70929

V^{1 2}

1

2r

s

MO

²o

lOge

A

b

a

!

(2.94)

We notę that the the second pair of factors amounts to n/(2n) which has a value of approximately 60 ohms. Most of the practical dielectric materials for the making of coaxial

transmission lines have relative dielectric permittivities of the order of 2.25 of which the

square root is 1.5, so the first factor is about (2/3). The logarithm function is commonly

greater than unity but is a slowly varying function of its argument. Hence the overall function never deprts much from 50 ohms. Values from 50 to 90 ohms are practical to

maunfacture, but values outside this rangę are diffiult to achieve with common

materials

and geometries.

The complex propagation constant is a+jp= VY Z = ju)VLC (2.95)

This shows that firstly there is no attenuation, not surprising in the light of the fact that we assume there are no losses, and that the velocity c = u>/(3is c =

1

VLC

1

Vpe • (2.96)

This result is independent of frequency, and equal to the velocity of light in the medium

of parameters pand e. Common values of erare 1 and about 2.25.

2

Losses R and G in coaxial lines we will discuss in a later chapter; however, we say now that R depends on frequency and G is generally negligible.

The reason for asserting that the resistance depends on frequency is closely related to our original assumption that the currents flow on the surface, but can only be fully explained in Chapter 9.