[TowerTalk] Open wire line convert

[n7ws@azstarnet.com]

At 10:43 PM 9/18/00 EDT, K7GCO@aol.com wrote:
>
><  a message dated 9/16/00 6:26:40 AM Pacific Daylight Time, n4kg@juno.com 
>writes:<    Hi Jay,
>   
>   I don't try to match the ladder line to 50 ohms.  I'm using my
>   ladder line fed antennas on several bands so I accept the 
>   mismatch at the antenna and use Johnson Matchboxes
>   at the transmitter end. KISS principle (Keep it simple stupid).
>   Works for me.  For 50 ohm antennas I just use CATV hard-line
>   in multiples of 1/2 WL.  For verticals, I use coaxial transformers
>   to transform 17 to 35 ohms up to 75 ohms +/- a bit.
>   
>   73,  Tom
>   
>  Every once in a while in the area of suggesting better ways to do things 
>someone comes along who has found the same thing and supports the cause 
>despite the brick bats of all the know it all's who even admit they have 
>never used or tried it (the weakest of credibilty positions).  Would you 
>believe I actually levitated out of my chair when I read Tom's Post here.
It 
>was obvious to me that he was a sharp and deadly analyst of transmission 
>theory able to see though all the conventional nonsense that is jammed down 
>our throat by the "Kraus Wannabes."  It takes some years to get a grasp of 
>financial and technical reality in Ham Radio and inparticular--low loss and 
>inexpensive transmission lines.  I only suggest and anyone is free to use 
>what they want but should at least allow the free flow of suggestions
without 
>constant reticule as it makes for a strong and informative Reflector.
>  
>  I am awarding Tom N4KG the "K7GCO Smart Transmission Line Amateur of the 
>Month Award #1" for high technical intelligence and good operating low cost 
>low loss practices.  He even used 1/2 WL multiples of CATV hard-line and
then 
>!/4 WL lines for matching.  Tell us more of what you have there Tom.  Others 
>have likewise illustrated great technical insights in other areas and will
be 
>recognized.  Recognition for "Technical Excellence" has been sadly
missing.   
>K7GCO >>
> 

I'm sure that I will qualify for your "Wet Blanket of the Month" award, but
here goes anyway.

With respect to using half-wavelength multiple cable lengths, let me use
the following example to make a point:

Assumptions.

1) 75 ohm CATV coax, Vp = 0.81, 0.82 dB/100' loss @ 100 MHz.

2) Zl = 50 +j0 @ 28.5 MHz

3) Since this stuff is usually used for longer runs, length trimmed to
223.57 ft.

With these conditions, the input impedance is 54.35 -j0 for an SWR of
1.09:1.  You expected 1.0:1 but the line attenuation upsets this
expectation.  The insertion loss for this run is 1.03 dB.

The phase constant in radians per meter (beta); is determined by:

beta = (2 * pi * sqrt(epsilon))/lamda,
 
where epsilon (1.525) is equal to 1 / Vp ^2.  

For the example line length, beta * length = 50.27 radians or 2880 degrees
of total phase shift.  Dividing by 180 degrees (one-half wavelength) we
find that the line is 16 half-wavelengths long at 28.5 MHz.

Now QSY down to 28.055 MHz.  Run the numbers again and you will find that
the line is now 15.75 half-wavelengts long, or an odd 1/4 wavelength long.
The new input Z (assuming no change in load Z) is now ~71.1 -j23.5 or an
SWR of 1.69. 

Is this meaningful?  I doubt it, but IMHO I believe it is pointless to try
and trim the line in the first place.  In the foregoing example, the 50 ohm
input SWR (1.69) is worse at 28.055 MHz than it would be if the load was
made to match the 75 ohm cable (1.50). The total insertion loss would be
lower as well.

As the line gets longer or the frequency increases, the effect becomes
worse, although the additional line attenuation masks the effect somewhat.

There is a case for trimming line lengths and that is where phased arrays
are used.  Even there, however, if close phase matching is desired, it is
better to keep the phasing lines short (in terms of wavelength multiples). 

As to my take on ladder line, it can be seen at:

 http://www.azstarnet.com/~n7ws/ladder.htm

73,

Wes Stewart  N7WS


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