possible scenarios.
• If the target is approaching the radar, the reflected signal frequency will be higher, indicating positive doppler shift.
• If the target is moving away from the radar, the reflected signal frequency will be lower, indicating negative doppler shift.
• If the target is stationary relative to the radar, there is no frequency change (i.e. zero doppler shift).

The frequency shift is proportional to relative velocity between radar system and the target. By measuring this shift, the radar can determine speed and direction of the target's motion.

## Police Radar based on doppler principle

The figure-2 depicts the modules used in police radar. It is used to detect and measure velocity of moving vehicles. As shown microwave signal generator is used as transmitter. Here gunn diode based oscillator is used to generate the microwave signal. Microwave signal is transmitted through horn antenna via RF circulator. The portion of transmitted signal leakage is used to compare with the reflected signal. RF Mixer produces sum and difference of these two input signal frequencies. The sum component is ignored and difference component is used which is due to doppler shift. This type of radar is referred as police radar. The doppler frequency after processing is fed to the radar scope or display unit. This display unit provides velocity of the moving vehicle.

Following formula can be used in police radar to calculate velocity of the vehicle.
Velocity (in miles/hour) = 0.26 * (Doppler Shift in Hz)/(Microwave Frequency in GHz)

### Summary

Overall, the Doppler radar system, grounded in the Doppler effect principle, serves as an essential tool in a wide range of applications, from meteorology to law enforcement. The ability to measure frequency shifts accurately enables precise monitoring and control in various environments. The application of Doppler radar in police radar systems exemplifies its practical utility, providing an effective means of maintaining road safety. As technology continues to evolve, the principles of Doppler radar will undoubtedly remain integral to advancements in radar systems and their applications.