ps8 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Problem Set No. 8 6.630 Electromagnetics Issued: Week 9 Fall Term 2006 Due: Week 10 -----------------------------------------------------------------------------Reading assignment: Section 2.4, 2.6; J. A. Kong, “Electromagnetic Wave Theory”. Problem P8.1 A TEM transmission line is driven by a voltage source Vo cos ω t at 100 MHz. The char­ acteristic impedance of the transmission line is Zo = 100 Ω for = o . The transmission line length is l = 75 cm Zo + − Vo cos ω t + V1 (t) − l = 75 cm z = −l z=0 z Z, ZL (a) Let = o , show that l = λ/4 . If the voltage at z = −l is 1 π , V1 (t) = √ Vo cos ω t − 4 2 what is the load impedance ZL ? (b) Let = 4 o , find the wavelength λ . What is the input impedance Zin at z = −l ? What is the voltage V1 (t) at z = −l ? Problem P8.2 Convert the following time domain expressions into their complex equivalents in the frequency domain, where we have defined A = Re Aejωt A = sin ω t A = −j (b) Find A. (i) A = j ejπ/4 (ii) A = x + y 3j ˆˆ (iii) A = A0 ejφ + j Example : (a)Find A. π (i) A = 3 sin ω t − 4 (ii) A = x sin ω t − y 2 cos ω t ˆ ˆ (iii) A = cos φ cos ω t Problem P8.3 Consider the TEM transmission line system connected to a time-harmonic voltage source as shown in the following figure. − Zo λ /8 − Zo + V − + VC − 3λ /4 + Zo VB − ZB + VA − λ /2 ∼ 2 Zo ZL = Zo (1-j ) ZC (a) (b) (c) (d) (e) ZA Find the impedance ZA in terms of Zo . Find the impedance ZB in terms of Zo . Find the impedance ZC in terms of Zo . Show that the time average power dissipated in ZC is |Vo |2 /8Z0 .Assume Zo is real. Find the voltage VL across the load ZL in terms of Vo and use VL to calculate the time average power dissipated in the load ZL in terms of Vo and Zo . Assume Zo is real. ...
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ps8 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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