= 25 ohms, and line #2 has R c2

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Barbra Skinner
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1 Soution for Aignment #3.A tranmiion-ine circuit i driven by a tep-function generator with V = 0 vot and RS =0 ohm. ine # ha ength of = cm. Both ine have the ame peed of trave, u = 0 cm/n. ine # ha characteritic reitance R c = 5 ohm, and ine # ha R c = 00 ohm. The oad i R = 00 ohm. (a) If =.5 cm, find the votage acro oad reitor for R 0 < t < n. (b) If = cm, find the votage acro oad reitor for R 0 < t < n. (c) Find the fina vaue of the oad votage, a t. (d) Ue BOUNCE to verify your anwer. Soution: Known parameter are: V = 0v, RS = 0 ohm, = cm, u = 0 cm/n, Rc = 5 ohm, R c = 00 ohm, R = 00 ohm, a =. 5 cm, b = cm. We can compute that: The votage appied on the tranmiion ine can be cacuated a Rc 5 50 V 0 = V = 0 =.74 v. Rc + R The refection coefficient at the ource i R Rc Γ = = = R + Rc The refection coefficient at the junction of ine # and # i Rc Rc 00 5 eeing from ine #Γ = = = 0. 6, eeing from ine # Γ =-0.6 Rc + Rc The refection coefficient at the oad i R Rc Γ = = = R + R c The time deay for ine # i t d = = = 0. n u 0 a.5 b The time deay for ine # i t d, q = = = 0. 5 n or t, = = = 0. n d b u 0 u 0

2 The bounce diagram and the votage acro oad reitor R for 0 < t < n for 5 = b a =. cm and cm are hown in Fig-, -,-3 and -4. The ret figure how reut at t=0.5 n, t=0.45 n, t=0.475 n and t=0.65n. Peae cacuate the votage at the ource end and at the junction to ee if your reut agree with BOUNCE. When time goe to infinite, the votage acro the oad can be cacuated by circuit theory a 0*00/(0+00)=6.5 v, a can be een from BOUNCE when you run for 3 n or more. Fig.- Bounce diagram for -a

3 Fig. -b Bounce diagram for -b 3

4 Fig -3 Votage at the oad for -a Fig -4 Votage at the oad for -b 4

5 5

6 .On a high-peed ogic board, a driver chip tak to a itener chip via a circuit interconnect 3 coniting of three path in erie, of ength = cm, = cm and =3 cm. The return current i carried by a ground ayer in the muti-ayer circuit board. 6

7 The interconnection i modeed a three tranmiion ine in erie, a hown in the figure. The characteritic reitance and peed-of-trave of each ine depend on the width of the conductor on the circuit board, and i cacuated uing the formua in Set # of the ca note. R =50 c R = c c3 60 For thi circuit, ohm, =30 ohm and u = R ohm. To keep the anayi impe ue 0 cm/n for a three tranmiion ine, athough for rea circuit the peed woud different for the three ine. The ource generate a tep-function votage of height V =0 vot with interna reitance R = 50ohm. The oad i R = 00 ohm. (a)make a bounce diagram for thi circuit. Ue the bounce diagram to make a graph howing the votage acro the generator termina and the votage acro the oad termina for 0 < t < n. (b) Find the fina vaue, a t, of the votage acro the generator termina and the votage at the oad. (c)ue the BOUNCE program to cacuate the ource votage and the oad votage and check that your anwer for part (a) i correct. Soution: Known parameter: = cm, = cm, =3 cm, R = 50ohm, R = 00 ohm., R 50 3 c3 = R R 60 ohm, V = 0 vot, u = ohm, c =30 ohm and 0 cm/n Computation: ince the ength of the ine are mutipe of, to write the time intance neaty, we define t d = = 0.05 n, o td = t d, t d = td, td3 = 3t d. We need to cacuate 0 t d 0 Since the interna reitance of the ource equa to (which i caed matched, you wi earn ater) the reitance of ine #, the refection i zero. The votage appied on ine # i initiay 5v. The refection coefficient at junction # and # i Rc Rc Γ = = = -0.5, Γ =0.5 Rc + Rc The refection coefficient at junction # and #3 i Rc3 Rc Γ3 = = = =0.333, Γ 3 = Rc3 + Rc The refection coefficient at the oad i R Rc Γ = = = 0.5 R + R c3 The bounce diagram i hown in Fig.-, and the votage at oad i in Fig.-. The cacuated votage at the oad by penci-paper i 6.735v, from BOUNCE it i 6.65v, the reative error i.5%, e than 5%. Note, ince the votage have ma difference, you houd abe the vaue on your graph to how the votage acro the oad. The fina vaue of the votage at the oad i 0*00/(50+00)=6.667v. When you run BOUNCE, peae eect ma number of cyce o to verify your cacuation at every t d time interva. c = 7

8 Fig. - The bounce diagram 8

9 Fig.- the BOUNCE reut. 3.The circuit hown above ha a hunt reitor, which repreent the input reitance of a chip connected acro the tranmiion path at a ditance of from the ource. The ength of the circuit interconnect are =4 cm and = cm. Both tranmiion ine have 50 ohm and u = 0 cm/n. The generator make a pue of ength 0.5 n and open-circuit votage V = 0 vot, and ha R = 40 ohm. The oad reitor are R M = 50 ohm and R = 00 ohm. (a) Find the votage acro the oad a a function of time for 0 < t <. 5 n. (b) Find the fina vaue of the oad votage, a t. Soution R c = 9

10 Known parameter: = 4 cm, = cm, Rc V0 = V = 5.6 V R + R c t d = = u 4 / 0 =0.4 n t d = = / 0 =0. n u R = 40 ohm, = R Rc Γ = = -0. (the generator i matched to the ine) R + Rc R Rc Γ = = /3 R + Rc Req Rc Γ J = = -/3 (where: R eq = Rc // RM = 5) Req + Rc Τ = + =/3 R 50 ohm, 0 cm/n, c u = V = 0 J Γ J Now we are ready to draw the bounce diagram and cacuate the time repone. Note that ince refection from the ource wi reach the oad at time outide the required range (i.e after.5 n) they were not cacuated in the bounce diagram. Ao for pace imitation; the vaue on the traiing edge were not written ince they are equa to the eading edge of the pue but with oppoite ign. The fina vaue of the votage wi be zero ince the ource i a pue ource. 0

12 (c) Ue BOUNCE to verify your anwer. The ma vaue of the votage wi not be hown on the bounce repone une you cick the moue a hown in the diagram beow

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