課程名稱︰高速數位系統電磁設計 課程性質︰選修 課程教師︰吳瑞北 開課學院：電資學院 開課系所︰電信所 考試日期（年月日）︰2008/4/14 考試時限（分鐘）：120 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Remark : The examination has six problem with total score 120%. You are suggested to do as many as possible. The score of the highest five will be added to get final score. 1.Briefly answer the following questions (a) Under what conditions the tx-line system can be classified as overdriven and underdriven cases? Which has a larger SI concern at receiving end,why? How about at sending end? (b) Under what conditions,a tx-line can be treated as short lines and modeled by lumped elements.Plot the equivalent lumped circuits in terms of T-and pi-model,respectively. (c) What does inter-symbol interference(ISI) mean? How to simulate ISI for digital systems? (d) What is single-line equivalent model? How to use it to discuss the SI effect on a multi-conductor system? 2.Assume that a capacitor is inserted in series into a long transmission line, shown in fig2. (a) Set up and solve for the exact TDR(Va(t)) and TDT(Vb(t)) waveforms, for an incident unit step,assuming the circuit is initially at rest. (b) Find the total area under the TDT waveform by integrating Vb(t) over time. (c) How TDR and TDT will change when the incident signal has a final rise time? Will the area under TDT change due to the finite rise time? fig2:同課本2.24, 但L改成C, load加上Zo 3.As shown in fig3, some engineers add series resistance at every junction of branches to reduce the reflection due to the juncture. (a)Find the value of R in terms of Zo so that the incident wave, when passing through the juncture, will not induce an reflected noise. (b)Please find amplitude of the transmitted wave after the juncture. 4.(a)Please describe the skin effect and proximity effect.What is the difference? (b)To illustrate the proximity effect,consider a microstrip transmission line shown in fig4. To model the non-uniform current distributions,the signal conductor is divided into 3 parts, with current flow I1,I2 and I3. Note that I3=I1 dur to structural symmetry. The voltages across the three parts should satisfy whwew M1>M2. Find the current ratio I2/I1 versus ferquencies. [ V ] =[ R+jwL jwM1 jwM2 ] [I1] V jwM1 R+jwL jwM1 I2 V jwM2 jwM1 R+jwL I3 5.Consider a wide plates of thickness t and width w over a perfect ground with height d in air,assumeing w>>d. (a) Given the voltage drop V0,find the electric field and from which,p.u.l. capacitance C. (b) Given the curretn drop I0,find the magnetic field and from which,p.u.l. inductance L. (c) Consider that plate is of finite conductivity σ. At high frequencies such that the skin depth δ<<t,please find the magnetic field inside the conductor, and from which, the resultant p.u.l. internal inductance Lint <Hint:use the magnetic energy> (d) Show that the total p.u.l. inductance for finite σ in (c) can also be obtained by treating the metal as PEC but retreating its surface by a certain depth.Find the depth. (e) Calculate the p.u.l. R at high frequencies. Show that R=wLint. <Hint:inside conductor, E=ηH*y; η=(jwμo/σ+jwεo)^0.5≒(jwμo/σ)^0.5 = (1+j)/(σε) > 附註:p.u.l. = per unit length 6. Consider coupled microstrip lines with cross section shown in fig6, where length is 10cm Zs=Zl=50Ω, Vs=2 volt, and Tr=100ps. In the absence of the central line, it is given that [C]=[ 123.2 -1.3 ] pF/m; [L]=[ 279.5 13.0 ] nH/m -1.3 123.2 13.0 279.5 (a) Determine the characteristic impedance and time delay of the transmission lines. (b) Plot approximately VL, Vnear, Vfar versus t for t<1.5nsec. To reduce the crosstalk, one way is to add a guard trace.e,g., trace#2, in between. In the three-line system, it is given [C]= [ 124.7 -10.6 -0.67 ] pF/m; [L]=[ 275.7 52.1 15.4 ]nH/m; -10.6 126.1 -10.6 52.1 272.2 52.1 -0.67 -10.6 124.7 15.4 52.4 275.7 (c)Let the guard trace be grounded. Find the resultant[C],[L] between lines 1 and 3. (d)Find the peak value of Vnear, and Vfar and compare with (b). (e)If the guard trace is grounded only at the two terminal points, there will be crosstalk noise propagating along the line and bouncing back and forth. Please discuss qualitative how it will affect the waveform in Vnear, and Vfar. fig6 同課本 fig3.3,但中間多了一根groung trace εr=4.3, trace間距0.5mm, trace寬1.0mm、厚0.1mm、與底層間距0.5mm --

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