[amsat-bb] Re: Best arrangemet and best distance

[i8cvs]

----- Original Message -----
From: "nader omer" <st2nh at yahoo.com>
To: <amsat-bb at amsat.org>
Sent: Friday, April 20, 2007 4:44 AM
Subject: [amsat-bb] Best arrangemet and best distance

Hello all
  I would like to know what the best
   arrangement and the best  distances  between
   vhf cross yagi antenna
  uhf cross yagi antenna
   l-band helical antenna
  s-band helical antenna
  over a  one cross boom
  73 de Nader -st2nh

Hi Nader, ST2NH

Any antenna has an aperture area that is the area around the antenna
in wich the energy of the radio wave enters and  is extracted from free
space.

For a dish the capture area is just the area of the mouth and obviously
you don't want to put a dish inside to another dish

For the same reason the capture areas of different antennas must be
spaced so that they do not overlap.

For a yagi the aperture area A can be "approximately" calculated using the
following formula:

                    / 2
         G  x  /\
A = -------------              [ square meters]
         4 x 3.14

Where:

G = the isotropic gain expressed in factor (not in dBi )
  /
/ \ = wavelenght expressed in meters

Example for a 2 meters yagi with  G= 13 dBi ( 20 time in factor)

                 2
        2.07     x  20
A = ----------------- =   6.79  [square meters]
          4 x 3.14

A circle with area A= 6.79 square meters has a radius
R= SQR( 6.79 / 3.14) = 1.47 meters.

This means that no other capture area generated by a different antenna
must overlap the above 6.79 square meters extending up to about a
distance of 1.47 meters from the boom.

Since the aperture area A of  any antenna is proportional to it's gain G
it follows that for the same wavelenght greater is the gain and greater
must be the distance from any other antenna in the system even if the
antennas are designed for different frequencies.

With this in mind and knowing the gain of  each antenna it is possible to
calculate the best distance from each antenna to the next one.

Supposing that the gain of a 70 cm antenna is 16 dBi or about 40 time in
power it follows that using the above formula  A= 1.50 square meters and
R= 0.69 meters

If the 2 meters and 70 cm antennas are to be placed over the same support
in the array than the distance between their booms must be not less than
1.47 + 0.69 = 2.16 meters and greater is better.

For a yagi the capture area is not exacly a circle but an ellipse by the way
the small error introduced by the above formula in the calculation of A
can be accepted.

For accurate calculation of  the aperture area A in a yagi the equations
discussed in the following article are recommended:

" Staking Yagis is a Science " by Steve Powlishen, K1FO, Ham Radio Magazine
May 1985

If someone is interested on this matter and cannot find the original article
I can send by email a 5 MB + zipped file.

73" de

i8CVS Domenico