Electrical Engineering - Converting From mV/m To Decayed mW (ERP)

Author

Converting From mV/m To Decayed mW (ERP)

Kaimbridge

2007-01-23, 8:25 pm

I've seen the different conversions for mW, mV, mV/m, dBm, mostly based
on 50 ohms.
What I'm interested in is converting a given field strength mV/m, at a
given distance for a particular frequency, to the equivalent (decayed)
baseline wattage.
For instance, in section 73.318, the FCC defines the FM blanket
overload boundary as 562 mV/m (115 dBu), having a distance equalling
..394 * KW^.5 (ERP), where (I believe) ".394" is supposed to be
50000^.5/562.
So, assuming flat terrain with "raw reception" (meaning no antenna and
line gain/loss), what would the equivalent ERP wattage be (i.e., if you
took a field strength meter and held it next to a transmitter, what
would the wattage be to produce 562 mV/m?)?
Since wattge can be found from mV/m, what would the equation for
decayed wattage (mW_d) be, given an ERP (KW_erp), frequency (MHz) and
distance (Km)? Instead of 50, should 2*Pi*60 Hz (~=~ 377) be used for
ohms?

~Kaimbridge~

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Richard Fry

2007-01-24, 9:25 am

"Kaimbridge" wrote:
>I've seen the different conversions for mW, mV, mV/m, dBm,
>mostly based on 50 ohms. What I'm interested in is converting
>a given field strength mV/m, at a given distance for a particular
>frequency, to the equivalent (decayed) baseline wattage.
_________________

The radiated power needed to generate a given, free-space field strength of
course depends on the length of the propagation path to that value of field
strength.

Re-arranging the FCC equation to solve for the radiated power needed to
generate 562 mV/m when distance in kilometers is known gives

P = D^2/0.1552

So if there is a need to limit the field strength to 562 mV/m at a location
1 km from the antenna, we see that ERP cannot exceed ~6.44 kW.

Another way of doing it is to massage this "classic" equation.

Field Strength in dB above 1 microvolt/meter =
104.77 + ERPi - 20 log (D)

where ERPi = Effective Radiated Power in dB referenced
to 1kW from an isotropic radiator
D = Distance in kilometers

It gives the same answer as the simpler equation above.

I think this will answer your question, if I understood it right.

RF

Kaimbridge@gmail.com

2007-01-27, 8:25 pm

On Jan 24, 2:45 pm, "mpm" <mpmill...@aol.com> wrote:
> On Jan 23, 8:29?pm, "Kaimbridge" <Kaimbri...@gmail.com> wrote:
>
>
> If I understand what you're asking, your question really centers
> around how to calculate Free Space Loss. The Friis Equation will
> allow you to do this, and it is a relatively simple matter to
> derive Free Space Path Loss in decibel form from the Friis Equation.

I'm not sure: Is this the same (or at least related to) W/m^2?
The problem I see with these is that, as distance approaches 0, KW
approahes oo and what I'm looking for shouldn't be greater than the
transmitter's erp.
What got me on this idea, is a few weeks go I was visiting up in the
NH White Mountains and was checking out the AM/FM bands (I'm a radio
geek! P=). When I got home, I went to the FCC site to create a
bandscan of the area. The designation used was the radius from a
point.
I quickly realized that this was less than ideal, as--using 100 km
radius, as an example--100 W stations at that distance would be listed
along with 50 and 100 KW! What would be much more useful would be a
listing of stations that provide--st least the theoretical baseline
value (i.e., not considering intervening local terrain or one's
receiver sensitivity and antenna gain)--a given mV/m or mW at that
point (thus listing 100 W stations out to 15 km, whereas 50 KW
stations out to 75 km and 100 KW to 130 km would be listed).
Think of it this way: If you turned on a 100 W lightbulb in the
middle of a field at night and held a book page right up to it, you
would be able to read it clearly; if you moved about 10 feet away
(with the book page still facing the lightblb, unobstructed), you
would have difficulty trying to read it, as only about the equivalent
of (e.g.) 50 mW of light may be hitting the page.

~Kaimbridge~

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Richard Fry

2007-01-28, 9:25 am

Kaimbridge@gmail.com wrote
> The problem I see with these is that, as distance approaches 0, KW
> approahes oo and what I'm looking for shouldn't be greater than the
> transmitter's erp. ... What would be much more useful would be a
> listing of stations that provide--st least the theoretical baseline
> value (i.e., not considering intervening local terrain or one's
> receiver sensitivity and antenna gain)--a given mV/m or mW at that
> point (thus listing 100 W stations out to 15 km, whereas 50 KW
> stations out to 75 km and 100 KW to 130 km would be listed).
_________________

Using the known ERP from the transmit antenna it is possible using various
algorithms to calculate the field strength that will exist at a distant
point for some defined condition(s). The FCC has done this for AM/FM/TV
broadcast stations, and the techniques are available to the public via the
FCC's website. Various broadcast-oriented commercial software programs also
are available to do this, although they are expensive.

For AM stations, the distant field is a function of the frequency, ERP,
path length, ground conductivity, terrain roughness, the ionosphere, and the
time of day.

For FM/TV stations, distant field is a function of ERP, the heights of the
transmit and receive antennas, reflections, atmospheric conditions, path
length, and the terrain profile along the path.

These are not simple relationships. For example, in order to provide
essentially equal signal strengths over most of their useful coverage areas,
the ERP needed from an FM station with a "high" antenna can be much less
than if the antenna is lower. Here is a plot showing this...
http://i62.photobucket.com/albums/h...assBCompare.gif

Unfortunately, there is no simple solution answering your queries.

RF

joseph2k

2007-01-31, 3:25 am

Kaimbridge@gmail.com wrote:

> On Jan 24, 2:45 pm, "mpm" <mpmill...@aol.com> wrote:
>
> I'm not sure: Is this the same (or at least related to) W/m^2?
> The problem I see with these is that, as distance approaches 0, KW
> approahes oo and what I'm looking for shouldn't be greater than the
> transmitter's erp.
> What got me on this idea, is a few weeks go I was visiting up in the
> NH White Mountains and was checking out the AM/FM bands (I'm a radio
> geek! P=). When I got home, I went to the FCC site to create a
> bandscan of the area. The designation used was the radius from a
> point.
> I quickly realized that this was less than ideal, as--using 100 km
> radius, as an example--100 W stations at that distance would be listed
> along with 50 and 100 KW! What would be much more useful would be a
> listing of stations that provide--st least the theoretical baseline
> value (i.e., not considering intervening local terrain or one's
> receiver sensitivity and antenna gain)--a given mV/m or mW at that
> point (thus listing 100 W stations out to 15 km, whereas 50 KW
> stations out to 75 km and 100 KW to 130 km would be listed).
> Think of it this way: If you turned on a 100 W lightbulb in the
> middle of a field at night and held a book page right up to it, you
> would be able to read it clearly; if you moved about 10 feet away
> (with the book page still facing the lightblb, unobstructed), you
> would have difficulty trying to read it, as only about the equivalent
> of (e.g.) 50 mW of light may be hitting the page.
>
> ~Kaimbridge~
>
> -----
> Wikipedia-Contributor Home Page:
>
> http://en.wikipedia.org/wiki/User:Kaimbridge
>
> ***** Void Where Permitted; Limit 0 Per Customer. *****

Unless i am more mistaken than usual, the basic reference distance for
radiated power is 1 meter from the phase center of the antenna. Of course
depending on wavelength / frequency this could mean sub-near field
measurements to normal (semi-far to far field) measurements.

--
JosephKK
Gegen dummheit kampfen die Gotter Selbst, vergebens.Â_Â_
--Schiller

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