Section 7.2 · Home exercises · 1 of 4
Home exercise 7.2.1: Plate spacing from a measured guide wavelength
Plate spacing from a measured guide wavelength
#In an air-filled parallel-plate waveguide excited in the TE mode at , a probe moved along finds field maxima of the same sign apart.
- Find the cutoff frequency and the plate spacing .
- Find , and .
- Which modes propagate in this guide at ?
- Find the angle of the zig-zag waves.
Strategy
Maxima of the same sign repeat after one guide wavelength, so . Then gives , and gives .
a)
, so , and
b)
, , .
c)
: TEM, TE and TM propagate.
d)
: .
Answer
Check
, , and .
Remark
This is how a slotted line works: a probe on a carriage measures the standing pattern or the phase along the guide, and the guide wavelength, not the free-space one, is read off. Note that between maxima of the same sign is one . Maxima of regardless of sign are only apart. Taking that distance as would give , which no waveguide mode can have: a useful check on the reading.