On Mar 22, 11:17*am, Roger Sparks wrote:
I think that a complex Zo would not be a transmission line, but would be an end point. *Any complex end point could be represented by a length of transmission line with a resistive termination. *Once that substitution was made, the problem should come back to the basic equations you presented here..

The characteristic impedance for a transmission line is
Zo = sqrt( (R + jwL) / (G + jwC) )

For a lossline (no resistance in the conductors, and no
conductance between the conductors), this simplifies to
Zo = sqrt( L / C )

So real lines actually have complex impedances. But the
math is simpler for ideal (lossless) lines and there is
much to be learned from studying the simplified examples.

But caution is needed when taking these results to
the real world of lines with loss.

...Keith

On Sun, 23 Mar 2008 03:42:36 -0700 (PDT)
Keith Dysart wrote:

On Mar 22, 11:17*am, Roger Sparks wrote:
I think that a complex Zo would not be a transmission line, but would be an end point. *Any complex end point could be represented by a length of transmission line with a resistive termination. *Once that substitution was made, the problem should come back to the basic equations you presented here.

The characteristic impedance for a transmission line is
Zo = sqrt( (R + jwL) / (G + jwC) )

For a lossline (no resistance in the conductors, and no
conductance between the conductors), this simplifies to
Zo = sqrt( L / C )

So real lines actually have complex impedances. But the
math is simpler for ideal (lossless) lines and there is
much to be learned from studying the simplified examples.

But caution is needed when taking these results to
the real world of lines with loss.

...Keith

Yes, I concur with these comments.

The characteristic impedance can also be found from

Zo = 1/(C*Vel)

where C is the capacitance of the line per unit distance and Vel is the velocity of the wave.

This second solution for Zo demonstrates the power storage capabilities of the transmission line over time.

But as you say, real lines also have resistance losses and other losses so use great care when taking these results into the real world

--
73, Roger, W7WKB

On Sun, 23 Mar 2008 05:10:26 -0700, Roger Sparks
wrote:

Zo =3D 1/(C*Vel)

where C is the capacitance of the line per unit distance and Vel is the vel=
ocity of the wave.

This second solution for Zo demonstrates the power storage capabilities of =
the transmission line over time.

What is old is new again.

Hasn't this "formula" been put in the ground once before? For one,
what is velocity but something that has to be computed first only to
find us refilling all the terms back into this shortcut? For two,
"power storage capabilities... over time?" Apparently the stake
missed the heart of this one.

= A0 =A 0 = A0 = A 0 Vs = A 0 =A 0 = A0 = A0 =A 0 = A0 = A 0

73's
Richard Clark, KB7QHC