Jerry R. Ehman wrote:
> . . . when you have
>two (or more) parallel conductors, distributed self capacitance and
>mutual inductance will cause the propagation of energy along those
>conductors to travel at less than the speed of light. For example, one
>table says that an open wire line (twinline) with either 1/2 inch or 1
>inch spacing using #18 conductors has a velocity factor of 95% (i.e.,
>the signal or energy is propagated at 95% of the speed of light.
If the conductors are perfect and the space around them is perfectly
empty, then the velocity of a (TEM) wave on the transmission line is
c, the speed of light in empty space -- independent of the diameter,
independent of the spacing, and even independent of the
cross-sectional shapes of the wires, as long as these properties are
uniform along the line.
For a TEM wave on any parallel-geometry transmission line, the wave
velocity is proportional to the square root of the product LC, where L
is the inductance per unit length and C is the capacitance per unit
length of the line. The characteristic impedance of the line is the
square root of the ratio L/C.
Thickening the wire increases C but reduces L by the same factor, so
that the product LC, and the velocity, is unchanged. The
characteristic impedance is reduced. Thinning the wire does not
change the velocity, but increases the impedance.
Increasing the distance between the wires increases L but reduces C by
the same factor, so that the product LC is unchanged. The
characteristic impedance is increased. And so forth.
Like you, I have seen it written that "open wire" line has a velocity
factor of about 95%. The 5% velocity reduction in this case is due to
the increased capacitance/length C caused by the dielectric spacers
(called "rungs" in "ladder line") that maintain the separation of the
wires. C is increased but L is not decreased by these spacers, so
wave velocity is reduced.
Lower-impedance (e.g., 72-ohm), closer-spaced, twin-lead tends to have
more of the space around the wires filled with solid plastic
dielectric than higher-impedance (e.g., 300-ohm), wider-spaced,
twin-lead. Therefore in practice lower-impedance twinlead has lower
velocity than higher-impedance twinlead. This is an effect of the
dielectric geometry, not of the wire spacing or diameter. With no
dielectric, or with the same dielectric geometry in both cases, 72-ohm
line would have the same velocity as 300-ohm line.
-Chuck.
Received on Wed Jun 17 1998 - 10:41:12 EDT
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