As derived, the equation for total average power at any point along the
line contains the term |fE1|^2, which is the square of the magnitude of
the forward voltage at that point. It might be more useful to replace
fE1 with a value which doesn't vary with position along the line, such
as fE2, the forward voltage at the load. The substitution is:

|fE1|^2 = |fE2|^2 * exp(2 * ax)

which gives the alternate formula

P1 = (|fE2|^2 / |Z0|) * (exp(2 * ax) * (1 - rho^2 * exp(-4 * ax)) *
cos(delta) + rho * (2 * sin(delta) * sin(2 * bx - 2 * psi)))

And, subtituting values for "forward power" and "reverse power":

P1 = fP - rP + (|fE2|^2 / |Z0|) * rho * 2 * sin(delta) * sin(2 *
bx - 2 * psi).

Roy Lewallen, W7EL


Roy Lewallen wrote:
Here's the calculation of total average power P1 at any point on a
transmission line. The point on the line is called point 1, and the
location of the load is called point 2. The distance between them is x.

. . .

= (|fE1|^2 / |Z0|) * ((1 - rho^2 * exp(-4 * ax)) * cos(delta) + rho *
exp(-2 * ax) * (2 * sin(delta) * sin(2 * bx - 2 * psi)))

Subtituting values for "forward power" and "reverse power", we have:

P1 = fP - rP + (|fE1|^2 / |Z0|) * rho * exp(-2 * ax) * 2 *
sin(delta) * sin(2 * bx - 2 * psi).
. . .