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Radiating Systems
EE-402
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Non Resonant Transmission Line :
The Conce t of Travelin DC
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Waves
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A non-resonant transmission line can be
defined as a line of infinite length OR that has
been terminated properly thru a resistorhaving value exactly equal to the
characteristic im edance of the line.
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This is also called properly terminated line.
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Such a line offers complete absorption of powerthat is sent thru its transmitting end to its load end.
This power is absorbed by the load resistance andany inherent resistance in the line.
The volta e and current waves in such a line are
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called the Traveling Waves and they move in phasewith one another from the source to the load end.
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Since a non resonant line can be an infinite
length line or a line that has a finite length
but that is terminated properly, the physical
length is not important.
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In its counterpart, i.e the resonant line,physical length is quite important.
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Consider the following diagram of a properly
terminated line:
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Consider the instant S1 is closed.
Immediately a voltage is developed across L1
that offers initial restriction in the currentflow, adhering to its nature.
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.
After some time, current starts to flow thru
L1 and C1 begins to charge.
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After some more time, C1 is fully charged and
the voltage across ab now appears across cd. At the same time, voltage is developed across
L2 n ft r m tim rr nt in th n
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loop starts to flow as the capacitor C2 begins
charging thru L1 and L2.
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After sometime, C2 will also charged to the
supply DC voltage and voltage across ef will
also be equal to voltage across cd.
The ammeter shall continuously indicate
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c arg ng curren as e capac ors o a eloops keep on charging.
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When all the capacitors shall be charged, theammeter will still be showing current as the
conductive loop will be completed thru the
resistor.
This current shall continue to flow as long as
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the switch S1 is closed. As soon as it is opened, this current shall stop
flowing.
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When the switch is closed, the capacitors
shall discharge thru the load resistor in the
same manner as they were charged.
Can you call the voltage transfer from the
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source to t e oad end Trave ing Vo tage
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The Circuit..
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The Waveform
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As obvious, the change of voltage (i.e the
building of positive voltage at the generator
end) reaches point A at T3.
It reaches point B at T5 and finally point C
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at T7. The sequence shall be repeated for all the
voltage levels of the alternating voltage
waveform.
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The time for the signal to reach the load end
where the line has been properly terminatedcan be calculated by the formula:
t=LC.
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The validity of this equation shall remain the
same no matter whether the signal is AC or
DC.
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So all of the instantaneous voltages that are
produced at the generator travel down the
line in the same sequence in which they aregenerated.
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point along the line, the resulting waveform
will be a duplicate of the generator
waveform.
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As the line is properly terminated, all the
power shall be absorbed by the load end and
there will not be any reflections of the un-absorbed power in the line.
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A resonant transmission line can be defined
as a line that has not been properly
terminated with a resistor having equal value
as of its characteristic impedance.
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In suc a case, un i e t e non-resonanttransmission line, the line length is critical.
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In certain cases such a line is terminated as
either a short circuit or an open circuit and
this sets some very interesting properties ofthis line.
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DC Applied To an Open Circuited
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Line
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A transmission line of finite lengthterminated in an open circuit is shown below:
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The sequence of events shall be the same.
As soon as the switch is closed, the capacitors
of the loops shall get charged thru their
respective inductors and as a result the
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app e vo age wou appear as s
traveling from the source end to the open
circuited load end.
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As the voltage reaches point c, the inductor L3
is placed between point c and g.
Obviously the voltages shall be equal at point cand g.
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inductor L3.
No current flow means the magnetic field across
the inductor L3 must collapse.
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Now the inductor opposes any change in the
current flow, hence it would oppose thischange in current flow due to collapsingmagnetic field.
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The open capacitance C3 would thus beprovided with additional charge thru theinductor which tend to oppose the seizure of
current due to equipotential points c and g.
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Since the energy stored in the magnetic field
is equal to the energy stored in the capacitor,the charge on the capacitor gets doubled.
This doubling of charge will eventually
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double the voltage across the capacitor C3. This sequence would follow backwards now.
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As a result capacitors C2 and C1 will also get a
voltage that is doubled as compared to the
applied voltage.
This effect would reach the source end and
would double the volta e there.
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This voltage movement in the opposite
direction is called reflection.
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This reflection occurred in the same polarity
as of the original charge. Hence it could be concluded that the
r fl ti n fr m n n ir it lin will
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always be of the same polarity and amplitudeas of the original incident voltage wave.
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When this reflected voltage reaches the
source, the action stops because of the
cancellation of the voltages. The current however, is reflected back but
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field across the inductor collapsed, thecurrent dropped to zero.