Indian Institute of Technology Indore
EE 305 Electromagnetic Waves
Tutorial 6
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1. Consider a dielectric-filled parallel plate waveguide with a = 2 cm. The refractive index is n = 1.5.
(a) Which TEm and TMm modes can propagate a 12 GHz signal in the waveguide?
(b) What would be the associated cutoff wavelengths in each case?
(c) What would be the associated group velocities in each case?
2. Calculate and list in ascending order the cut-off frequencies (in terms of the cut-off frequency of the
dominant mode) of an air-filled rectangular waveguide (cross-section dimensions a b) for the following
modes: TE01, TE10, TE11, TE20, and TM11, if a = 2b.
3. Determine the cross-sectional dimensions (a and b) of an air-filled rectangular waveguide that is required
to operate over the frequency range 8.2 GHz to 12.4 GHz and satisfy the following conditions: (a) only one
mode exists in the guide, (b) the lowest operating frequency is 25% higher than the cut-off frequency of the
dominant mode, and (c) the highest operating frequency is 5% lower than the cut-off frequency of the next
higher order mode.
4. An empty X-band (8.2-12.4 GHz) rectangular waveguide, with dimensions of 2.286 cm by 1.016 cm, is
to be connected to an X-band waveguide of the same dimensions but filled with lossless polystyrene (r =
2.56). To avoid reflections, an X-band waveguide (of the same dimensions) quarter-wavelength long
section is inserted between the two. Assume dominant mode propagation and that matching is to be made
at l0 GHz.
(a) Determine the wave impedance of the quarter-wavelength section waveguide.
(b) Determine the dielectric constant of the lossless medium that must be used to fill the quarter wavelength
section waveguide.
(c) Determine the length (in cm) of the quarter-wavelength section waveguide.
