课程名称︰微波工程 课程性质︰选修 课程教师︰庄晴光 开课学院：电资学院 开课系所︰电机系 考试日期（年月日）︰2008/04/21 考试时限（分钟）：180 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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. ---------------------------------------------------------------------------- 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 黄色为正向 蓝色为负向 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? -------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------- 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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