[Antennas] coax 'sweet length'

Mon Oct 11 12:10:05 EDT 2004

Dear Danny,
I will hope that everyone has a copy of the Transmission Line Equations from
some edition of the ARRL Antenna Book, because there are so many complicated
symbols therein, I don't want to try to reproduce it in ASCII text. If
anyone has the 17th Edition, they are found as Eq13 on page 24-10 or as Eq19
on page 27-29.
In those equations, the term beta * length is the electrical length of the
line in radians. Thus, for a 1/2 wavelength line, the term beta * length is
pi radians (180 degrees).
Also, in those equations, the hyperbolic functions reduce to simple
trigonometric functions when the loss coefficient, alpha, is zero (a
lossless line).
Therefore, after substituting -1 for the cos(beta*length) terms and
substituting zero for the sin(beta*length) terms, the equations reduce to
Zin = Zload.
That same mathematical result is found when using any of the other tools at
one's disposal, whether it be the Smith Chart or a computer program that
implements the Transmission Line Equations.
Bob Lay (W9DMK), Dahlgren, VA
w9dmk at crosslink.net
Home Pages: http://www.qsl.net/w9dmk
http://zaffora.f2o.org/W9DMK/W9dmk.html
http://meltingpot.fortunecity.com/albania/784
----- Original Message -----
From: "Dan Richardson" <k6mhe at arrl.net>
To: <antennas at mailman.qth.net>
Sent: Monday, October 11, 2004 11:12 AM
Subject: Re: [Antennas] coax 'sweet length'
> Bob,
>> My final comment on this - at this time. I too had thought they were
> exactly the same until Roy Lewallen corrected me on that some time ago.
>> Very 73
> Danny
>>>>> At 07:48 AM 10/11/2004, you wrote:
> >Dear Danny,
> >
> >Then I have to consider the possibility that the TLW program is in error.
> >
> >There are several programs at my Web site that give results to the
contrary.
> >
> >However, put all the programs aside and just look at your Smith Chart. No
> >matter what point you put your finger on, if you then move around the
chart
> >180 electrical degrees (that's moving all the way around to where you
> >started), then you have EXACTLY the same impedance you started with.
> >
> >Bob Lay (W9DMK), Dahlgren, VA
> >w9dmk at crosslink.net
> >Home Pages: http://www.qsl.net/w9dmk
> >http://zaffora.f2o.org/W9DMK/W9dmk.html
> >http://meltingpot.fortunecity.com/albania/784
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