電磁學(二) 第一次期中考(Mid-Term #1) [三班共同考題,單面共 6 題；Closed-book Exam.]
Time：2019/03/26, 10:10 ~ 12:00 am;
Total score: 100 points
(注意: 僅可使用國家考試用型計算機;第二、四題需用 Smith Chart 繪圖方法求解，並請於答案卷上也同時標示利用 Smith
Chart 所求得的答案。不論有無作答，Smith Chart 兩張都要寫上姓名學號並一齊繳回。)
1. {15%} For a lossy (α = 0.02 Np/λ) 50-Ω
transmission-line system (length ℓ = 9.25λ)
terminated with ZL = 30 + j40 Ω shown as below.
Find (a) ZIN(ℓ); (b) Г(0); (c) Г(ℓ/2) {5% each}.
2. {20%} A 50 (Ω) transmission line of length d1 = λ/8 is connected to a normalized load impedance ZL,n = 0.5
followed by a double-stub tuner spaced an (3/8)λ apart (d12 = 3λ/8), as shown below. (a) Find the required
lengths l1 and l2 of the short-circuited stubs to achieve a match
d12
d1
between the line and the load. (plot your procedures on Smith
Load
chart) {15%}. (b) Plot a ‘forbidden region’ where those ZL’s are
impossible to achieve matching by this double-stub tuner. How to
Y0
Y0
determine the forbidden region of ZL on the Smith chart?
Describe your method briefly and plot your result on a simplified
Smith chart on your answer sheet {5%}.
3 {10%} Consider the three lossless lines with lengths of λ/4 as
shown in figure below. Let Zo = 50 Ω, calculate the Zin looking
into Line 3.
4. {20%} A 50-Ω transmission line operates at 160 MHz and is terminated by a load of 50 + j30 Ω. Use Smith
chart to find (a) Г {5%}; (b) VSWR {5%}; (c) If its wave speed is c/2 and the input impedance is to be made
real, the minimum possible length of the line and the corresponding input impedance {10%}.
5. {15%} A time-domain reflectometry is used to test the transmission line system shown below. Using the
sketch of Vs(t) observed on the TDR scope as shown, determine the values of Zo1, l1, and R1 {5% each}.
Assume the phase velocity of the waves to be 20 cm/ns on each line.
RS =50 Ω
1V +
-
+
𝒱s(t)
-
●
Z01, ℓ1
R1
Z02 = 75 Ω
RL =
75 Ω
6. {20%} A 10-m-long lossless transmission line feeds a load having a load
impedance of ZL = 35+j10 Ω. The load voltage is VL= √2 × 50𝑐𝑐𝑐𝑐𝑐𝑐108 𝑡𝑡
(V). The voltage applied to the line is Vin = √2 × 66𝑐𝑐𝑐𝑐𝑐𝑐(108 𝑡𝑡 + 31𝑜𝑜 )
(V). Calculate the distributed inductance and capacitance of the
transmission line.
P1
Zin = 39.343 - j30.856 (Ω)
Г(0) = (ZL - Z0) / (ZL + Z0) = 0.5j
Г(ℓ/2) = Г(0)𝑒𝑒 −2γ𝑙𝑙 = 0.416
P2
Possible Solution #1
lstub1,SC = 0.05624λ, lstub2,SC = 0.05043λ
Possible Solution #2
lstub1,SC = 0.1150λ, lstub2,SC = 0.3788λ
(b)
Forbidden Region
P3
Zin, line3 = 200 Ω.
P4
(a) Г = 0.287∠73°
(b) VSWR = 1.81
(c) β= 6.7, 2βlmin = 73°
lmin= 0.095λ, Rin = 90 Ω
P5
[Zo1, l1, R1] = [50 Ω, 10cm, 50 Ω]
P6
𝐿𝐿
R0 = 73 Ω = � , β = ω/vp = 2/3, vp = ω/β = 1.5×108 m/s = 1/√𝐿𝐿𝐿𝐿
𝐶𝐶
L = 0.487 μH, C = 91.324 pF