Transmission Lines

  1. A load impedance ZT = (100−j50)Ω is connected to a source through a wavelength long lossless
    transmission line of characteristic impedance Z0 = 50Ω, as shown below. Determine the average
    power delivered to the load by the generator. How does your answer change if the length of the
    transmission line is 1.18λ?
  2. A resistive load of R = 10Ω is to be connected to a 50Ω source, operating at f = 103.1 MHz.
    Design a transmission line circuit connecting source and load for maximum power transfer. For
    your design, what is the reduction (in percent) in power dissipated in the load if the frequency
    is changed to f = 91.5 MHz?
  3. A lossless transmission line (Z0 = 50Ω, r = 2.25) is terminated in a load impedance consisting of
    a resistance R = 25Ω in series with an inductance L = 60nH. The transmission line is excited by
    a sinusoidal voltage of frequency f = 200 MHz. Using the Smith chart, determine the distance
    from the termination (in meters) to the first voltage minimum and the first current minimum
    on the line. Furthermore, determine (i) the standing-wave ratio on the line and (ii) the input
    impedance of the line if the line is 1.2 m long.
  4. A lossless 75Ω coaxial cable is terminated in an unknown load impedance ZT . From standingwave measurements the standing-wave ratio was found as 2.5 and the nearest voltage maximum
    was 0.35λ from the termination. Determine the unknown load impedance, both analytically and
    graphically using the Smith Chart.
  5. A lossless transmission line section of length l = 3m (Z0 = 50Ω, r = 2.25) is terminated in an
    unknown impedance ZT . The input impedance of the line at f = 40 MHz has been determined
    as Zin = (20 − j10)Ω. Use the Smith chart to answer the following questions: (a) Determine
    the voltage standing-wave ratio on the line; (b) determine the load impedance and reflection
    coefficient at the termination; (c) determine the distance (in meters) from the termination to the
    nearest voltage minimum; (d) determine the distance (in meters) from the termination to the nearest current minimum.