August 2012
Intermediate to advanced
360 pages
10h 14m
English
Content preview from RF and Microwave Engineering: Fundamentals of Wireless Communications
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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 Ro1 = Ro2 = 2 mm.
Determine
a. the relative permittivity εr of the dielectric material.
b. the inner radii Ri1 and Ri2 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 Ro3 = 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: Ri3 = Ri2.
a. Calculate the characteristic impedance Z03 of the quarter-wave transformer.
b. What is the value of the relative permittivity εr3 of the dielectric ...
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