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Old March 15th 07, 06:38 PM posted to rec.radio.amateur.antenna
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First recorded activity by RadioBanter: Dec 2006
Posts: 1,169
Default One word answers...


Lets escape from mixed analysis of VSWR in transient scenarios.

Visualise a series circuit of a battery of 100V and negligible internal
resistance, a 100 ohm ideal resistor, and an open switch. This circuit is
connected to a lossless (ie ideal) transmission line with surge impedance
(or characteristic impedance, Zo) of 100 ohms which is open circuit at
the far end. It takes T seconds for a wave to travel from one end of the
line to the other.

The scenario is a source impedance matched to the transmission line, with
unmatched load.

When the switch is closed, current flows into the line. Until t=2T
seconds, the current If that flows into the line equals 100V/(100+100
ohms) = 0.5A, during which time the resistor dissipates heat at the rate
of I^2*R = 100W. The voltage of the wave Vf travelling from the source is
I*Zo = 50V. This situation is constant until t=2T seconds.

At precisely t=T seconds, the wave travelling from the source end reaches
the open end of the line, and a reflected wave is established to satisfy
the conditions that I at the end of the line must be zero. The reflected
wave must have current equal and opposite to the forward wave, so Ir=-If,
the negative sign indicates that the wave travels in the opposite
direction. Considering the reflected wave, Vr=Zo*Ir = 50V, so the total
voltage at the o/c end is Vf+Vr = 50+50 = 100V.

At precisely t=2T seconds, the reflected wave reaches the source end of
the line, and the voltage at the line terminals instantly becomes Vf+Vr
or 100V. At that instant, the current from the source falls to zero, and
the dissipation in the source resistor also falls to zero. This situation
continues indefinitely.

My questions a

How much of the energy that was contained in the reflected wave was
dissipated in the source resistor?

Does existence of a reflected wave necessarily increase dissipation in
the equivalent source resistance?

Is the reflected wave necessarily absorbed (or partly absorbed) by the
equivalent source resistance?

Are the principles that apply to this example inconsistent with the
general case (eg dc, ac, transient, steady state etc)?

One word answers should be sufficient.

Owen
 
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