On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote:

Hi Walt,

1: The input impedance of a lossless half-wave (180°) transmission line
There are two parts to the following statement:
terminated in a physical short circuit is zero ohms, a short circuit,
which is the causal relationship;
but a VIRTUAL short circuit because it was achieved only by the interference
between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to
the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short
terminating the line.
this is the correlationship.

Without the cause, there is no correlation.

There is nothing to be disputed beyond that.

The reflected current wave on return to the input encountered no phase change during its
travel, thus the current reflection coefficient is in phase with that of the source current, allowing the
short circuit to occur.

Allowing, as a verb, suggests causality. The cause is established in
the short. All intermediary apparatus merely maintain the
correlation. There is nothing to be disputed beyond that.

2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open
circuit
which is the causal relationship;
is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the
interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°)
returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open
circuit terminating the line.
this is the correlationship.

The current reflection coefficient occurs in the same manner as with the
half-wave line above.

It is merely the correlation to an existing, physical open without
which the VIRTUAL short circuit would disappear. All intermediary
apparatus merely maintain the correlation. There is nothing to be
disputed beyond that.

These two examples can be confirmed by referring to any reputable text concerning transmission line theory.
There is nothing to be disputed beyond that.

The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the
current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be
found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both
physical and virtual short or open circuits placed on a transmission line can cause reflections.

And here we get to the nut of the matter - causality. It is already
established that either the physical short, or physical open, whose
absence would render any correlation invalid, dominates the action.
The proof follows the quality of the physical open or the physical
short. A poor physical open or poor physical short will never be
improved by ANY transmission line mechanics. On the other hand, poor
transmission line mechanics will never deliver the action of the best
physical short or the best physical open.

We have thus proved that the virtual short circuit established at the stub point is actually performing as a
real short circuit.

There is nothing to be disputed beyond that. This is not, however, a
proof that the VIRTUAL short (or open) is the cause.

This may appear to be a criticism of semantics (English to some).
However, engineering relies on a far stricter degree of meaning than
most endeavors. Correlation is not Causality is one particular
admonition that comes to mind from the field of logic. It applies
here too.

Walt, it seems to me that you have a need to distinguish VIRTUAL from
physical for reasons other than the transmission line mechanics of
combining loads (or as I distinguished in other threads, routing
energies). A VIRTUAL short or open is metaphor, and it is an useful
metaphor for describing systems. What I see beyond these examples you
have provided are statements (in other discussions) that tend to
confer a reality to the VIRTUAL which is obviously a contradiction on
the face of it. Other than that, there is absolutely nothing in your
published work that is in dispute.

73's
Richard Clark, KB7QHC