FMCW
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Frequency Modulated Continuous-wave radar (FM-CW) 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. 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: Failed to parse (Missing texvc executable; please see math/README to configure.): k = \frac {\Delta{f_{radar}}} {\Delta{t_{radar}}} , where Failed to parse (Missing texvc executable; please see math/README to configure.): f_{radar}
is the radar frequency sweep amount and Failed to parse (Missing texvc executable; please see math/README to configure.): t_{radar}
is the time to complete the frequency sweep.
Then, Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta{f_{echo}} = t_rk , rearrange to a more useful: Failed to parse (Missing texvc executable; please see math/README to configure.): t_r = \frac {\Delta{f_{echo}}} {k} , where Failed to parse (Missing texvc executable; please see math/README to configure.): 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: Failed to parse (Missing texvc executable; please see math/README to configure.): dist_{oneway} = \frac {ct_r}{2} , where Failed to parse (Missing texvc executable; please see math/README to configure.): c is the speed of light. External links
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