課程名稱︰電磁學(二) 課程性質︰電機工程學系大二必修 課程教師︰吳瑞北 開課學院：電機資訊學院 開課系所︰電機工程學系 考試日期（年月日）︰2019/4/19 考試時限（分鐘）：10:20-12:10 試題 : 1. (a) Calculate the capacitance, internal and external inductances per length of a transmission line consisting of two long parallel conducting wires of radius a that carry currents in opposite directions. The axes of the wires are separated by a distance 2d. Assume d >> a. (15%) Fig.1(a) https://imgur.com/OTYyo6a (b) Find the per-unit-length mutual inductance between a single-wire and a two-wire telephone line shown below. (5%) Fig.1(b) https://imgur.com/5GZrz9X 2. Two identical transmission lines are weakly coupled. The length is 10cm, the propagation velocity vp = 2 × 10^8 m/s, characteristic impedence Zo = 50 Ω and the mutual inductance and mutual capacitance per unit length of coupled line are Lm = 15 nH/m and Cm = 4 pF/m. The excitation is Vg, as shown in the following figure. Fig.2 https://imgur.com/CCXuZ4v (a) (7%) Find the induced voltage waveform of line 2 at z = 0 and z = 10cm. (b) (7%) Find the induced voltage waveform of line 2 at z = 0 and z = 10cm when line 2 is open-circuited at z = 10cm and matched at z = 0. (c) (6%) Find Zo such that the induced voltage waveform of line 2 can only propagate in negative z direction. 3. (a) (6%) For the lossless transmission-line system shown below. Find the ratio Zo1/Zo2 if Zin = 25Ω Fig.3(a) https://imgur.com/qJ01Mkg (b) (7%) The voltage standing pattern of a transmission line with chatacter- istic impedence Zo = 100Ω terminated in an unknown impedence ZR below. Find ZR. Fig.3(b) https://imgur.com/95el0tK (c) (7%) For the transmission line system has Zo1 = 50Ω, Zo2 = 20Ω, β1 = β2 = 2π/λ, as shown below. Please prove that the system is a resonant system. Fig.3(c) https://imgur.com/eDFbx1B 4. In the system shown in Figure 4, the switches are in position A and C at t<0 The right switch turns to D position at t = 0 and then turns back to C posi- tion at t = T/2. At t = 4T, the left switch turns to B position. Fig.4 https://imgur.com/TR3FLci Plot the line voltage along the transmission line at: (a) (5%) t < 0. (b) (5%) t = T/4. (c) (5%) t = 3T/4. (d) (5%) t = 9T/2. 5. (a) (5%) In Figure 5(a), Zo1 = Zo2 = 50Ω, R1 = 60Ω, R2 = 200Ω. Find the voltage reflection coefficient Γv at junction A-A'. Fig.5(a) https://imgur.com/is9CJ90 (b) (5%) In Figure 5(b), Zo1 = Zo3, Zo2 = Zo4 = 2Zo1, and the power of the incident wave P. Calculate the reflected power at junction A-A'. Fig.5(b) https://imgur.com/bBHZbSk (c) For the transmission line shown as Figure 5 (c1), the line voltage at z = 0 is measured as Figure 5 (c2), Fig.5(c1&c2) https://imgur.com/D05umiD i. (5%) Please determine whether circuit element inside the network N is R, L or C. Note there is only one circuit element in N. ii. (5%) Find the value of Zo2/Zo1. 6. The system is shown in Figure 6. Fig.6 https://imgur.com/s6OU1me (a) (5%) Plot the line voltage bounce diagram for the system above up to time t = 4.5μs. (b) (5%) Plot the line current bounce diagram for the system above up to time t = 4.5μs. (c) (10%) Please use load-line technique to derive the time-domain line voltage at z = 0 versus t up to t = 4.5μs for the system above. Be sure to write down the voltage-current relationship of source and load end, respectively. -- Her sword shines, a dream that all warriors scattered in battle, past present, and future, hold and mournfully exalt as their final moments approach. She carries their will as her pride, bidding them to remain steadfast in their loyalty. Now the undefeated king sings aloud the name of the miracle she holds in her hands. Its name is... —Irisviel von Einzbern《Fate/Zero》 https://imgur.com/dk95fnl --

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