ECE 3300 Midterm I October 3, 2014 Name: Note that the point distribution is: Problem 1 25 points Problem 2 25 points Problem 3 25 points Problem 4 25 points Problem 5 25 points Choose 4 problems to be graded. If you don’t clearly indicate which problems you want graded, I’ll just grade the first four. I will not give you the best four out of five. 1. (25 points) You are given the following system of point charges in free space, with values q1=-­‐0.5µC, q2=0.5µC, and q3=-­‐1µC. a. (15) What is the (vector) electric field at the point x? b. (10) If a point charge of 0.5µC were placed at point x, then what is the (vector) force acting upon it? 2. (25 points) You are given a coaxial transmission line to use at a frequency f = 0.5 GHz. The metal conductors are copper (σc=5.8x107 S/m, µr=1.0) with inner radius a=0.815 mm and outer radius b=5.25 mm. The insulating material is polyethylene (εr=2.25, σ=1x10-­‐4 S/m, µr=1.0). a. (10) Calculate the line parameters R’, L’, G’, C’ b. (5) Calculate the phase velocity on the line and the wavelength λ c. (5) Calculate the characteristic impedance of the line Zo d. (5) If the length of the line is 10 cm, does it need to be treated as a transmission line? 3. (25 points) Given the transmission line system: with the following parameters: Zo=75Ω, Zg=(100+j50)Ω, ZL=(100-­‐j50)Ω, up=0.8c, l=2.4 m, and 𝑣! (𝑡) = 5 cos 2𝜋×10! 𝑡 − 𝜋/2 a. (5) Calculate the reflectance coefficient Γ b. (5) Calculate the VSWR c. (10) Calculate the input impedance seen by the source, Zin d. (5) Calculate the voltage 𝑉!" 4. (25 points) You need to use the following transmission line to achieve a desired reactance. Assume that Zo=50Ω, f=100 MHz, and up=0.7c. a. (5) If you want to achieve an equivalent inductance with the shortest length line, what should ZL be and why? b. (10) Using your response to a., what should the length of the line be to achieve Zin=j75? c. (5) What is the equivalent inductance value Leq? d. (5) If you used the same length line, but instead used a load impedance of 1/ZL, what would be the new value of Zin? 5. (25 points) Consider the following system consisting of a long feed line that terminates into two transmission lines (in parallel) of lengths indicated. Each branch line is connected to an antenna, with antenna impedances as indicated. a.
b.
c.
d.
(5) If Z1=100Ω, then what is Zin,1? (5) If Z2=100Ω, then what is Zin,2? (5) What is ZL? (5) If Zg=75Ω, then what does Zin need to be in order to maximize power transfer to the feed line? e. (5) What should Zo be?