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# R: Satellite Builder Question

• Subject: R: [amsat-bb] Satellite Builder Question
• From: "i8cvs" <domenico.i8cvs@xxxxxx>
• Date: Thu, 15 May 2003 03:39:30 +0200

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----- Original Message -----
From: Bob Bruninga <bruninga@usna.edu>
To: John M. Franke <j.m.franke@larc.nasa.gov>
Cc: <amsat-bb@AMSAT.Org>
Sent: Wednesday, May 14, 2003 2:55 PM
Subject: Re: [amsat-bb] Satellite Builder Question

> I asked about how to calculate field strength given TX power:
>
> On Thu, 8 May 2003, John M. Franke said to See the WEB page:
>
> > http://www.astron.nl/craf/conv.htm
>
> Which explains the relationship between power and field stength is
>
>   (P*G)/(4pi*d^2) = (E^2)/(120*pi)   Where G is gain, d is distance
>
> And notice that wavelength does not enter into it.  That is where I was
> getting all messed up, because the maximum voltage that can be induced in
> a 1 meter length of wire depends on frequency.  But since the question was
> not "what voltage will be induced in a wire", but "what is the field
> strength", then the above gives the answer without respect to frequency.
>
> Thus, my 2W transmitter on our spacecraft generates 7.7 Volts per meter at
> one meter no matter what the frequency.
>
> Thanks to all who responded.
>
> Bob
>

Bob,

The above equation shoves that :

(P*G)= the EIRP of your antenna when the power P is expressed in watt and
G is the isotropic gain of the antenna expressed in factor (not dB)

(4pi*d^2) = the geometrical surface of  a  sphere.

If we express in meters the distance d  from the sphere center than the
sphere surface is computed in square meters or  (4pi*d^2) = square meters

Now put your antenna in the center of the sphere and radiate your
EIRP in one arbitrary direction at a distance d  from the center.

(P*G) / (4pi*d^2)=  the power density in watt/m^2 collected by the sphere
surface at a distance d  from the antenna along  its radiation axis or in
other words it is the power in W collected in to a square meter of free
space at a distance d from the antenna along the direction of radiation.

The second term of the equation  means that  (120*pi)= 377 ohm

377 ohm is the caracteristic impedance of the free space that must be
considered as a transmission line having infinite lenght and so by the
ohm law the second term of the equation means that

(E^2) / 377 = W/m^2

where W is the power density collected by the surface of  one square meter
of free space at a distance d from the antenna and again by the ohm law
the "Field Strenght" or in other words the voltage that can be measured
across one side of  free space of the above discussed square meter is:

E = SQR (377*((P*G) / (4pi*d^2)       expressed [ V/m]

As you pointed out correctly  the frequency is not involved in calculation
of the "Field Strenght" because the power collected in to a square meter of
free space having impedance of 377 ohm is not frequency depended.

Wery often we state that the attenuation at the same distance from the
antenna increases increasing the frequency but this is correct only because
we compute the attenuation in dB considering the capture area of a receiving
isotropic antenna wich area decreases increasing the frequency.

Of coarse the same power density in W collected  in to a square meter of
free space,as you pointed out correctly gives the same Field Strenght"  E
measured in V/m  no matter  the frequency.

Best 73" de i8CVS Domenico

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