Keith Dysart wrote:
Actually, the transmission line input impedance is quite real,
formed from distributed capacitance and inductance. Like most two
terminal circuits, it can be reduced to simpler form.

I didn't say virtual impedances are not real. I
said they are not causes of anything and are,
instead, effects of superposition incapable of
causing anything in the complete absence of a
physical impedance.

You have for a long while now, confused cause
and effect. Maybe you should review the three
separate definitions of "impedance" given in
the IEEE Dictionary.
--
73, Cecil http://www.w5dxp.com

On Apr 9, 9:40*pm, Cecil Moore wrote:
Keith Dysart wrote:
Actually, the transmission line input impedance is quite real,
formed from distributed capacitance and inductance. Like most two
terminal circuits, it can be reduced to simpler form.

I didn't say virtual impedances are not real. I
said they are not causes of anything and are,
instead, effects of superposition incapable of
causing anything in the complete absence of a
physical impedance.

But the distributed capacitance and inductance
are physical impedances.

You have for a long while now, confused cause
and effect. Maybe you should review the three
separate definitions of "impedance" given in
the IEEE Dictionary.

Neither 'virtual impedance' nor 'impedance, virtual'
are in the dictionary (at least the 7th Edition).

...Keith

Keith Dysart wrote:
But the distributed capacitance and inductance
are physical impedances.

But they are constant, i.e. there is no physical
impedance *discontinuity*. The reflection coefficient
inside a homogeneous piece of transmission line is
(Z0-Z0)/(Z0+Z0)=0, i.e. there can be no reflections.
The reflection coefficient in free space is
(1.0-1.0)/(1.0+1.0)=0, i.e. there can be no reflections
in free space.

Neither 'virtual impedance' nor 'impedance, virtual'
are in the dictionary (at least the 7th Edition).

"Virtual" essentially means that no physical impedor
exists. The virtual impedance definition is covered
by definition (B), the ratio of voltage to current
which *causes* the impedance. A virtual impedance
is an *effect*, not a cause.
--
73, Cecil http://www.w5dxp.com

On Apr 10, 7:52*am, Cecil Moore wrote:
Keith Dysart wrote:
But the distributed capacitance and inductance
are physical impedances.

But they are constant, i.e. there is no physical
impedance *discontinuity*. The reflection coefficient
inside a homogeneous piece of transmission line is
(Z0-Z0)/(Z0+Z0)=0, i.e. there can be no reflections.
The reflection coefficient in free space is
(1.0-1.0)/(1.0+1.0)=0, i.e. there can be no reflections
in free space.

Neither 'virtual impedance' nor 'impedance, virtual'
are in the dictionary (at least the 7th Edition).

"Virtual" essentially means that no physical impedor
exists. The virtual impedance definition is covered
by definition (B), the ratio of voltage to current
which *causes* the impedance. A virtual impedance
is an *effect*, not a cause.

The transmission line definitely falls into
definition (C), "A physical device or combination of
devices whose impedance as defined in definition (A) or
(B) can be determined." The TL is a combination of
devices, a lot of very small ones, and its impedance
can be determined.

Using 26 pf/ft as a representative value for
RG-58, dividing the 45 degree section into 45
pieces, applying the normal rules for parallel and
series circuit elements, the impedance at the
entry to the line is trivially (using Excel) calculated
to be 50.443 /_ 90. Subdividing into smaller
elements would increase accuracy. If I could remember
my calculus, the exact answer could be derived.

There is no need for forward or reflected waves
at all; just basic AC circuit theory.

...Keith

Keith Dysart wrote:
There is no need for forward or reflected waves
at all; just basic AC circuit theory.

Now do it in free space. EM waves are EM waves
no matter what the medium.
--
73, Cecil http://www.w5dxp.com