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︰毛绍纲
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）︰2020/4/17
考试时限（分钟）：10:20-12:10
试题 :
1. In the system shown in Fig.1, the switch is closed at t = 0. Assume source
voltage Vg(t) to be a direct voltage of 60 V, please draw (a) the line vol-
age and (b) the line current bounce diagrams (up to t = 5μs). Then, please
sketch (c) the voltage and (d) the line current versus z for t = 2.75μs.
Fig.1 https://imgur.com/1mcNQp1
Time domain analysis of a transmission-line system.
2. In the system shown in Fig.2.1, an incident wave of voltage V+(V+ = 60V)
strikes the discontinuity from the left, i.e. from line 1.
(a) please find the reflected wave voltage into line 1.
Fig.2.1 https://imgur.com/S8h4B6a
Reflection at a transmission-line discontinuity.
(b) Now, let's try to consider the transmission line system in Fig.2.2 where
a (+) wave carrying power P is incident on the junction a-a'from line 1
connected to the other two lines (line 2 and line 3). Please find:
(i) the power reflected into line 1;
(ii) the power transmitted into line 2;
(iii) the power transmitted into line 3;
Fig.2.2 https://imgur.com/ohDLDIy
Reflection at a junction involving three lines.
(c) Lastly, in the system shown in Fig.2.3, a (+) wave carrying power P is
incident on the junction a-a' from line 1 connected to a junction cons-
isting of three lines and a resistive network. Please find the value of
R for which there is no reflected wave into line 1.
Fig.2.3 https://imgur.com/rjxWhif
A system of three lines with a resistive network at the
junction.
3. In the system shown in Fig.3, the switch S is closed at t = 0, with the
lines uncharged and with zero current in the inductor. Please calculate the
solution for the line voltage versus time at (a) z = 0 and (b) z = l+.
Fig.3 https://imgur.com/dwL0PlQ
A system of two lines with an inductance at the junction.
4. In the system shown in Fig.4 (a), the switch S is closed at t = 0. The line
voltage variations with time at z = 0 and z = l for the first 5μs are
observed to be as shown in Fig.4 (b) and (c), respectively.
(a) Find the values of Vo, Rg, RL, and T.
(b) Plot the line current variations with time at z = 0 and z = l for the
first 7μs.
Fig.4 https://imgur.com/Y6GSbbW
5. The system shown in Fig.5 consists of a series inductor of value 200 nH at
the junction between the two lines. Assume that the inductor is initially
of zero current.
(a) Please plot line voltage and current variations with time at the input
z = 0.
(b) Also clearly mark the steady state voltage and current.
Fig.5 https://imgur.com/ZToOP9T
6. Two parallel transmission lines are aligned in the z direction as shown in
Fig.6a. The distributed circuit model of weakly coupling between these two
transmission line is shown in Fig.6b. Lm and Cm are per-unit-length mutual
inductance and mutual capacitance, repectively. With time-domain weakly
coupling analysis, we know that forward and backward crosstalk voltage are
V2+(z,t) = zKfV1'(t-z/vp)
V2-(z,t) = Kb[V1(t-z/vp)-V1(t-2l/vp + z/vp)]
respectively. If Vg(t) in Fig.6a is
4Vo cos^2(pit/2T) , for 0 < t < T
Vg(t) =
0 , otherwise
please answer the following questions:
(a) Find V2+(l,t)
(b) Find V2-(0.75l,t)
(Note:For the above two questions, you have to list all answers with its
corresponding t regions respectively).
(c) Plot V2+(l,t) in Fig.6a from t = 0 up to t = 2T.
(d) Plot V2-(0.75l,t) in Fig.6b from t = 0 up to t = 2.5T
(e) If we have known Lm = 0.16μH/m and Cm = 3.8pF/m in Fig.6b, please
calculate forward and backward coefficient Kf & Kb. Assume Zo = 200Ω
and vp = 0.125 × 10^9 m/s in Fig.6a.
Fig.6 https://imgur.com/Hx5VzIb