电磁场作业5

Homework 05

8.1 An air-filled section of an X-band (8.2 – 12.4 GHz) rectangular waveguide of length l is used as a delay line. Assume that the inside dimensions of the waveguide are 0.9 in. (2.286 cm), and 0.4 in. (1.016 cm) and that it operates at its dominant mode. Determine its length so that the delay at 10 GHz is 2 μs.

8.2 A standard X-band (8.2 - 12.4 GHz) rectangular waveguide with inner dimensions of 0.9 in. (2.286 cm) and 0.4 in. (1.016 cm) is filled with lossless polystyrene (εr = 2.56). For the lowest-order mode of the waveguide, determine at 10 GHz the following values.

(a) Cutoff frequency (in GHz).

(b) Guide wavelength (in cm).

(c) Wave impedance.

(d) Phase velocity (in m / s).

(e) Group velocity (in m / s).

8.3 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 (εr= 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 10 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.

9.1 Design a circular waveguide filled with a lossless dielectric medium whose relative permeability is unity. The waveguide must operate in a single dominant mode over a bandwidth of 1.5 GHz. Assume that the radius of the guide is 1.12 cm.

(a) Find the dielectric constant of the medium that must fill the cavity to meet the desired design specifications.

(b) Find the lower and upper frequencies of operation.

9.4 The cross section of a cylindrical waveguide is a half circle,

as shown in Figure P9-4. Derive simplified expressions for the

vector potential component, electric and magnetic fields,

eigenvalues, and cutoff frequencies for TE z modes and TM z

modes.

FIGURE P9-4