3.5 Problems
3.1. Determine the input impedance in Example 3.6 from Equation 3.78.
3.2. Reproduce the example shown in Figure 3.24 for RI = 15 Ω and RA = 10 Ω. Plot uin(t) and uA(t) as functions of time. Compare your results with simulation results from a circuit simulator.
3.3. Match the load impedance ZA = (120 − j80)Ω to an input impedance of Zin = 50 Ω using the Smith chart diagram. As a matching circuit consider a serial line and a short-circuited stub line with characteristic impedances of Z0 = 50 Ω. Determine the lengths of the air-filled lines (εr = 1) for a frequency of f = 1 GHz.
3.4. In order to determine the characteristic impedance of a loss-less transmission line we measure the capacitance of a short line segment as C = 1.5 pF. The length of the line segment is 
= 12 mm. The line is filled with a homogeneous dielectric material (εr = 1.44).
= 12 mm. The line is filled with a homogeneous dielectric material (εr = 1.44).
1. Calculate the propagation velocity c of an electromagnetic wave on the line.
2. Determine the characteristic impedance Z0 of the line.
3. Compute the inductance per unit length L′.
In the following the frequency is give as f = 250 MHz.
4. Specify the propagation constant γ.
5. Determine the input impedance Zin of an open-circuited line (t = 25 cm). (Hint: The light speed in vacuum is c0 = 3 · 108 m/s).
t = 25 cm). (Hint: The light speed in vacuum is c0 = 3 · 108 m/s).
3.5. Consider an ...
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