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The Physics Behind Target Detection (4/5)

Electronic Product Design


5 mins read

Radar Image

As the topic of this article progresses deeper into the implementation realm, often there is a need to check back with the theoretical principles. In the far most beginning of this blog post series, an introduction to RADAR techniques was disclosed. If there is any doubt of what is meant by that, it is recommended to visit the introductory blog post.


Doppler RADAR technique implementation

The BGT24MTR11 (BGT24M) can be configured to work in both Doppler mode and FMCW mode. In an essence, these modes are clearly understood in theory but in the practical sense, some additional explanation is necessary.

The system block diagram presented in a previous post could be of some help in understanding while reading the continuing descriptions. First to observe is a Doppler RADAR technique implementation.


From the viewpoint of a BGT24M chip, the external PLL is set to lock on one fixed frequency without any ramp or modulation. In that case, the frequency of the RADAR is controlled with external PLL and not the BGT24M itself. Electrically, the PLL provides a charge pump analog output that drives BGT24M internal voltage-controlled oscillator.


The VCO will then oscillate with one single and stable frequency i.e. 24.12 GHz. This signal is then amplified and fed through the Tx analog front-end and then into an antenna to be freely emitted into surrounding space. When such a continuous wave of a constant frequency hits a moving target, two things will happen in conjunction: reflection with a Doppler shift of the signal in question. The reflected signal is then captured by the RADAR’s receiver antenna of the RADAR system. The frequency shift of the reflected signal depends on the velocity of the target. If the velocity is zero there is no shift, and the Doppler radar can’t detect stand-still targets. Some examples of a Doppler shift depending on the target velocity for 24.12 GHz are shown below.

Back in the signal chain, a received signal is amplified by the BGT24M internal low noise amplifier and multiplied with an original (un-shifted) signal, the one which is also sent to the Tx circuit. This physical level operation creates a new signal with a frequency equal to the frequency shift between emitted and received signals. This new signal is now present at the output of the BGT24M. The external amplifier circuit is then used for amplification prior to ADC sampling by a microcontroller.


After a predetermined number of samples is captured by the ADCs, the microcontroller starts the FFT algorithm which gives the spectrum of the received signal. Peaks in the spectrum are found and from them, the velocity of the target is calculated. In a conclusion, the Doppler RADAR technique can only determine target velocity and not the range.

Velocity calculation formula
  • fD = Doppler frequency [Hz]
  • λ = the wavelength of the transmitted frequency [m]
  • v = radial velocity [m/s]

Sometimes, the velocity of the target by itself is an insufficient parameter. The spatial position of a target in a relative distance to the ‘observer’ (RADAR) is a more important parameter. This can be achieved by implementing the FMCW RADAR technique. By increasing the capability of the technique there is also an increase in system complexity. As described in the previous paragraph an external PLL is also used here. This time, the PLL generates a sawtooth linear frequency ramp signal.

Generated sawtooth signal

The PLL starts from a defined base frequency and increases it at regular intervals up to the maximum specified frequency. The PLL’s output will control the BGT24M VCO oscillator which will provide described frequency-modulated continuous-wave signal for amplification and then emission by the Tx front end and the antenna.

Emmited to recevied signal time difference

The emitted signal is indicated with green color. As stated previously, the emitted signal is increasing from minimum to maximum frequency within a bandwidth range shown as value B on the graph. When an emitted signal is reflected from the target it will be picked up on the receiver side with some delay. This is indicated with a blue signal in the graph. Delay Ts is the time required for a signal to travel to the target and back to the receiver. Since it is easier to compare frequencies than to measure time delay, the range to the target can be calculated in the following way:

Distance calculation formula
  • c0 = speed of light = 3·10e8 m/s
  • Δt = delay time [s]
  • Δf = measured frequency difference [Hz]
  • R = distance between the antenna and the target [m]
  • df/dt = frequency shift per unit of time

The distance measurement is accomplished by comparing the frequency of the received signal to a reference (emitted signal). This is done in the same way as it was with the Doppler technique by the signal multiplication. If the target is moving relative to the receiver, the echo signal gets a Doppler frequency fD. In that case, RADAR will not only measure the difference in frequency caused by the signal propagation time delay but also the difference caused by the Doppler shift. Some secondary error effects can often be neglected.

In the up following post, more details on the FMCW RADAR technique are discussed.