**Definition DISTORTIONLESS LINE**

**A transmission line** is said to be distortionless when attenuation constant ‘α’ is frequency independent and the phase shift constant ‘β’ is linearly dependent on the frequency.

**Condition for line to be distortionless**

** **R/L=G/C

(a) **Propagation constant**

Ỳ= (R+jωL)(G+jωC)

Or Ỳ= RG(1+jωL/R) (1+jωC/G)

If R/L=G/C

Put value of R/L in equation of Ỳ

Thus Ỳ= RG(1+jωC/G)(1+jωC/G)

Or Ỳ= RG(1+jωC/G)

Also Ỳ=α+jβ

Comparing Real and Imaginary parts, we get

α=RG

and jβ= RGjωC/G

=jω RC/G

Or β=ω L/C C (R/G=L/C)

Thus β=ω LC

The above results show that α is frequency independent and β is frequency dependent

(b) **Characteristic impedance**

** **Z_{0}= √R+jωL/G+jωC

Z_{0} =R/G=L/C

(c) **Phase velocity:-**

** **V_{p}=ω/β

Substituting value of β in above expression,we get

V_{p}=ω/ω LC

Thus v_{p}=1/ LC

Note: If you do not know about the basics of transmission line then please read the article transmission line and its types.

Last time I have also discussed the lossless transmission line and its condition.