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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.