[TowerTalk] 50:75 ohm transformation (LONG)

WE9V Chad Kurszewski Chad_Kurszewski@css.mot.com
Wed, 10 Feb 1999 11:16:55 -0600

>There is no reason I know of why a stack shouldn't behave just fine on the
>end of a half-wave multiple of 75-ohm.

Because, at over 200' or so, you may not cover the entire (contest)
portion of 10M with an "acceptable" match.

For example:
My back tower is 280' from antenna to shack.  It has a tribander on it.
So I could do the trick of a half-wave multiple of 40M to work on 
CATV is typically ~ 81% velocity factor.  I've measured it to be
more like 86-87%.  Let's assume 81% anyway.
A physical half-wave on 7.075MHz is 983/7.075/0.81 = 56.27'.
A close multiple to 280' is 5 half-waves = 281.35'.  Darn close.

281.35' is 347.345' electrical, which is exactly TWENTY (20) half-
waves at 28.300 MHz.  Nice!

But wait...

It's also only 19.7877 half waves at 28.0 MHz and 20.423 half waves
at 28.9 MHz.  Now, let's look further at that 20.423 number.  It's
20 half-waves, plus an extra 0.423 half wave.  That's nearly half
of a half-wave.  It's otherwise known as a quarter wave.  And
if you know a little about the Smith Chart, you know that a quarter
wave changes the impedance the most!  Remember, it can change an
open circuit into a short circuit!!  Zero ohms into nearly infinity!

Okay, back to the 50 ohm antenna.

Here are the honest-to-goodness results from HP MDS (Hewlett-Packard's
Microwave Design System) which I use often here at work (I'm an
RF design engineer).

A lossless 281.35' 75-ohm line will indeed show a perfect 50 ohms
at 28.3 MHz.  Here is a graph of the rest of the frequencies:
Freq  SWR
28.0  1.65:1
28.1  1.40:1
28.3  1.00:1
28.6  1.65:1
28.8  2.08:1
29.0  2.25:1 (worst case)

So, with a 281' piece of CATV, the simulation shows that you will
have a 2:1 SWR bandwidth of 0.92 MHz.  So if you were to put the
dip at 28.5Mhz, you'd have >2:1 SWR at 28.0 and 28.9 MHz.
Remember, this is just what the CATV hardline introduces and assumes
a perfect 50 ohm load.  You throw in reactances and changing
impedances over a frequency range and you can get something drastically

Now, if you have a 500' run out to the top of the tower, you are talking
about 36 half-waves at 28.3 MHz.  Your 2:1 bandwidth is now decreased
to 0.25 MHz.  If you cut this thing for CW, you'll have a 2.2:1 SWR
in the phone band, guaranteed!!

Lastly, one thing not many people talk about is what is called
mismatch loss.  It's a loss mechanism due to, you guess it, mismatch.
If you operate a 50 ohm device into a 2.25:1 condition (without a tuner,
and assuming your radio doesn't back down the power), you will have
an additional 0.7dB loss!  Of course, the majority of that loss can
be "avoided" by using a tuner, or adjusting the tuning of your
amplifier to match this new impedance.

So, bottom line:
If you're using 10M and your run is short, go ahead and try to use
the half-wave multiple.  If your run is long, you better think twice.

Chad Kurszewski, WE9V                       e-mail:  WE9V@qth.com
The Official "Sultans of Shwing" Web Site:  http://www.QTH.com/sos

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