Transmission Line Parameters PDF

Faraday’s Law Applications 1 1. Inductors. 2. Transformers. 3. Electrical Generators. 4. Electrical Motors. 5. Transmission Lines.  Transmission Line Parameters 2 Transmission lines are used to transmit electric energy (power distribution at low frequen...

Faraday’s Law Applications 1 1. Inductors. 2. Transformers. 3. Electrical Generators. 4. Electrical Motors. 5. Transmission Lines.  Transmission Line Parameters 2 Transmission lines are used to transmit electric energy (power distribution at low frequency) and signals (communication at high frequency) from one point to another, specially from a source to a load. Coaxial Line Two Wire Line Planar Line  Transmission Line Parameters 3 Transmission line circuit model R, L, C & G are functions of the transmission line configuration and materials  Transmission Line Parameters 4 1. Coaxial Line At Low frequencies: Resistance 1 1 Rin  / m Rout  / m c  a 2 c (c 2  b 2 )  Transmission Line Parameters 5 1. Coaxial Line Internal Inductance Ir H u 2  2a 1 1 2 we    H dv  LI 2 2 2 1 a 2 r 2 I 2 I 2 we     rdrd dz  z 0 r 0  0 8 a 2 4 16  Lin  H /m 8  Transmission Line Parameters 6 1. Coaxial Line Inductance I I H u B  u   N  B.ds 2r 2r 1 b I I b    drdz  ln z 0 r  a 2 r 2 a   b L L ln H /m I 2 a  Transmission Line Parameters 7 1. Coaxial Line Capacitance Q E ur 2rL b Q Q b Vab   dr  ln r a 2rL 2 L a Q 2 C C F /m V ln b a LC    Transmission Line Parameters 8 1. Coaxial Line Conductance E Q ur R  E.dl  V ab  1 2rL   E.dS I L G Q b Vab  ln 2 L a 2 L Q Q 2 C  IL     rd dz  G /m  2rL  ln b G   0 z 0 a  Transmission Line Parameters 9 2. Two Wire Line At Low Frequencies: Resistance 2 R / m c  a 2  Transmission Line Parameters 10 2. Two Wire Line Inductance I I H u B u 2r 2r 1 d I I d 12    drdz  ln z 0 r  a 2r 2 a  d L12  ln H /m 2 a  Transmission Line Parameters 11 2. Two Wire Line Inductance L1  L12  L1in  Lin  8 1 d L1  (  2 ln )107 2 a 1 d L1  (  ln )2107 4 a 7 d L1  210 ln 1/4 ae  Transmission Line Parameters 12 2. Two Wire Line Inductance d 7 L2  210 ln 1/4 ae d 7 Lcircuit  L1  L2  410 ln 1/4 ae 7 d Lcircuit  410 ln a' H / m a '  ae0.25  Transmission Line Parameters 13 2. Two Wire Line Capacitance  d L12  ln LC   2 a 2 C12  F /m ln d a Conductance C  2  G12  /m G  ln d a  Transmission Line Parameters 14 3. Planar Line At High Frequency: 2 b d b R / m C  F /m L H /m G /m b d b d   skin depth  Transmission Line Parameters 15 4. Power Lines (single-phase and three-phase)