I have not followed the whole thread, but at the bottom line, the impact
of a complex Zo on power is an attenuation factor. It can be shown as
follows.

The general equations a

Vf = [[(R+jwL)/(G+jwC)]^0.5]*If

Vr = [[(R+1wL)/(G+jwC)]^0.5]*Ir.

A numerical example for typical 50 ohm cable at 30 MHZ follows:

Assume C = 30E-12 F/ft. Therefore L = 0.075E-6 H/ft [50 ohm lossless].

Assume 1/R [G] 1E-8 [100 megohms][lossy dielectric]

Finally, assume R = 10 ohm [moderate rf resistance].

The resulting Zo for the assumed conditions is
[[(10+jw7.5E-8)/(1E-8+jw30E-12)]^0.5] ohms.

|Zo| = [[(10+j14.137)/(1E-8+j0.00565)]^0.5] = 55.360 ohms.

Determine the relative phase shift as follows:

atan[10+j14.137] = 54.7257 degrees.

atan[1E-8+j0.00565] = 89.99989859 degrees [approximately 90].

The relative phase shift for the assumed complex Zo at 30 MHZ is 54.7257
- 89.99989 degrees [35.274 degrees].

Result: Zo = 55.360 ohms @ 35.274 degrees.

Therefore Vf = If*[55.360 degrees]

Therefore Pf(load) = Vf(source)*If(source)*cos(35.274) = 81.63% of maximum.

The transmission line does not care if the signal is left to right or
right to left; or forward and reflected. The effect is to introduce a
mirror image to both the Vr and Ir terms.

I hope I have not been redundant to other posts on this thread!

Deacon Dave, W1MCE