Reference no: EM132301950

Assignment Outcomes

The assignment will help you in assessing your understanding on the transmission line circuits and their solutions, in applying smith chart in analyzing and solving transmission line problems, impedance matching and also differentiate between various important antenna parameters. Specifically:

1. Analyze transmission line circuits based on the voltage and current distributions on them;

2. Apply Smith chart for analyzing and solving transmission-line problems and for impedance matching;

3. Discuss and analyze the important terminologies related to antennas.

Question 1.

a. A radio transmitter is connected to an antenna having impedance 8 + j40 Ω with a 50 Ω coaxial cable. If the transmitter can deliver 30 W to the load, how much power is delivered to the antenna?

b. A lossless 50 ohms transmission line is connected to unknown load impedance. Voltage measurements along the line reveal that the maximum and minimum voltage values are (√2 + 1)volts and (√2 - 1) volts respectively. The distance at which maximum voltage is observed has been found to be 15λ/16. Determine:

i. The load reflection
ii. Load impedance

Question 2.

a. Discuss the practical importance of the antenna beam width.

b. For an Omni-directional antenna the measurements show the Half Power Beam Width (HPBW) in vertical and horizontal planes are 30^o and 20^o respectively, antenna has loss resistance of 25Ω and efficiency η=0.8.Find:

i. Antenna's gain in dB, and
ii. Radiation resistance.

Question 3.

a. A 75 Ω lossless transmission line is terminated into a load 100 + j150 Ω . For this line, find:
i. Reflection coefficient;
ii. Voltage standing voltage ratio;

b. An antenna receiving a signal of 500 MHz has the following specifications: input power P_rad = 3.25 kW; effective area of antenna A_eff = 3.5 m²; total efficiency of antenna e₀ = 42%; radiation efficiency of antenna e_cd = 65%; tilt angle of the received signal Ψ = 350. Determine
i. Gain of the antenna (in dB)
ii. Maximum radiation intensity of the antenna (in dB)
iii. If the power radiated from the antenna is doubled, discuss how it affects the directivity of the antenna using necessary equations.

Question 4.

a. A 15-m length of 300 Ω line must be connected to a 3-m length of 150 Ω line that is terminated in a 150 Ω resistor. Assuming all lines are lossless, find the VSWR on the 300 Ω line. In order to match the two sections, a quarter wavelength line of characteristic impedance Z0 is added. Find the appropriate Z₀. Assume a working frequency of 50 MHz.

b. An antenna with input impedance of Z_L = 150 + j200Ω is to be matched with a feeding transmission line of 400Ω characteristic impedance. Feeding transmission line length is 37cm and it is propagating a wave of wavelength of 15 cm. Use smith chart to answer the following:

i. Distance of 1^st V_max and 1^st V_min from load;

ii. Number of voltage maximas and voltage minimas on this line;

iii. Distance and length of an open series stub to match the antenna with the transmission line.