LOSSLESS TRANSMISSION LINE AND ITS CONDITION
CHARACTERISTIC IMPEDANCE ,Z0
DEFINITION I:- Z0 is defined as the ratio of the square root of series impedance per unit length ,Z to the square root of shut admittance per unit length,Ỳ
DEFINITION 2:- The characteristic impedance , Z0 of a line is defined as the ratio of the forward voltage wave ,Vfto the forward current wave ,If at any point on the line.
DEFINITION 3:- z0 IS defined as the minus of the ratio of the reflected voltage wave . Vr to the reflected current wave , Ir at any point on the line,
Characteristic impedance ,Z0 is also called Surge imperdance.
LOSSLESS TRANSMISSION LINES
A transmission line is said to be lossless if the conductors of line are perfect that is cnductivity σc=∞ and the dielectric medium between the lines is lossless that is conductivity σd=0
Condition for a line to be lossless
For loss less line,
(a) Attenuation Constant α=0
(b) Propagation constant
Also as Ỳ=(R+jωL)(G+jωC)
As R=0, G=0
Thus propagation constant Ỳ=j ω LC
(c) Phase shift constant
By comparing imaginary parts of Ỳ, we get
Phase shift constant β=ω LC
(d) Characteristic impedance,
Thus Z0 is pure reactance (that is in the form of inductance or capacitance).
(e) Phase velocity or the velocity of propagation in lossless line,
By putting value of β,we get
Thus vp=ω/ω LC