Transmission Lines Input Impedance
-
Upload
zesi-villamor-delos-santos -
Category
Documents
-
view
228 -
download
1
Transcript of Transmission Lines Input Impedance
-
7/25/2019 Transmission Lines Input Impedance
1/18
Input ImpedanceJesi V. Delos Santos
Tobi Roque B. Santamaria
-
7/25/2019 Transmission Lines Input Impedance
2/18
What is Input Impedance
or Z(input)
Impedance presented to the transmitter tothe transmission line and its load antenna
Or simply the line impedance seen at thebeginning of the transmission line
-
7/25/2019 Transmission Lines Input Impedance
3/18
What is Input Impedance
The input impedance of any length of a
uniform transmission line terminated in its
characteristic impedance (non reflectively)is equal to the characteristic impedance of
the line.
-
7/25/2019 Transmission Lines Input Impedance
4/18
Recall
What is a Matched Line? r = 0
A transmission line whose characteristic
impedance is the same as its terminations.
In this manner, there is complete
absorption of the incident power, and there
are no wave reflections back to the
source.
Also called matched transmission line, or
matching line.
-
7/25/2019 Transmission Lines Input Impedance
5/18
Recall
What is a Mismatched Line?
Simply not a Matched Line
Its impedances are not equal
There is a reflection
If open( r = 1) if shorted( r = -1)
-
7/25/2019 Transmission Lines Input Impedance
6/18
Lossy
LosslessLossless case (=0, =j, tanh(l) = jtanl)
Input Impedance Formula
tanh
tanh
0
0
0
L
Lin
ZZ
ZZZZ
tan
tan
0
0
0
L
Lin
jZZ
jZZZZ
Recall:
tanh(jA) = jtanA
-
7/25/2019 Transmission Lines Input Impedance
7/18
Short-Circuit/Open-Circuit
Short Circuit Line
-
7/25/2019 Transmission Lines Input Impedance
8/18
Open Circuited Line
-
7/25/2019 Transmission Lines Input Impedance
9/18
Short-Circuit/Open-Circuit
For a line of known length l, measurements of its input impedance,
one when terminated in a short circuit and another when terminated
in an open circuit, can be used to find its characteristic impedance
Z0 and electrical length
-
7/25/2019 Transmission Lines Input Impedance
10/18
Special Line Cases
Recall for Lossless
Half-wave section in a lossless case(l=/2, l=):
Quarter-wave section in a lossless case(l=/4, l=/2):
tan
tan
0
0
0
L
Lin
jZZ
jZZZZ
Lin ZZ
L
in
Z
ZZ
2
0
-
7/25/2019 Transmission Lines Input Impedance
11/18
Problems(lots of problems)
1. A 50- lossless transmission line is
terminated with a load impedance of
25+75. What is the input impedance at a
distance of 5 from the load?
Ans: 25 + j75
-
7/25/2019 Transmission Lines Input Impedance
12/18
Problems(lots of problems)
2. Find the input impedance in ohms for a
50 lossless transmission line, 3.5 long, if
the load is 20 +j75.
Ans: 20 + j75
-
7/25/2019 Transmission Lines Input Impedance
13/18
Problems(lots of problems)
3. A radio transmission line of 300
impedance is to be connected to an antenna
having an input impedance of 150 . What
is the impedance of a quarter-wavematching line?
Ans: 212
-
7/25/2019 Transmission Lines Input Impedance
14/18
Problems(lots of problems)
4. A section of low-loss transmission line is
0.40 wavelengths long and is terminated in a
short circuit. Its characteristic impedance is
73 + j0 . The frequency of operation is 200Mhz. Determine the input reactance of the
line section, and the value of inductance or
capacitance to which it is equivalent.Ans: ZinSC = -j53.4, C = 14.9pF
-
7/25/2019 Transmission Lines Input Impedance
15/18
Problems(lots of problems)
5. A 6-m section 150- lossless
transmission line is terminated in a load ZL =
(150 j50) , determine its input impedance
if = 0.4/m.
Ans: 115.70 + j27.42
-
7/25/2019 Transmission Lines Input Impedance
16/18
Problems(lots of problems)
6. A 50- lossless line is terminated in a
load impedance ZL = (30 j20) . Find the
input impedance if it is .33 long.
Ans: 102 + j2.54
-
7/25/2019 Transmission Lines Input Impedance
17/18
Problems(lots of problems)
7. A 75- resistive load is preceded by a /4
section of a 50- lossless line, which itself is
preceded by another /4 section of a 100-
line. What is the input impedance?
Ans: 300
-
7/25/2019 Transmission Lines Input Impedance
18/18
Problems(lots of problems)
8. A lossless transmission line of electrical
length l= 0.35 is terminated in a load
impedance as shown in Fig. Find Zin.
Ans: 64.8 + j38.3