MIT6_013S09_pset07

MIT6_013S09_pset07 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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0 z z = - A 0 Load = R L MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 7 (five problems) Suggested Reading: Course notes: Sections 7.2.3, 7.3.1 –7.3.2, 8.3.1, 3.5 Problem 7.1 A lossless air-filled TEM line operating at f [Hz] is terminated with a load R L , and |V(z)| across the line is measured, as illustrated. (a) Based on the |V(z)| illustration, what are: (i) f [Hz]? |V(z)| max (ii) VSWR? (iii) Z o [Ohms]? |V(z)| min (iv) C [F/m] of the line? (v) L [Hy/m] of the line? (vi) Γ ? (vii) Fraction of power |V (z)| reflected by the load? 2 volts (b) Based on the second figure, what is the 1 volt Load = Z L Ω unknown complex load impedance Z L ? A 0 z Smith chart is attached z = - λ /8 0 and may be used. (c) The load of part (b) is matched using a capacitor C m shunting the TEM line at z = -A m ; what values of C m and A m produce a match with minimum A m ? A second Smith chart is attached and may be used. “Shunting” means placed across the line rather than in series with it. Problem 7.2 A radio ham with a low budget wants to match her antenna for better performance at 50 MHz. She therefore tests her antenna with a small pickup coil and tiny neon bulb that lights up every d = 2 meters as she slides it along the powered Z o = 300-ohm twin-lead antenna feed wire. - 1 -
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(a) The VSWR = 3 on the twin lead antenna feed wire, and the bulb is brightest one meter from the antenna port. What is the complex impedance Z A of the antenna port? (b) The ham now wants to add in either series or parallel with the antenna feed line the shortest possible short-circuited stub of 300-ohm twin-lead wire that would achieve a near-perfect match for the antenna. (i) How long should this stub be (S), (ii) should it be in series or parallel with the feed line, and (iii) how far (A) from the antenna port should it be attached? Problem 7.3 Determine the Thevenin equivalent for each circuit below.
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MIT6_013S09_pset07 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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