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Old March 2nd 07, 04:33 AM posted to rec.radio.amateur.antenna
Owen Duffy Owen Duffy is offline
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First recorded activity by RadioBanter: Dec 2006
Posts: 1,169
Default The power explanation

Owen Duffy wrote in
:

As an exercise, think of a generator that has a Thevenin equivalent of
some voltage V and a series impedance of R+j0, connected to a half
wave of lossless transmission line where Zo=R. To give a numerical
example, lets make V=100 and R=50, so Vr=50 and "reflected power"=50.
How much of the "reflected power" is dissipated in the generator. In
this case, the generator dissipates less heat than were it terminated
in 50 ohms.


Ok, the solution:

Lets examine the matched load scenario for a start, the 100V generator
with 50 ohms internal resistance and a matched 50 ohm load. The current
is 100/(50+50) or 1A, the power in the load is 1^2*50 or 50W, the power
dissipated in the source is 1^2*50 or 50W.

No lets look at the scenario with the o/c half wave lossless line
attached to the generator. In the steady state, current from the
generator is zero, dissipation in the generator is 0^2*50 or 0, voltage
at the generator terminals and at the o/c (load end) of the line is 100V.
At the o/c load end, the complex reflection coefficient is 1, so Vf=50V,
Vr=50V and "reflected power"=50^2/50 or 50W.

But, wait a minute, there is 50W of "reflected power" on the line, the
line is matched to the source, and there is zero dissipation in the
source, less than when it has a matched load.

Don't take anything above to mean that I represent that a simple linear
model is a good representation of a transmitter PA.

This simple example that shows that existence of "reflected power" on a
transmission line does not necessarily result in some or all of the
"reflected power" being dissipated in the generator.

I will leave it to Cecil to take to confuse this simple example with some
photon based complication.

Owen