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）︰2006/4/24 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 : 1.Briefly answer the following queations (a)Under what condition, the tx-line system can be classified as overdriven and underdriven cases? (b)Under what conditions, the tx-line can be terated as short lines and modeled by lumped elements. (c)What does inter-symbol interference(ISI) mean? How to simulate ISIfor digital system? 2.Design a 50Ω stripline with the cross section in fig1 , where the substrate is FR4 with dielectric constant 4.0. (a) Assume that H=1.5mm, T=0.02mm, and the strip lies symmetrically between the top and bottom ground planes. Find W. (b) Create an equivalent circuit model for the 50Ω transmission line of 1 inch long, Assume that the driver has a minimun rise time of 100ps. Hint:you may need the formula Z0=60/(εr)^0.5 *ln(4H/0.67π(T+0.8W) ) ohm 3.Consider a transmission line as shown in fig2, where Z0=50Ω and Zs=25Ω. A step pulse of 2V in incident at t=0. (a) Please plot the voltage versus time over t=0 to 1.2ns at the both ends. (b) Repeat (a) but assume that an ideal diode is inserted between Vs and Zs and the transmission line is initially un-charged. fig2:與課本fig2.2一樣,Vs=2v,Td=200ps 4.Consider a strip line system shown in fig3, with the cross section shown in fig 1. (a) Plot the waveforms at the test point and compare it with the "exact" waveform when the branch for the test point is not inserted. (b) Repeat (a) but with a smaller length, say lo=5mm, will the "measurement error" be reduced? (c) Repeat (a) but with the branch of a higher characteristic impedance, say 100Ω. Will the "measurement error" be reduced? 5.Assume that two component, U1 and U2, need to communicate with each other via an 4-bit-wide 5 inch long high-speed digital bus. The driving buffers on component U1 have a source impedance of Rs=50Ω and a swing of 0 to 1 V. The dielectric constant of the board is 4.0,the tx-line is assumed to be a perfect conductor, and the receiver has very small capacitance and can be assumed open circuited. fig4 depicts the circuit topology. The tx-line short-circuit capacitance and inductance matrices are [C]=[ 115.4 -9.1 -0.7 -0.3 ] pF/m; [L]=[ 296 46 13 6 ] nH/m -9.1 116.6 -9.1 -0.7 46 294 46 13 -0.7 -9.1 116.6 -9.1 13 46 294 46 -0.3 -0.7 -9.1 115.4 6 13 46 296 ╭─────┬──────────┬─────╮ │Component ├──────────┤Component │ fig4 │ U1 ├──────────┤ U2 │ ╰─────┴──────────┴─────╯ (a) Determine the maximum variation in impedance variation and propagation delay on the tx-line due to crosstalk. (b) Find the variation of the received voltages due to crosstalk effects. 6.Consider two strongly coupled transmission line with resistance ZL at both sending and receiving ends as shown in fig5. Let the short circuit capacitance and inductance matriced by [C]=[ 1 -kc ] and [L]=[ 1 kL ], respectively. -kc 1 kL 1 (a) Find the even mode capacitance and inductance, and base on which the even mode impedance Ze and mode velocity. (b) Repeat (a) for the odd mode and find odd mode impedance Zo and mode velocity The problem shown in fig1 can reduced to a superposition of two problems one with even mode excitation, i.e., V/2 and V/2 at lines 1 and 2, while the other with odd mode excitation,i.e., V/2 and -V/2 at line 1 and 2. For each mode excitation, one can find the total voltage at both ends. (c) Find the matched load resistance,i.e., the value of resistance ZL in terms of Zo and Ze, at which the far end noise is zero. (d) In the case of (c), find the saturated near end noise in term of kC and kL. Please find the simplified formula when kC and kL are very small and compare it with the expression of weakly coupled approximation as obtained in the text book. fig5:與課本fig3.3一樣 --

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