Roy Lewallen wrote in
:

For all the fluff about
photons, optics, non-dissipative sources, and the like, I have yet to
see an equation that relates the dissipation in the resistance in one
of those painfully simple circuits to the "reflected power" in the
transmission line it's connected to.


I saw the challenge and note the lack of response.

Let me offer a steady state solution.

In the case of a simple source being an ideal AC voltage generator of Vs
and an ideal series resistance Rs of Ro, and that Zo=Ro, for any
arbitrary load, at the source terminals, Vf=Vs/2, Vl=Vf+Vr=Vs/2+Vr, and
the voltage difference across Rs is Vs/2-Vr (noting that Vr is a complex
quantity and can have a magnitude from 0 to Vs/2 at any phase angle),
therfore dissipation in Rs is given by:

Prs=(Vs/2-Vr)^2/Rs where Vs is the o/c source voltage, Vr is the complex
reflected wave voltage equivalent, Rs is the source resistance.

Clearly, dissipation in Rs is related to Vr, but it is not simply
proportional to the square of Vr as believed by many who lack the basics
of linear circuit theory to come to a correct understanding.

Roy, is that a solution?

Owen