Page 526 - Engineering Electromagnetics, 8th Edition

508 ENGINEERING ELECTROMAGNETICS

r r

Figure 13.25 See Problems 13.17 and 13.18.

has been fabricated witha5mm width. Determine the power loss in dB for
waves transmitted through the junction.
13.11 A parallel-plate waveguide is known to have a cutoff wavelength for the
m = 1TE and TM modes of λ c1 = 4.1 mm. The guide is operated at
wavelength λ = 1.0 mm. How many modes propagate?
13.12 A parallel-plate guide is to be constructed for operation in the TEM mode
only over the frequency range 0 < f < 3 GHz. The dielectric between
plates is to be teflon ( = 2.1). Determine the maximum allowable plate

r
separation, d.
13.13 A lossless parallel-plate waveguide is known to propagate the m = 2TE
and TM modes at frequencies as low as 10 GHz. If the plate separation is
1 cm, determine the dielectric constant of the medium between plates.
13.14 A d = 1cm parallel-plate guide is made with glass (n = 1.45) between
plates. If the operating frequency is 32 GHz, which modes will propagate?
13.15 For the guide of Problem 13.14, and at the 32 GHz frequency, determine the
difference between the group delays of the highest-order mode (TE or TM)
and the TEM mode. Assume a propagation distance of 10 cm.
13.16 The cutoff frequency of the m = 1TE and TM modes in an air-filled
parallel-plate guide is known to be f c1 = 7.5 GHz. The guide is used at
wavelength λ = 1.5 cm. Find the group velocity of the m = 2TE and TM
modes.
13.17 A parallel-plate guide is partially filled with two lossless dielectrics

(Figure 13.25) where r1 = 4.0, r2 = 2.1, and d = 1 cm. At a certain
frequency, it is found that the TM 1 mode propagates through the guide
without suffering any reflective loss at the dielectric interface. (a) Find this
frequency. (b)Is the guide operating at a single TM mode at the frequency
found in part (a)? Hint: Remember Brewster’s angle?
13.18 In the guide of Figure 13.25, it is found that m = 1 modes propagating
from left to right totally reflect at the interface, so that no power is
transmitted into the region of dielectric constant .(a) Determine the

r2
range of frequencies over which this will occur. (b) Does your part (a)
answer in any way relate to the cutoff frequency for m = 1 modes in either
region? Hint: Remember the critical angle?