In the numerical example I posted, I calculated the average real power
incident at the load (that is, the power calculated from the forward
voltage and current waves), and the average real reflected power at the
load (that is, the power calculated from the reverse voltage and current
waves). The "reflected power" is greater than the "incident power".
However, the net power exiting the line and entering the load is a
positive value. That's because the net power isn't equal to the "forward
power" minus the "reverse power" at that point. I gave the equation for
total power in that analysis, and if you plug in the numbers, you'll see
that the total power is correct.

If you are interested in calculating the "reactive power" for some
reason, you can easily do so from the complex voltages and currents
which have been calculated for you.

And for those who are wondering about your question, the absolute value
of a complex number is the magnitude of that number. In the example I
gave, all the complex values were given in polar form, with the first
part being the magnitude.

Roy Lewallen, W7EL

Cecil Moore wrote:
Cecil Moore wrote:

Some people here seem to incorrectly think you can
have a return gain with a passive network...


Does anyone remember what is the absolute value of a
complex number?


Found the answer in, "Higher Mathematics for Engineers and Physicists".
I suspect the square of the absolute value of the voltage reflection
coefficient is the volt-amp reflection coefficient, not the power
reflection coefficient.

With a complex characteristic impedance, what is being reflected is
volt-amps. I suspect the reflected volt-amps can be higher than the
incident volt-amps. I seriously doubt that the reflected watts
can be higher than the incident watts. The correct *power* reflection
coefficient therefore may be something like |Re(rho)|^2 where 'Re'
means "the real part of". The simpler |rho|^2 may be the volt-amp
reflection coefficient when Z0 is complex.

Using deductive reasoning, since the real part of the voltage
reflection coefficient cannot be greater than 1.0, it seems to
me that |1.0|^2 may be the maximum power reflection coefficient.
The complex voltage reflection coefficient squared may be the
volt-amp reflection coefficient which can be greater than 1.0.

In a transmission line with a complex characteristic impedance, the
reflected voltage and reflected current would not be in phase.
Therefore, their product would be volt-amps, not watts. Reflected
watts could be obtained from Vref*Iref*cos(theta) which would always
be less than (or equal to) Vref*Iref.