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Re: Power divider for X-yagis

----- Original Message -----
From: "Joop & Tineke Verdoes" <joop.verdoes@nameplanet.com>
To: <amsat-bb@amsat.org>
Sent: Friday, May 26, 2006 10:51 AM
Subject: [amsat-bb] Power divider for X-yagis

> Hello to you all.
> When buidling a phasing harness for (switchable) circularly polarised
> crossed-Yagis one needs a device to split the line from the TRX to the
> two legs of the yagi.
> In the ARRL antenna handbook (and others) I see quart lambda 36 ohm
> transformers in the figures.
> In my current state of confusion I have the following questions.

Hi Joop, PA1JAV

Assuming that the impedance of each leg of the yagi is 50 ohm than two
legs in parallel make the resulting impedance of the antenna equal to
25 ohm
To match 25 ohm impedance of the antenna to 50 ohm impedance of a
transmission line we can use the property of impedance transformation
given by a 1/4 electrical wavelengh long transmission line wich
characteristic impedance is Zo = SQR ( 25 x 50 ) = 35.4 ohm  or about
36 ohm in this case.

> 1- this 36 ohm transformer is apparently a square pipe with a round rod
> to which three N sockets connect. Where do I find "the right" formula
> for calculating the characteristic impendance for square pipe with a
> round rod in it. I coulnd't find it in any of the ARRL or RSGB books I
> have. (but I might have gone blind for just this :-)) On the net I found
> different formulas.

If you look at the Microwave Handbook Volume 2 of the RSGB edited
by M.W.Dixon, G3PRF page 13.11 you will find that for a square tube
with air as dielectric and equal sides with inside dimension (D) and a
round inner conductor of outside diameter ( d ) the characteristic impedance
Zo can be computed using the following formula where (D) and (d) are
expressed in millimeters.

                              1.178 D
Zo= 138 log      ( ----------- )
                      10         d

> 2- this 36 ohm transformer correctly transforms the two parallel
> impedances of the 50ohm lines to the legs of the yagi (so 25 ohms
> combined) to the 50 ohms of the TRX. But.....seen from the yagi there is
> a mis-match, impacting the received signal.

The impedance transformation is made at sacrifice of the SWR but only
inside the 1/4 wavelenght long matching line wich is 35.4 / 25 = 1.41
as seen with the antenna as a source while receiving and 50 / 35.4 = 1.41
as seen by the antenna as a load while transmitting.
In both situation the loss of power inside the above matching line due to
a SWR = 1.41 is in the order of  35 dB wich is insignificant.

> Wouldn't it be better to use a Wilkinson power divider/combiner, from
> either (70.7 ohm) square pipe or coax? There isn't much difference in
> the work to make one or the other, so I might as well do this the best
> way.
Assuming that the impedance of each leg of the yagi is 50 ohm than a  75 ohm
1/4 electrical wavelenght long matching line made with RG-11 or RG-59
coax cable connected in series to one leg will make an impedance
transformation of  75^2 / 50 = 112.5 ohm as seen at the other end.
If you do the same for the other leg and you put two 112.5 ohm in parallel
to a T adapter than you have a load impedance of 56 ohm to be connected to
any 50 ohm feed line with a theoretical SWR of only 1.12

This metod is convenient up to 144 MHz  and is more economical than using
a 36 ohm maching line made with square tubing.

Above 144 MHz the 36 ohm maching line made with square tubing is preferred
for several reason.

> I really would appreciate some help here.
> Thanks
> Joop, PA1JAV
Best 73" de

i8CVS Domenico
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