# 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

Z0=Z/Y =R+jωL/G+jωc

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.

Z0=Vf/If

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,

Z0= -Vr/Ir

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

R=0=G

For loss less line,

(a)    Attenuation Constant       α=0

(b)   Propagation constant

Ỳ=α+jβ=jβ                                               (α=0)

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,

Z0=R+jωL/G+jωc

As                                          R=0=G

Z0=L/C

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,

Vp=ω/β

By putting value of β,we get

Thus                          vp=ω/ω LC

Or                                      vp=1/LC