The "impedance" of free space/ air is 377 ohms. Thus the ratio of RF field
voltage and current will be
fixed and related to the power density - unless the field is distorted.

As another crude approximation, assume that (unless you know a radiation
pattern) that the unwanted signal's power is equally distributed over a
sphere or maybe a hemisphere.

R. J. & Ed-

The calculations R. J. refers to apply to a field at a distance - called "far
field". Up close, radiation patterns are complex and not easily predicted.

For the sake of discussion, lets carry this free space impedance topic a bit
further. If you know transmitted power and the type of antenna, you can
approximate the effective radiated power. For example, a half wave dipole and
a quarter wave ground plane have about the same gain, 2.1 dB. If you are
concerned about worst-case, you should assume a handheld radio with a
rubber-duckie antenna, has the same gain as a full size ground plane. (You
could also add some gain due to reflecting surfaces, just to be safe.)

Suppose your handheld radio has five watts output. For a gain of 2.1 dB, the
effective isotropic radiated power is about 8 watts. This power illuminates
the inner surface area of a sphere equal to (4/3) Pi R-squared, where R is the
distance.

At some distance the field strength will equal an amount that will interfere
with the defibrillator. Suppose that critical field strength is one Volt per
Meter. One Volt squared, divided by 377 equals 2.7 milliWatts per square
Meter.

Working this backwards with the sphere, 4/3 Pi R-squared divided by 8 watts
equals the power (2.7 mW) per square meter at distance R. You can calculate
that the minimum distance R equals 0.072 Meters, which is less than 3 inches.
(Please don't hold any errors against me. Check it yourself!)

Since this distance is well within the near-field region, there is an
uncertainty that depends on whether there is electric coupling or magnetic
coupling. To be absolutely sure there is no interference, you could back off a
couple of wavelengths, say fifteen feet on two meters. (Others may say ten
times 3 inches would be enough.)

How does this one Volt per Meter assumption compare with the defibrillator
specifications? If the spec is higher, then there seems little to worry about.

73, Fred, K4DII

Seems like we want to say 8 watts/(4*pi*r^2) =
..0027w/m^2, and that yields a radius of about 15.4 meters, which would
actually be a good approximation of far field for 2M wavelength.


Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.

73, Fred, K4DII

Seems like we want to say 8 watts/(4*pi*r^2) =
..0027w/m^2, and that yields a radius of about 15.4 meters, which would
actually be a good approximation of far field for 2M wavelength.


Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.

73, Fred, K4DII

Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.



Caught again!

I took another look at my earlier calculations and found that not only did I
have the wrong formula for the area of a sphere, I had my equation upside down!
I ended up with something like watts per square meter equals square meters per
watt. Yes, the power is spread over a greater area, but that did not
compensate for the really stupid mistake.

So, if one volt per meter equals 2.7 milliWatts per square Meter, that field
strength would be generated by a five watt handheld radio at a distance of 15.4
Meters, which is about 50 Feet. This is sounding serious unless the
defibrillator has a greater tolerance. I certainly hope it does, since we are
often irradiated by passing mobile radios running 50 watts or so, at closer
distances than 50 feet.

Lets see - 50 watts is ten dB greater, so the distance would be about 3 times
as great as 5 watts, or about 150 feet for one volt per meter. Or, maybe I
should just keep my mouth shut to keep from screwing up again!

73, Fred, K4DII

Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.



Caught again!

I took another look at my earlier calculations and found that not only did I
have the wrong formula for the area of a sphere, I had my equation upside down!
I ended up with something like watts per square meter equals square meters per
watt. Yes, the power is spread over a greater area, but that did not
compensate for the really stupid mistake.

So, if one volt per meter equals 2.7 milliWatts per square Meter, that field
strength would be generated by a five watt handheld radio at a distance of 15.4
Meters, which is about 50 Feet. This is sounding serious unless the
defibrillator has a greater tolerance. I certainly hope it does, since we are
often irradiated by passing mobile radios running 50 watts or so, at closer
distances than 50 feet.

Lets see - 50 watts is ten dB greater, so the distance would be about 3 times
as great as 5 watts, or about 150 feet for one volt per meter. Or, maybe I
should just keep my mouth shut to keep from screwing up again!

73, Fred, K4DII

One of the tech support people at Guidant actually sent us some
information regardint the testing limits on my wife's device. In the
area of interest to hams, it thas been tested at a field strength of
140 V/m RMS over a frequency of 500 KHz to 6 GHz..

Thanks for the discussion and information,
Ed Bailen - N5KZW

On 04 Jun 2004 00:17:10 GMT, (Fred McKenzie) wrote:

Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.



Caught again!

I took another look at my earlier calculations and found that not only did I
have the wrong formula for the area of a sphere, I had my equation upside down!
I ended up with something like watts per square meter equals square meters per
watt. Yes, the power is spread over a greater area, but that did not
compensate for the really stupid mistake.

So, if one volt per meter equals 2.7 milliWatts per square Meter, that field
strength would be generated by a five watt handheld radio at a distance of 15.4
Meters, which is about 50 Feet. This is sounding serious unless the
defibrillator has a greater tolerance. I certainly hope it does, since we are
often irradiated by passing mobile radios running 50 watts or so, at closer
distances than 50 feet.

Lets see - 50 watts is ten dB greater, so the distance would be about 3 times
as great as 5 watts, or about 150 feet for one volt per meter. Or, maybe I
should just keep my mouth shut to keep from screwing up again!

73, Fred, K4DII

One of the tech support people at Guidant actually sent us some
information regardint the testing limits on my wife's device. In the
area of interest to hams, it thas been tested at a field strength of
140 V/m RMS over a frequency of 500 KHz to 6 GHz..

Thanks for the discussion and information,
Ed Bailen - N5KZW

On 04 Jun 2004 00:17:10 GMT, (Fred McKenzie) wrote:

Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.



Caught again!

I took another look at my earlier calculations and found that not only did I
have the wrong formula for the area of a sphere, I had my equation upside down!
I ended up with something like watts per square meter equals square meters per
watt. Yes, the power is spread over a greater area, but that did not
compensate for the really stupid mistake.

So, if one volt per meter equals 2.7 milliWatts per square Meter, that field
strength would be generated by a five watt handheld radio at a distance of 15.4
Meters, which is about 50 Feet. This is sounding serious unless the
defibrillator has a greater tolerance. I certainly hope it does, since we are
often irradiated by passing mobile radios running 50 watts or so, at closer
distances than 50 feet.

Lets see - 50 watts is ten dB greater, so the distance would be about 3 times
as great as 5 watts, or about 150 feet for one volt per meter. Or, maybe I
should just keep my mouth shut to keep from screwing up again!

73, Fred, K4DII

I'm not going to check you gentlemen's math -- it sounds like you've
gone through that pretty thoroughly. But I'll point out that you're
calculating the field strength from an isotropic source in free space.
Let me remind the readers that this is the absolute lowest possible gain
an efficient antenna can have. A dipole in free space produces a field
strength about 2 dB greater than this in some direction; an isotropic
source over ground produces a field strength 3 dB greater. So this rough
estimate of field strength is always lower than the field that a real
antenna can produce in some direction.

_RF Exposure and You_ (Hare, ARRL) has some excellent information on how
to approximate field strength of real antennas. And of course modeling
programs do the same thing. But under no circumstances would I depend on
either one, or even better-than-average amateur measurements, to make
any determination that might impact human life or safety.

Roy Lewallen, W7EL

Fred McKenzie wrote:

Tom-

You caught me!

I don't have a calculator handy, but it seems to me that the correct formula
yields an even lower power when spread over three times the area.



Caught again!

I took another look at my earlier calculations and found that not only did I
have the wrong formula for the area of a sphere, I had my equation upside down!
I ended up with something like watts per square meter equals square meters per
watt. Yes, the power is spread over a greater area, but that did not
compensate for the really stupid mistake.

So, if one volt per meter equals 2.7 milliWatts per square Meter, that field
strength would be generated by a five watt handheld radio at a distance of 15.4
Meters, which is about 50 Feet. This is sounding serious unless the
defibrillator has a greater tolerance. I certainly hope it does, since we are
often irradiated by passing mobile radios running 50 watts or so, at closer
distances than 50 feet.

Lets see - 50 watts is ten dB greater, so the distance would be about 3 times
as great as 5 watts, or about 150 feet for one volt per meter. Or, maybe I
should just keep my mouth shut to keep from screwing up again!

73, Fred, K4DII