RF and Microwave Engineering: Fundamentals of Wireless Communications

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 R_I = 15 Ω and R_A = 10 Ω. Plot u_in(t) and u_A(t) as functions of time. Compare your results with simulation results from a circuit simulator.

3.3. Match the load impedance Z_A = (120 − j80)Ω to an input impedance of Z_in = 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 (ε_r = 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 (ε_r = 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 Z_in of an open-circuited line (_t = 25 cm). (Hint: The light speed in vacuum is c₀ = 3 · 10⁸ m/s).

3.5. Consider an ...