RF and Microwave Engineering: Fundamentals of Wireless Communications

5.8 Problems

5.1. The scattering matrix S of a two-port network is given as

5.91

The port reference impedance is Z₀ = 50 Ω.

a. Determine the properties of the network: is it matched? Is it reciprocal? Is it symmetric? Is is loss-less? Give reasons for your answers.

b. Calculate the reflection loss (RL) and the insertion loss (IL).

c. Renormalize the scattering matrix to a new port reference impedance of Z_{0, new} = 100 Ω.

5.2. With a vector network analyser we measure a reflection coefficient of at the input terminals of an antenna. Port reference impedance is Z₀ = 50 Ω.

a. Determine the input impedance Z_A of the antenna.

We connect the antenna to a transmission line with a characteristic impedance of Z_0L = 75 Ω. The incident active power on the transmission line is set to P_a1 = 1 W.

a. Calculate the reflected power P_b1 at the antenna terminals and the power P_acc that is accepted by the antenna.

5.3. Determine the scattering matrices of the two-port networks given in Figure 5.24. The port reference impedance is Z₀ for all ports.

Figure 5.24 Series impedance, T- and π-network (Problem 5.3).

5.4. Figure 5.25 shows a cascade connection of three two-port networks. An unknown ...