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S TANDING W AVES
When the load is matched,
and
and the line is flat. However, mismatches of the load
resulting in reflected waves leads to the formation of standing waves, where the magnitude of the
voltage on the line is not constant.
Thus, the
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S HORT C IRCUIT T ERMINATION C ASE
In this case,
This means that the voltage and current on the line are:
What we find is that the current is at a maximum at the load (as is
expected for a short circuit), and the voltage is 0.
To find the input
Edmund Li
G ENERAL T RANSMISSION L INE E QUATIONS (L UMPED ELEMENT
CIRCUIT MODEL )
Although the schematic representation of a
transmission line is a two wire line, in understanding
the transmission line effects, we can subdivide the
transmission line into
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MATCHED IMPEDANCES
A DMITTANCE S MITH C HARTS
An impedance Smith Chart can be used for normalized admittances, where
(conductance) and the circles become circles (susceptance).
circles become
circles
The transmission line is said to be matched t
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A DMIITANCE ON THE S MITH C HART
The smith chart can also be used for normalized admittances. It can be used to convert between
impedance and admittances based on the fact that in normalized form, the input impedance
of a load
connected to a lin
Edmund Li
S LOTTED T RANSMISSION L INE
The slotted line is an instrument used to measure the unknown
impedance of a load , although vector network analysers have gained
more popularity with technological developments.
A slotted line is a transmission line
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1.
2.
3.
Marking the normalized load admittance and drawing the corresponding S circle.
Draw the g=1 circle, which is also the
circle.
Find the two points of intersection (which tend to be complex conjugates)
4.
Determine the load transmission l
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THE LOSSLESS TRANSMISSION
LINE
In many practical cases, the loss of the line is very small and can be neglected such that
thus, the propagation constant becomes:
and
Since:
In the lossless case the characteristic impedance is a real number,
And
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T IME A VERAGE P OWER
The average power along the transmission line at point z is given by:
Which simplifies to:
Which consists of the incident power delivered to the load minus the reflected power
.
thus
plays a big role in determining the amou
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Example
. The slotted line method was used to find the unknown load impedance.
A short circuit was initially placed at the load resulting in
minima as shown in the first figure at z=0.2, 2.2, 4.2 cm
The short circuit was replaced with an unknown
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A PPLICATIONS OF S HORT C IRCUITED & O PEN C IRCUITED TL
N E T W O R K A N A LY S ER
The network analyser is an instrument that can measure the impedance of any load connected to its input
terminals after calibration.
When used to measure the in