Transmission Lines Input Impedance

7/25/2019 Transmission Lines Input Impedance

1/18

Input ImpedanceJesi V. Delos Santos

Tobi Roque B. Santamaria


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


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.


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.


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)


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


7/18

Short-Circuit/Open-Circuit

Short Circuit Line


8/18

Open Circuited Line


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


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


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


12/18


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


13/18


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


14/18


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


15/18


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


16/18


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


17/18


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


18/18


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

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Transmission Lines Input Impedance