RF and Microwave Engineering: Fundamentals of Wireless Communications

4.10 Problems

4.1. Derive the relations in Equations 4.80 and 4.81 for the termination of differential and common mode. Calculate values of R₁, R₂ and R₃ for the coupled microstrip line from Example 4.18 and a ratio of s/h = 1. Estimate differential and common mode impedance from the graphs in Figure 4.29.

4.2. Calculate the cut-off frequencies of the first six modes in a R260 rectangular waveguide (a = 8.636 mm, b = 4.318 mm). Determine the characteristic line impedance of a TE₁₀ wave at a frequency of .

4.3. Consider two coaxial lines with characteristic impedances of Z₀₁ = 75 Ω and Z₀₂  =  125 Ω. Both lines are filled with homogeneous dielectric material. The propagation speed of electromagnetic waves on the line is 0.81c₀ (81% of the vacuum light speed). Both lines have the same outer radius R_o1 = R_o2 = 2 mm.

Determine

a. the relative permittivity ε_r of the dielectric material.

b. the inner radii R_i1 and R_i2 of the coaxial lines.

At a frequency of f = 10 GHz the two coaxial lines shall be matched by a coaxial quarter-wave transformer with an outer radius R_o3 = 2 mm that equals the outer radii of the other two lines. The inner radius of the coaxial quarter-wave transformer equals the inner radius of line 2: R_i3 = R_i2.

a. Calculate the characteristic impedance Z₀₃ of the quarter-wave transformer.

b. What is the value of the relative permittivity ε_r3 of the dielectric ...