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What is a Frequency Modulated Continuous Wave Radar or FMCW Radar?

A Frequency Modulated Continuous Wave Radar or FMCW Radar system is a special type of radar system that measures both distance and velocity of moving objects. This is achieved by continuously varying the frequency of the transmitted signal by a modulating signal at a known rate over a fixed time period. A variety of frequency modulation techniques, such as sawtooth modulation, triangular modulation, sine wave modulation, square wave modulation, and stepped modulation, can be used with sawtooth and triangular wave modulations being most widely used to change the frequency pattern of the emitted radio wave.

FMCW radar systems measure the frequency difference (Δf, due to run time) between the transmitted and received echo signal for calculating the distance, and it also measures the Doppler frequency (due to the Doppler effect) for calculating the speed of the object.

Fig. 1 Signal transmitted from the antenna in FMCW

How Does FMCW Radar System Work?

Fig.2 Block diagram of FMCW radar system

In an FMCW system, the transmitter antenna emits frequency modulated continuous radio waves, and the reflected signal from the target is received by the receiving antenna. The output of the receiving antenna is given to the mixer stage of the receiver via a pre-amplifier. In the mixer circuit, a part of the frequency-modulated transmitted signal is mixed with the received signal, producing a new signal, which can be used to determine the distance (R) and/or velocity of the moving object. The frequency of the new signal is the difference between the frequency of the transmitted and received (reflected) signal.

Now the signal from the mixer output passes through a lowpass filter, where clutter signals (unwanted echo signals from stationary objects such as buildings, hills) are filtered out. Finally, the signal passes via an amplifier, A/D converter, and is then fed into a computer for processing to calculate the distance and velocity of the object.

Advantages of FMCW Radars

Limitations of FMCW Radars

How is the Distance of the Moving Object Calculated?

Fig.3 Ranging with FMCW radar system (sawtooth modulation)

In the FMCW technique, the received signal frequency differs from the transmitted signal frequency by an amount Δf due to the run time delay between the transmitted and received signal. The mixer stage of the receiver circuit calculates this frequency difference Δf by mixing the received signal frequency with the transmitted frequency. This frequency difference is called “beat frequency”. This frequency difference Δf is proportional to distance (R) and can be used to calculate the distance as per the following formula.

This frequency is proportional to distance (R) and can be used to calculate the distance as per the following formula.

Distance (R) = (c x Δf) / Kf x 2 metre

Where R = Distance between the radar system to the object.

The slope of frequency change or frequency shift per unit time (i.e., sweep rate) Kf = BW/T.

BW = Frequency sweep bandwidth; T = Frequency sweep time.

C = Speed of light (speed of radio wave).

How is the Velocity of a Moving Object Calculated?

Fig.4 Ranging with FMCW radar system (sawtooth modulation)

The receiver system of the FMCW radar system not only measures the frequency difference Δf (due to run time) for calculating the distance, but it also measures the Doppler frequency (due to the Doppler effect) for calculating the speed of the object by using the following formula.

If the target is moving with some velocity Vo at an angle θ to the line joining the radar, then Vr = Vo cos(θ) is the radial velocity

Here, f_{t} - Frequency of transmitted signal in Hz

f_{r} - Frequency of received signal in Hz

f_{dop} - Doppler Frequency in Hz

C - Speed of light = 3 x 108 m/s

The Doppler Effect tells us that a moving object relative to the radar system alters the frequency of the return signal to the radar system. The expression for Doppler frequency f_{dop} is given below, which depends upon the transmitted signal frequency (ft), or wavelength λ, and radial velocity (V_{r}) of the object.

If the moving object is approaching the radar, then the frequency of the entire echo signal increases (i.e height up) by f_{r} + f_{dop}, and if the object is moving away from the radar, then the frequency of the entire echo signal reduces (height down) by f_{r} - f_{dop}. In fig.4, the frequency of echo signal height is shown in the green graph of figure.

Applications of FMCW Radars

Features of FMCW radars, such as high accuracy, repeatability, reliability, and non-contact measurement of distance in harsh conditions, make them suitable for use in applications such as unmanned aircraft as altimeters, blast furnaces of a steel mill, transportation applications (including automotive collision avoidance radars and marine radars), oil & LNG tankers & storage tanks to measure product volumes. These radars are also used in imaging, and detection, security sensors against intrusion, human vital-sign detection & measurement, and industrial applications for the verification of product dimensions in automated systems.

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