Roy Lewallen wrote:
Roger wrote:

Could you better describe how you determine that the source has a Z0
equal to the line Z0? I can guess that you use a Thévenin equivalent
circuit and set the series resistor to Z0.

Probably the simplest way is to put the entire source circuitry into a
black box. Measure the terminal voltage with the box terminals open
circuited, and the current with the terminals short circuited. The ratio
of these is the source impedance. If you replace the box with a Thevenin
or Norton equivalent, this will be the value of the equivalent circuit's
impedance component (a resistor for most of our examples).

If the driving circuitry consists of a perfect voltage source in series
with a resistance, the source Z will be the resistance; if it consists
of a perfect current source in parallel with a resistance, the source Z
will be the resistance. You can readily see that the open circuit V
divided by the short circuit I of these two simple circuits equals the
value of the resistance.

The power output of the Thévenin equivalent circuit follows the load.

Sorry, I don't understand this. Can you express it as an equation?


There seems to be some confusion as to the terms "Thévenin equivalent
circuit", "ideal voltage source", and how impedance follows these
sources.

Two sources we all have access to are these links:

Voltage source:
http://en.wikipedia.org/wiki/Voltage_source
Thévenin equivalent circuit:
http://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem

Three important observations about the ideal voltage source:

1. The voltage is maintained, no matter what current flows through the
source. Presumably, this would also mean that the voltage would be
maintained if a negative current flowed through the source. Thus, if we
set the voltage to 1 volt, the voltage would remain 1v even if we
supplied an infinite amount of power to the source.

2. The idea voltage source can ADSORB an infinite amount of power while
maintaining voltage. In this capacity, it is like a variable resistor,
capable of changing resistance to maintain a design voltage, no matter
what current is supplied to it.

3. The idea voltage source has an infinite impedance at the design
voltage, not a zero impedance as many have suggested. Zero internal
resistance is assumed to reasonably allow the ideal voltage source to
supply or adsorb current without changing voltage internally. It is not
zero impedance with the result that voltage drops to zero if external
power FLOWS INTO the ideal source.

Current flows into the ideal voltage source when the applied voltage
exceeds the design voltage. At the point the current reverses, we have
voltage/zero current, which is infinite impedance.

Two things to notice about the Thévenin equivalent circuit:

1. It contains an ideal voltage source "IN SERIES" with a resistor.
This has important implications when externally supplied voltage exceeds
the design voltage. Any returning power would not only reverse the
current flow in the ideal voltage source, it would develop voltage
across the internal series resistor. The output Thevenin voltage would
be the design voltage plus the voltage developed in the resistor.

2. The impedance of the Thevenin equivalent source would be infinite at
the design voltage because a voltage will existed from the ideal source
but current does not flow. This is true no matter what the design
impedance is for the Thevenin source.

Please notice in the link about the Thevenin circuit, a reference to a
"Thévenin-equivalent resistance". This resistance uses the ideal
voltage source set to zero. This appears to be the circuit that entered
the discussion at some point, justifying a negative 1 reflection factor.


Therefore, when the load delivers power, the Thévenin equivalent
circuit adsorbs power. Right?

Certainly, any energy leaving the transmission line must enter the
circuitry to which it's connected. Is that what you mean?

Roy Lewallen, W7EL

If the rules found in the links are acceptable, I could agree that
energy be allowed to enter the connected circuitry. I think we will
find that the returning power from a reflected wave is either completely
reflected with no change in energy, or adds to the voltage, thus
increasing the current flow and power contained in the system.

73, Roger, W7WKB