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FMCW and the Doppler effects (5/5)

Electronic Product Design

Radar

5 mins read

It wouldn’t be fair not to mention some great principles used in FMCW technique. Some of those techniques could be potentially used in other fields of engineering if the same circumstances are enveloping the project requirements. Since the basic principle of the FMCW technique is described in previous posts, this article discusses some more precise methods of the RADAR system using the technique in question.

 

RADAR’s range and resolution

Trying to spot a high-altitude airplane on the RADAR while seamlessly mistaking it for a close-by bird, or another way around would bring many disasters in aero navigation and control. Also, the same problem can be found in the realms of embedded RADAR usage. The key importance here is the RADAR’s range and resolution. By suitable choice of the frequency change in time the resolution can be determined, and by choice of the duration of the frequency increase, the maximum non-ambiguous range is defined. The maximum frequency shift and steepness of the frequency sweep edge can be varied depending on the capabilities of the technology implemented circuit. The maximum unambiguous range is determined by the necessary temporal overlap of the (delayed) received signal with the transmitted signal.

 

This is usually much larger than the energetic range, due to the quadratic loss of signal energy in space propagation. For the range resolution of an FMCW radar, the bandwidth (BW) of the transmitted signal is decisive. However, the technical possibilities of Fast Fourier Transformation used in signal processing are limited in time. The resolution of the FMCW radar is determined by the frequency change that occurs within this time limit. As with any radar in the FMCW radar, besides the allocated bandwidth, the antenna beam-width determines the angular resolution in detecting objects.

 

FMCW technology – modulation patterns

A simple modulation pattern was introduced in the previous post. To better understand the possibilities of the FMCW technology, a list of commonly used modulation patterns are presented. Several possible modulation patterns can be used for different measurement purposes:

 

  • Sawtooth modulation
    This modulation pattern is used in a relatively large range (maximum distance) combined with a negligible influence of Doppler frequency (for example, a maritime navigation radar).
  • Triangular modulation
    This modulation allows easy separation of the difference frequency Δf of the Doppler frequency fD
  • Square-wave modulation (frequency-shift keying, FSK)
    This modulation is used for a very precise distance measurement at close range by phase comparison of the two echo signal frequencies. It has the disadvantage, that the echo signals from several targets cannot be separated from each other, and that this process enables only a small unambiguous measuring range.
  • Stepped modulation (staircase voltage)
    This is used for interferometric measurements and expands the unambiguous measuring range.
  • Sinusoidal modulation
    Sinusoidal modulation forms have been used in the past. These could be easily realized by a motor turning a capacitor plate in the resonance chamber of the transmitter oscillator. The radar then used only the relatively linear part of the sine function near the zero crossings.

 

Every human-made system is prone to functional errors. The scale of errors depends on the attention the system development team had dedicated to the fundamental principles and laws of physics that govern the processes in use. Knowing the essence of the Doppler technique in RADAR use involves and emphasizes the possible Doppler shift error in the FMCW technique that could result in a false RADAR image.

 

Up until this part of the RADAR post series, only the sawtooth linear frequency ramp is considered. To make things more interesting, a change to the triangular ramp frequency modulation of the RADAR signal is made. For this modulation scheme to take place, the external PLL is configured to generate a triangular ramp. In a triangular-shaped frequency-changing, a distance measurement can be performed on both the rising and on the falling edge. The echoed signal is shifted due to the propagation delay of a signal.

 

Without a Doppler effect, frequency differences during the rising edge and falling edge of a ramp are the same. However, if the target is moving and a Doppler frequency shift occurs in the echo, the following situation is introduced as an important one. A Doppler frequency shifts the echo signal in height (green graph in the graph below). It appears the sum of the frequency difference Δf and the Doppler frequency fD at the rising edge, and the difference between these two frequencies at the falling edge.

 

This enables the possibility of making an accurate distance determination, despite the frequency shift caused by the Doppler frequency, which then consists of the arithmetic average of the two parts of measurements at different edges of the triangular pattern. At the same time, the accurate Doppler frequency can be determined from two measurements. The difference between the two different frequencies is twice the Doppler frequency. Since the two differential frequencies, however, are not simultaneously available, this comparison requires digital signal processing, with intermediate storage of the measured results.