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看板NTU-Exam
标题[试题] 高速数位系统电磁设计 期中考
时间Mon Apr 14 15:47:01 2008
课程名称︰高速数位系统电磁设计
课程性质︰选修
课程教师︰吴瑞北
开课学院:电资学院
开课系所︰电信所
考试日期(年月日)︰2008/4/14
考试时限(分钟):120
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
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:同课本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) >
附注: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 同课本 fig3.3,但中间多了一根groung trace
εr=4.3, trace间距0.5mm, trace宽1.0mm、厚0.1mm、与底层间距0.5mm
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