课程名称︰电磁学(二)
课程性质︰电机工程学系大二必修
课程教师︰吴瑞北
开课学院：电机资讯学院
开课系所︰电机工程学系
考试日期（年月日）︰2019/4/19
考试时限（分钟）：10:20-12:10
试题 :
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.