[Antennas] coax 'sweet lenght'

[Robert Lay]

Dear Bob Nielsen,

> On Sun, Oct 10, 2004 at 06:26:46PM -0700, Dan Richardson wrote:
> > At 04:38 PM 10/10/2004, Ron wrote:
> > >  If you want to measure the match between an antenna and it's feed
line,
> > >measure it at the antenna's feed point, to measure it 1/2 wl
(electrical)
> > >(or multiples of) away from it is the next best place to measure it.
> >
> > That is correct, however, the impedance magnitude is the same at
> > ½-wavelength (or odd multiples thereof) but, if there is a reactive
> > component, the sign will be opposite. For it to exactly be the same
> > impedance with the correct sign (angle) the feed line must be
> > one-wavelength or multiples thereof.
>
> No, it will be the same for 1/2-wavelength or multiples.  The round trip
> path (transmitter-antenna-transmitter) is one-wavelength, so what you
> measure (excluding the effect of loss) is the same as if the
> transmission line had zero length.  The magnitude (absolute value of
> impedance) is the same for any length of transmission line.

You were doing all right until your last sentence. The magnitude of the
impedance seen looking into a transmission line is NOT the same for any
length of transmission line. For example, take a  transmission line
terminated in Za (where Za > Zo) and vary the length of line over the range
from 0 length to one half wavelength. You will find that the magnitude of
the impedance seen looking into the line will vary from a value of Za  to Zo
and then to Za/2, then back to Zo and then to Za (at lengths of 1/8
wavelength, 1/4 wavelength, 3/8 wavelength, 1/2 wavelength), etc.

If you start with the load, Za, being smaller than Zo, then the results are
the same except at the 1/4 wavelength point the magnitude of the impedance
seen looking into the line will be twice Za.

For the case of the lossless and flat line (Za = Zo) the magnitude of the
impedance seen looking into the line is independant of the line length.

And yes, Danny was wrong.

Bob Lay (W9DMK), Dahlgren, VA
w9dmk at crosslink.net
Home Pages: http://www.qsl.net/w9dmk
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