Determine if the network is symmetric and if loss less -

Question

1. For the circuit consisting of air transmission line shown below, Rs = 100Ω, Zo = 50Ω, ZL = 100 - j50Ω, length I = 0.2λ.

Determine:

a The ABCD matrix of the transmission line

b. The input impedance

c. The output impedance

2. For the circuit shown below, Z_L = 100 - j50Ω, determine

a. The input impedance

3. A certain two port network is measured and the following S-parameter is measured at a frequency:

[s] = [0.1∠0° 2∠90°]
         [2∠90° 0.4∠0°]

a Determine if the network is symmetric and if loss less

b. If a short circuit is placed at port 2, what will be the resulting return loss at port (i.e., convert to 1 port matrix)

4. A 3-port RF circuit has an unusual flow diagram as shown in figure. The arrows show how the amplitude of the wave transfers between ports when all ports are matched.

a Write down the general S-parameters for this circuit

b. Is this a reci procal and I ossless circuit?

c. Determine the equivalent 2-port scattering matrix if port 3 is open-circuited

5. The electric field in free space is given by E' = 1X10^-6(x' + y') cos(2ΠX10⁹ - βz) V/m.

a) Which direction is the wave propagating?

b) What is the operating frequency

c) Determine β

d) Determine the corresponding H-field