RadioBanter - View Single Post

Cecil Moore · August 27th 06, 07:36 PM posted to rec.radio.amateur.antenna

wrote:
I've come around to that conservation of energy stuff ;-)

I'm glad - most folks here ignore it. :-)

I understand that your argument involves the energy that enters the
line before it knows anything about the load, the energy that enters in
an initial transient, but unless you can show that nothing happens
during the initial transient to deliver some or all of that initial
energy to the load, your argument has a hole.

Let's return to the one second long lossless transmission line.
From a 100 watt transmitter, at the end of second number one,
the line will contain 100 joules and the load will have accepted
zero joules. Since the load is rejecting 1/2 of the incident energy,
at the end of the 2nd second, the source will have supplied 200 joules,
there will be 150 joules of energy in the line, and 50 joules will have
been accepted by the load. If the source is equipped with a
circulator+load, this is steady-state with 150 joules of energy stored
in the transmission line.

At t=0:
zero joules zero joules
100w--------one-second long feedline------load rho^2=0.5
Pfor=0-- --Pref=0 Pload=0

At t=1:
100 joules zero joules
100w--------one-second long feedline------load
Pfor=100w-- --Pref=0 Pload=0

At t=2:
150 joules 50 joules
100w--------one-second long feedline------load
Pfor=100w-- --Pref=50w Pload=50w

You're presupposing that there is some energy that enters the line
during an initial transient that cannot leave until you shut the source
off, so you get the 100J related to the 100W net power flow and 100J
that went into the line before the source knew about the load.. and
then there's another 100J that enters somehow? I guess to set up the
reflected wave?

Yes, at the end of the 2nd second, the source has supplied 200 joules
and the load has accepted 50 joules. That leaves 150 joules left over
that cannot be any place except in the line according to the
conservation of energy principle. In a circulator+load system, we
have reached steady state with 150 joules in the transmission line
that will not reach the load until after the source is powered down.

The argument is circular.

Proving that confusion exists. It's actually not circular. It's
based on cause, effect, and the conservation of energy principle.
I apologize if I have not explained it in a way that is easy to
understand. Please bear with me.

It's all linear cause and effect. With an ideal auto-tuner
at the source, none of the reflected energy is accepted back by
the source. Half the energy incident upon the load is rejected. There
is no other place for the extra energy to be except inside the
transmission line. I have an EXCEL spreadsheet that might help you
sort all of this out. A copy of its output is available at:

http://www.qsl.net/w5dxp/1secsgat.gif
--
73, Cecil http://www.qsl.net/w5dxp