Find the impedance of the quarter wavelength

Reference no: EM131469735

2017 Assignment

Question 1:

Consider a transmission line with a characteristic impedance of Z_o = 50?. Use a Smith Chart sheet to show the following landmark points:

i. The matched point

ii. Z = 0Ω

iii. Z = ∞Ω

iv. Y = 0Ω

v. Y = ∞Ω

vi. Position where the inductive reactance is +jZo

vii. Position where the capacitive reactance is -jZo

viii. State why admittance (Y) is used designing using Smith Charts [4]

Question 2:

Assuming the characteristic impedance of the transmission line (Z_o) is 50?, use a separate Smith chart to plot the following load impedances and then find the corresponding admittances and de-normalise (give values in 1/? or mhos)

i. Z_L1 = ?50 + j50? [3]

Z_L2= 20? - j10? [3]

Question 3:

a. Assuming a transmission line With characteristic impedance (Z_o) = 50? and a load impedance (Z_L) = 40? - j25 ? is connected to the distal end of the transmission line, use a separate Smith Chart sheet to find the following:

i. The de-normalised input impedance at 0.2λ from the load

ii. The de-normalised input impedance at 8.4λ from the load

iii. The reflection coefficient reflection coefficient (?), the VSWR and the return loss (in dB)

Note: Move in a clockwise direction from the load (Z_L) toward the generator (TWG)

b. A transmission line with a characteristic impedance (Z_o) of 50? has a load impedance (Z_L) of 30- j40? attached to the distal end. It is necessary to use a quarter wavelength transformer or matching section to match the impedance of the line (Z_o) to the impedance of the load (Z_L), but in order to do this we must first deal with the reactive part of the load. Use a separate Smith Chart to solve this problem.

i. Find the length of 50? transmission line required to make the load look purely resistive (real) to enable a quarter wavelength matching section to be implemented.

ii. Find the impedance of the quarter wavelength matching section required to match the real part of the impedance that has been moved onto the horizontal line.

iii. Provide a diagram of the overall arrangement.

Reference no: EM131469735

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