By M. Schetzen
The booklet starts off with a easy dialogue of the Doppler influence and its quite a few functions, and the way Doppler radar can be utilized for the stabilization and navigation of airplane. A quasi-static approximation of the Doppler spectrum is gifted in addition to illustrations and discussions to aid the reader achieve an intuitive knowing of the approximation and its boundaries. A precis of the mathematical options required for improvement of an actual thought is then awarded utilizing the case of a slim beam antenna. this is often via the improvement of the precise concept for the overall case, that's graphically illustrated and in comparison with the quasi-static approximation. basic stipulations for which the quasi-static approximation blunders will be over the top – in particular as utilized to laser Doppler radars and low-flying airplane – are presented.
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Extra resources for Airborne Doppler Radar
The receiver thus observes the time between crests to be Dt ¼ t2 À t1 ¼ 1h ns i 1À f0 c (2:14) The time between crests is, of course, one period of the received sinusoid so that its frequency is fs ¼ ! 1 1 ¼ f0 Dt 1 À ns =c (2:15) Now consider the case in which ns ¼ 0 so that only the receiver is moving. The time between crests is one period of the sinusoid, which is t 0 ¼ 1=f0 . The distance between crests in the medium thus is d ¼ ct0 ¼ c=f0 . Because the relative velocity between the wave and the receiver is (c þ nr), the receiver will observe the time between crests to be Dt ¼ d c 1 ¼ c þ nr f 0 c þ nr (2:16) The sinusoidal frequency observed by the receiver thus is fr ¼ h 1 nr i ¼ f0 1 þ Dt c (2:17) We now consider the case in which both the receiver and the source are moving.
2:20) (2:21) By comparing Eq. 13) and Eq. 21), we note that the electromagnetic case and the sonic case agree only to the ﬁrst power of the ratio of the source velocity to the wave velocity. We thus can see that the Doppler shift for electromagnetic and for sonic waves can be considered to be given by Eq. 4) only if the source and receiver velocities are small compared with the corresponding wave velocity. 3 The Doppler effect of electromagnetic waves has also been used in rheology to measure the ﬂow of ﬂuids.
12), is the mean frequency of the quasi-static Doppler spectrum. Thus, for small antenna beamwidths, we would expect that the frequency assigned to the beam center given by Eq. 6), d(ue , 0), is a good approximation to dqs . The program plots of the quasi-static Doppler frequency are graphs of the normalized quasi-static Doppler frequency, which is ðl=vÞdqs . The reason for this normalization is that the graphs are then independent of wavelength and aircraft velocity. Furthermore, for convenience in using the graphs, dqs is in hertz.
Airborne Doppler Radar by M. Schetzen