課程名稱︰微波工程
課程性質︰選修
課程教師︰莊晴光
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰2008/04/21
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
This is an in-class examination. You can bring in an A4 note and a scientific
calculator. The solution sheets must be from sole work of yours.
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Problem(1): 25 points
Fig1 consists of a lossy transmission line characterized by the complex
characteristic impedance Z0, complex propagation constant γ=(β-jα),
and length L. The transmission line is terminated by a complex load ZL=Z0=
RL+jωL, and excited by an ideal voltage source Vs of internal complex
impedance Zs=Rs+jXs.
(a)Show that when ZL=Z0, Zin=Z0=ZL.
(b)Base on the voltage-traveling-wave definition of the reflection cofficient,
what is the input reflection coefficient(at source)?
(c)Base on the voltage-traveling-wave definition of the reflection coefficient,
what is the power entering the transmission line under the matched condition?
Repeat (b) and (c) based on the power-wave definition of the reflection
coefficient(under current Γi expresion).
(d)What is the input reflection coefficient?
(e)What is the power entering the transmission line uinder the matched
condition.
Zs=Rs+jXs ╭──────╮
╭ ▄ ──┤Z0,γ=β-jα├──╮
│ ╰──────╯ │
+ ╭→ ▌ ZL=RL+jωL
Vc │ │
- Zin │
│ │
╰──────────────╯
------------------------------------------------------------------------------
Problem(2) 25 points
Fig2 show the asymmetric coupled lines consisting of two printed metal strips
of wigth W1 and W2,respectively.
V1=Ac*e(-rc*z) + Ac*e(rc*z) + Aπ*e(-rπ*z) + Aπ*e(rπ*z)
※e()=expontial 黃色為正向 藍色為負向
voltage traveling waves at line 1.
The assymmetric coupled lines support two propagation modes,namely, c mode(in
phase) and π mode (out of phase). Thus the assymmetric coupled lines can be
characterized by the propagation constants γc and γπ, the model voltage
rations of Rc and Rπ, the characteristic admittances of (Yc1 , Yc2) and
(Yπ1 , Yπ2), respectively.
(a)Given the general expression of the voltage traveling waves at line 1, as
shown in Fig1, write the expression of voltage traveling waves at line 2, and
current traveling waves at line and line2,respectively.
(b)If W1=W2 ,the asymmetric coupled lines become the symmetric coupled lines.
Discuss why Rc=1 and Rπ=-1?
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Problem(3) 20 points
A non-ideal series inductor is modeled by a series connection of L and R as
shown in Fig3. Derive the two-port S-parameter based on the power-wave
definition. The referenced impedances at port 1 and port 2 are Z01(r01+ jx01)
and Z02(r02+jx02), respectively.
referenced impedance referenced impedance
at source:Z01 at load:Z02
L R
│ ╭──────︷──～─────────╮ │
│ │ │ │
╰→ ▌ ▌ ←╯
│ │
╰───────────────────╯
Fig3 Modeling a series lossy inductor by s-parameter
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Problem(4) 30points
It can be shown that the Wilkinson power divider as illustrated in Fig4 will
result in a thre-port S-parameter expression listed in the figure, where Y3*3
Ye2*2, and Yo2*2 represent the augmented y parameter of the original, even-
and odd-symmetric, three-port power divider, respectively.
(a) Show that the final S3*3 parameter can be experssed by:
S3*3=[ (Z0^2-2R01*R02)/ S12=S21 S13=S31 ]
(Z0^2+2Z01*Z02)
-j(2Z0*R01^0.5*R02^0.5)/ (Z0^2*Riso-4R01*R02^2)/ S23=S32
(Z0^2+2R01*R02) (Z0^2+2R01*R02)
-j(2Z0*R01^0.5*R02^0.5)/ -2*R02*(R01*RISO-Z0^2)/ S33=S22
(Z0^2+2R01*R02) (Z0^2+2R01*R02)*(2R02+RISO)
(b)Show that Z0^2 =2*R01*R02 and Riso =2*R02 will lead to S11=S22=S33=S23=S32=0
(C)If S32(or S23) should have the minimum isolation of 30dB, what is the
maxmium percentage of variation of Riso from the desired value of 2*R02?
(2*R02 ± ？% )
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