Question

Electromagnetics

Question B1.

(a) A generator with Vg = 300 V, and Zg = 50 Ω is connected to a load ZL =75 Ω through a 50-Ω lossless transmission line of length, l = 0.15λ. Determine the,

(i) Zin, the input impedance of the line at the generator end;

(ii) input current I i and voltage Vi ;

(iii) time-average power delivered to the line, = 0.5 x Re{V .I*};

(iv) load voltage VL, and current, IL; and

(v) the time-average power delivered to the load, = 0.5 x Re{VL .IL*};how does compare to ? Explain?

(vi) compute the time average power delivered by the generator, Pg , and the time average power dissipated in Zg . Is conservation of power satisfied?. [12 marks]

(b) A team of scientists is designing a radar as a probe for measuring the depth of the ice layer over the antarctic land mass. In order to measure a detectable echo due to the reflection by the ice-rock boundary, the thickness of the ice sheet should not exceed three skin depths. If ε' = 3 a n d ε'' = 10-2 for ice and if the maximum anticipated ice thickness in the area under exploration is 1.2 km, what frequency range is useable with the radar? [6 marks]

(c) A 0.5-MHz antenna carried by an airplane flying over the ocean surface generates a wave that approaches the water surface in the form of a normally incident plane wave with an electricfield amplitude of 3,000 (V/m). Sea water is characterized by μr = 1, εr = 72, and σ = 4 S/m. The plane is trying to communicate a message to a submarine submerged at a depth d below the water surface. The submarine’s receiver requires a minimum signal of 0.01 μV/m amplitude, what is the maximum depth d to which successful communication is still possible? [7 marks]

Answer 1

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