Section 6 3 TRƯỜNG ĐIỆN TỪ

No Slide Title Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jor[.]

Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India 6.3 Transmission-Line Discontinuity 6.3-3 Transmission-Line Discontinuity (+) Z01, v p1 (++) (–) I + + I– I ++ + + V+ + V– V ++ – – Z 02, vp2 6.3-4 V   V – V   B.C  I   I –  I    –  V V V I  , I– – , I   Z01 Z 01 Z02 V  V  V  V    Z01 Z01 Z02 Z02   V V  V  V  Z01     Z02     Z02 V 1  1  V   Z01   Z01   6.3-5 V – Z02 – Z0l    V Z02  Z0l Z01 (+) Z02 6.3-6 Define Voltage Transmission Coefficient, V  V   V – V– V    1    V V V  V 1   Current Transmission Coefficient, I  I   I – C    1   I I  C 1 –  I– I 6.3-7 Note that P    V I  V V   C I  1   V  1    I  1  2 V  I  1    P  P   6.3-8 Three Lines in Cascade 50  Z 0l = 50  Z 02 = 100  T1 = s T2 = s + Z03 = 50  50  –V o T3 = s – (t)  = 1/3  =  V = 4/3 1/2  = –1/3  = –1/3 V = 2/3 V = 2/3  = 2/3 t, s 12 4/9 –2/9 –2/81 2/27 2/243 4/81 4/9 10 4/92 4/729 14 4/93 6.3-9 Vg t   t  n  1 V0 t       t  2nT2  T0  n 0   T0 T1  T2  T3  4/9 4/92 10 4/93 14 and so on t, s 6.3-10 (t) V g(t) System System h(t)  – Vg (t –  ) h( ) d 6.3-11 For Vg (t) = cos t ,  V0 t   cos  t     n 1        2nT2  T0  d n 0    1    n 0     n   cos  t       2nT2  T0  d n 1     cos  t  2nT2  T0  n 0    6.3-12 n    j 2 nT2 T0  V       e n 0     jT0   j 2T2   e   e   n 0   jT0 e   j 2T2 1 e  n 6.3-13 Vo ( )  49 – j2T 1– e 49 Vo ( ) max  0.5 1–19 49 Vo ( )  0.4 119 6.3-14 Vo ( ) 0.5 0.4  2T2  T2  2T2 2 T2  Junction of Three Lines  Line Li Z ne  50  6.3-15 P  Z0 = 50  00 1 Line Z0  ne Li Z0 50  50  100  6.3-16 100  50 50    100  50 250 V 1     C 1    100  C eff  C  50  100 2 12  C    3 15 6.3-17  C eff 50  C  50  100 1 6  C    3 15 Pref1  P  P 25 Ptrans2 =V  Ceff2 P 12 48   P P 15 75 6.3-18 Ptrans3 =V  Ceff3 P 12 24   P P 15 75 48 24 Note that   1 25 75 75