FMCW

Ranging with an FMCW radar system: if the (caused by a possible Doppler frequency f_D) error can be ignored and the transmitters power is linearly frequency modulated, then the time delay (Δt) is proportionally the difference of the transmitted and the received signal (Δf) at any time.

Frequency Modulated Continuous-wave radar is a short range measuring radar set. This kind of radar is often used as “radar altimeter” to measure the exact height during the landing procedure of aircraft.

Technical introduction

(FMCW) is a radar system where a known stable frequency continuous wave radio energy is modulated by a triangular modulation signal so that it varies gradually and then mixes with the signal reflected from a target object with this transmit signal to produce a beat signal.

Variations of modulation are possible (sine, sawtooth, etc), but the triangle modulation is used in FM-CW radars where both range and velocity are desired. As shown in the Figure the received waveform (green) is simply a delayed replica of the transmitted waveform (red). The time delay is a measure of the range.

With the advent of modern electronics, the use of Digital Signal Processing is used for most detection processing. The beat signals are passed through an Analog to Digital converter, and digital processing is performed on the result.

FM-CW radars can be built with one antenna using either a circulator, or circular polarization. Most modern systems use one transmitter antenna and multiple receiver antennas. Because the transmitter is on continuously at effectively the same frequency as the receiver, special care must be exercised to avoid overloading the receiver stages.

As explained in the literature, FMCW ranging for a linear ramp waveform is given in the following set of equations:

$k = \frac {\Delta{f_{radar}}} {\Delta{t_{radar}}}$, where f_radar is the radar frequency sweep amount and t_radar is the time to complete the frequency sweep.

Then, Δf_echo = t_rk, rearrange to a more useful: $t_r = \frac {\Delta{f_{echo}}} {k}$, where t_r is the round trip time of the radar energy.

It is then a trivial matter to calculate the physical one-way distance for an idealized typical case as: $dist_{oneway} = \frac {ct_r}{2}$, where c is the speed of light.

Bibliography

• Luck, David G. C. Frequency Modulated Radar, published by McGraw-Hill, New York, 1949, 466 pages.
• Stimson, George W. Introduction to Airborne Radar, 2nd ed., SciTech Publishing, 584 pages.

External links

• Fairly modern invention mechanization
• Practical overview of FMCW and FMICW radar signal processing www.advsolned.com