On Thu, 29 Mar 2007 22:20:48 GMT, Owen Duffy wrote:

Walter Maxwell wrote in
:

...
voltage and current values of rho at the matching point which produces
either a virtual short or a virtual open circuit that causes the
re-reflection. I have shown this to be true in my QEX article of
...

Walt,

I am talking about the steady state.

Hi Owen, so am I. The value of (Vf+Vr)/(If-Ir)= Zi is the result of the convergence of all reflected waves.

I see discussion about this need for total re-reflection at the source,
and some even describing the function of an ATU as a "total re-
reflector", and it makes me wonder why we are grappling with re-
reflection at the source end of the line in the steady state.

If we don't consider re-reflected waves at the source end of the line the source is never going to deliver all
of its available power.

My understanding is that:
1. The ratio of elecric field to magnetic field per unit length (or V/I)
in an infinite transmission line is constrained by the geometry of the
line and the permeability and permittivity of the components carrying the
two fields. That ratio is expressed as Zo.
2. If a wave with V/I=Zo reaches the end of the line, and the load does
not permit V/I to be Zo (ie a mismatch), a reflected wave is launched,
and it is of magnitude and phase such that (Vf+Vr)/If-Ir)=Zl (all complex
values).

This is true.

In the steady state, after all has settled (ie converged), the
transmission line reaches an equilibrium where the source V/I
characteristic is consistent with (Vf+Vr)/If-Ir) at the input end of the
line.

Not yet. There is more to be done.

Why is it necessary to complicate the analysis with tracking multiple re-
reflections, potentially an infinite number of reflections of diminishing
significance, an analysis that converges in the limit on the answer given
by the solution of the source V/I characteristic and (Vf+Vr)/If-Ir) at
the input end of the line (which is the equivalent input impedance). Note
that (Vf+Vr)/If-Ir) at the input end of the line is determined solely by
the tranmission line propagation constant, length, Zo and the far end
load impedance, for avoidance of doubt, source impedance is not
relevant.

Without inserting some sort of matching device between the source and the line input for causing re-reflection
of Vr and Ir, (Vf+Vr)/(If-Ir) will not equal source V/I, and consequently the source will not deliver all its
available power. When Vr and Ir are caused to be re-reflected in phase with Vf and If, respectively, the
source will deliver all its available power, because the line-input Z will now equal source Z = V/I.
Therefore, the source impedance is totally relevant.

The matching device that causes Vr and Ir to be re-reflected is either a virtual oc or a virtual sc, which is
produced by adjustment of the device that orients the appropriate relationship between the forward and
reflected voltages and between the forward and reflected currents.

Such an approach does not require invention of virtual re-reflectors or
virtual s/c or o/c, or ATUs or pi couplers with virtual properties.

Well Owen, then how do you explain re-reflection at the souce in the absence of z virtual sc or oc?

Walt