At 11:08 AM 6/26/2005, Wes Cosand wrote:
>Folks:
>
>I am embarrassed to ask a question I should be able to figure out but my
>Handbook and Antenna Book aren't proving sufficient to overcome my ignorance.
No need to be embarassed... Most of the amateur literature doesn't deal
much with E field strengths (V/m), except in the RF safety area (where all
the standards are given in terms of E or H field limits).
>How can I calculate the field strength in volts/meter as a function of
>distance from an isotropic antenna emitting a given power in watts? (Let's
>ignore the near field/far field issue.) Where does a ham go for this kind
>of information?
Why, you go here.. and you'll get several answers, hopefully all the same.
Isotropic antenna radiates in all directions equally. So, you take your
radiated power and figure out what the power density (watts/square meter)
is at the distance of interest. The surface area of a sphere is 4*pi*r^2
Then, you convert the watts/square meter to volts/meter by using the
impedance of free space, which is approximately 377 ohms (actually it's
120*pi).
A digression: This is a bit weird at first, but here's how to look at it:
Power density = E field * H field (that is, the electric field times the
magnetic field) or
Equation 1: Watts/meter^2 = (Volts/meter) * (Amps/meter) (you can see how
the units work out...
But, also, impedance is the ratio of the electric and magnetic fields, just
like Ohm's law for circuits: Equation 2: Ohms = (Volts/meter) / (Amps/meter)
So, we put in 377= (Volts/meter)/(Amps/meter)
Or, rearranging a bit:
Equation 3: Amps/meter = (Volts/meter)/377
Substituting 3 into 1:
Equation 4: Watts/meter^2 = (Volts/meter) * [(Volts/meter) / 377]
or Watts/meter^2 = (Volts/meter)^2 / 377
or, reversing it for what you want to compute:
Equation 5: (Volts/meter)^2 = (Watts/meter^2) * 377
-- end digression..
So you have your power density as:
Equation 6: Watts/meter^2 = P / (4 *pi * r^2)
Then we substitute into eq 5:
Equation 7: (Volts/meter)^2 = P / (4 * pi * r^2) * 377
I'll go back to 120 pi instead of 377, so I can cancel some of the terms:
Equation 7a: (V/m)^2 = P * 1/4 * (1/pi) * (1/r^2) * 120 * pi = P * 30 / r^2
Finally resulting in:
V/m = sqrt(P*30)/r
To put a practical face on some of the numbers...
Consider a 100W transmitter, at a distance of 1km from an isotropic radiator:
sqrt(100*3)/1000 = 17.3E-3 V/m
or, maybe 1000km -> 17.3 uV/m
Typical safe exposure limits for power densities are typically in the
milliwatt/cm^2 range, or, 1 mW/cm^2 = 10 W/m^2
Converting that 10W/m^2 into Efield:
sqrt(10* 377) = sqrt(3770) = 61.4 V/m, a field strength you'll see in lots
of regulatory literature.
Most antennas aren't isotropic, of course... But that's where you get into
EIRP Equivalent Isotropic Radiated Power.. The EIRP is the power into an
isotropic antenna that produces the same field as the actual power going
into the actual (gain) antenna.
>Thanks
>
>Wes, WZ7I
>
>
>
>_______________________________________________
>
>See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless
>Weather Stations", and lot's more. Call Toll Free, 1-800-333-9041 with
>any questions and ask for Sherman, W2FLA.
>
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_______________________________________________
See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless Weather
Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any questions
and ask for Sherman, W2FLA.
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