Section 7.1 · Worked examples · 1 of 1
Worked example 7.1.1: Pulse dispersion in an X-band radar feed
One short calculation tied to Application 7.1.1. It uses only the group delay, Eq. (7.1.24), and the universal formulas (7.1.25), with the WR-90 data quoted from Section 7.3. Read the given quantities, produce the formula yourself, and only then put the numbers in.
Pulse dispersion in an X-band radar feed
#Given. of air-filled WR-90 between an X-band radar and its antenna. TE mode, (, Section 7.3). Carrier .
Find. (a) , , , , (b) the group delay of the run and the free-space delay, (c) the group delays at and , (d) the spreading of a pulse () and of a pulse ().
The universal formulas of the general analysis hold for the TE mode of any guide once is known. Each spectral component crosses the guide in its own group delay
and a pulse of bandwidth spreads by about .
and :
, against in free space: the guide adds .
: , . : , . An band is smeared over .
At
pulse: , negligible. pulse: , more than three times the pulse length.
The finite difference of part (c), , agrees with the derivative at the centre to within the curvature of . Also .
The group delay is sensitive to : a cutoff rounded to would already give . Ordinary radar pulses pass undistorted. Nanosecond or wideband chirped signals need a short feed, a carrier high in the band, or equalisation in the receiver.
cf. Application 7.1.1