082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

582 Chapter 19 Ordinary differential equations I
Case3: ρ(l)=0
Consider now the case in which the load impedance is equal to the characteristic
impedance, thatis
Z L
=Z 0
This time, ρ(l) = 0 and hence v(z) = v 1
e −jβz . The magnitude of this complex
exponential is shown plotted in Figure 19.13 and is a horizontal straight line with
|v(z)| = 1 for all values ofz.
y(z)
2
1
0
2 4 6 8 10 z
Figure19.13
Voltage onatransmissionline with a reflection coefficient of ρ(l) = 0.
No standing wave component is present and the line is said to be matched. This
is the ideal case for power transfer because it represents the case in which all of the
input wave isdelivered tothe load and nothing isreflected back.
Case4:ageneralcase
Oftenitisdifficulttoarrangeforaperfectlymatchedtransmissionline.MoregenerallythepeakvoltageonthelineappearsliketheoneshowninFigure19.14.Herean
assumed reflection coefficient of ρ(l) = 0.187 −j 0.015 isused.
y(z)
2
1
0
2 4 6 8 10 z
Figure19.14
Voltage onatransmissionline with a reflection coefficient of ρ(l) = 0.187 − j0.015.
The standing wave component is still present although it is of smaller magnitude
than seen for the open- or short-circuit loads. Most of the input wave is transferred
tothe load but a proportion isreflected back and interferes.
The standing wave pattern of a transmission line can be measured by a special
piece of apparatus known as a slotted line. The device consists of a length of transmissionlinewithaslotintowhichasmallprobeisinserted.Theprobeisusedtofind
thevoltageasafunctionofdistanceasitismovedalongthelinetowardsanunknown
load. The equations presented above can be used with the results of the slotted line
experiment todetermine the reflection coefficient ofthe load.