Roy Lewallen wrote in message ...

The power density is related to E and H fields by the Poynting vector, where

PD = E X H

I'm not going to derive this one -- you can find it in any
electromagnetics text.

In the far field in a lossless medium, E is in time phase with H.
Consequently, the magnitude of PD is simply |E| * |H|. The latter two
have to be RMS values for PD in watts; for peak values, you need an
addition factor of 1/2. Again in the far field, E/H = Z0, where Z0 is
the impedance of the medium. The definition of Z0 is generally defined
in terms of the permittivity and permeability of the medium, and the far
field E/H relationship follows from it. That's another one I won't
derive here, and that you can easily find in a text. In a lossless
medium, Z0 is purely real, making the math simple.

So, (dealing now only with magnitudes) given that PD = E * H and Z0 =
E/H, it follows that PD = E^2/Z0 = H^2 * Z0. Solving for E gives the
equation you're asking about.



Thanks Roy, i'm gonna look up these derivations.



Here's something else I'm wondering about. If you get an answer
of 1 uV/meter, does this mean that a perfect conductor of 1 meter
length placed in this field (polarized with the E field) will measure
1uV RMS if you measure the AC voltage on the ends?

No, it doesn't quite work out that way, because of the triangular
current distribution on the 1 meter wire (assuming that the wavelength
is 1 meter). The "effective height" of a wire that's short in terms
of wavelength turns out to be 1/2 the actual length.



Well, that sounds reasonable and is why i asked what people used
on the receiving end for field-strength measurements. Would the above
be valid for wavelength than one meter? Perhaps i'm totally off
because the 1 uV/meter might mean that one would measure the 1uV RMS
across 1 meter of the medium in question (377 Ohms for free-space, no
wire involved at all?)?



In the real world,
what sort of receiving antenna do they use to measure E fields?

Near field E intensity is typically measured with a short probe. Far
field measurement is done with conventional antennas. In the far field,
once the E, H, or power density is known, the other two can be calculated.



Short probe that may be much shorter than one wavelength,
unfortunately?



Obviously, the recieve antenna will affect the measurement...perhaps
you want something broadband, so as not to favor a particular
frequency (a resonance on the receive antenna will throw off the
reading)? Perhaps something as isotropic as possible, so orientation
is not as critical. How does the FCC measure it, what equipment do
they use?

To my knowledge, the FCC doesn't do any measurements. Test labs doing
far field measurements typically use a conical dipole for the HF range,
and log periodic antenna for VHF and UHF. Although these are inherently
broadband, the dipole in particular varies a great deal with frequency.
So each antenna comes with a correction factor table. That's why EMI
measurement antennas, though simple, are expensive.



That's what i wanted to read, that they use a correction factor
table so that they can take out the natural resonance(s) of the
receive antenna. And it makes total sense that they would use a
different antenna for each frequency range.

The tricky part of making the correction factor table would be
that ideally, you would have an isotropic radiator that was perfectly
wide-band, and feed this with known input powers. This being
impossible, i would imagine that they might take advantage of the
reciprocity of antennas, and use the same antenna for both transmit
and receive, and then divide the correction factor by two, 1/2
correction for each antenna.



Some of the FCC Part 15 measurements I've been involved with are
actually done within the near field, but are done with standard antennas
nonetheless. Although the conversion from power density to field
strength isn't entirely valid, everybody plays by the same rules. I
think some of the FCC rules for safety now required for amateurs are
also in this category.

I haven't seen quantitative near field measurements being done, just
qualitative ones using a short probe.

Roy Lewallen, W7EL


Perhaps the far-field measurements would require too sensitive a
field-strength meter? Or maybe it's just more convenient to measure
up close.


Slick

Dr. Slick wrote:
Roy Lewallen wrote in message ...
. . .

No, it doesn't quite work out that way, because of the triangular
current distribution on the 1 meter wire (assuming that the wavelength
is 1 meter). The "effective height" of a wire that's short in terms
of wavelength turns out to be 1/2 the actual length.




Well, that sounds reasonable and is why i asked what people used
on the receiving end for field-strength measurements. Would the above
be valid for wavelength than one meter? Perhaps i'm totally off
because the 1 uV/meter might mean that one would measure the 1uV RMS
across 1 meter of the medium in question (377 Ohms for free-space, no
wire involved at all?)?

It's valid only as long as the length of the wire is a half
wavelength (actually, 1/4 wavelength for a single wire, half
wavelength for a dipole).

Here's the problem with that transformer concept again. A field is not a
voltage. So you can't measure it with a voltmeter. You can convert the
fields to voltages and currents by use of a transducer -- an antenna --
then you can measure the voltage and current from the antenna with
ordinary meters.

Good thing, too. Otherwise we'd all get electrocuted by the Earth's 100
volt/meter field. (And that's on a day with no storm nearby.)

The relationship between the fields, voltages, and currents is nicely
expressed by Maxwell's equations.





In the real world,

what sort of receiving antenna do they use to measure E fields?

Near field E intensity is typically measured with a short probe. Far
field measurement is done with conventional antennas. In the far field,
once the E, H, or power density is known, the other two can be calculated.




Short probe that may be much shorter than one wavelength,
unfortunately?

Yep.

. . .


Some of the FCC Part 15 measurements I've been involved with are
actually done within the near field, but are done with standard antennas
nonetheless. Although the conversion from power density to field
strength isn't entirely valid, everybody plays by the same rules. I
think some of the FCC rules for safety now required for amateurs are
also in this category.

I haven't seen quantitative near field measurements being done, just
qualitative ones using a short probe.

Roy Lewallen, W7EL



Perhaps the far-field measurements would require too sensitive a
field-strength meter? Or maybe it's just more convenient to measure
up close.

No, it's far field measurements that are more common. One problem with
making near field measurements is that the near field varies all over
the map with the type of antenna and the exact spot where you're making
the measurement. And it's of no importance at all to anything very far
away at all. I've only seen near field probing done to locate the source
of a problem emission. Compliance measurements are usually done with
far-field techniques, in or at least at the fringes of the far field.
The "within the near field" measurements I'm referring to are HF
measurements done at distances that aren't firmly in the far field. (The
far field boundary depends on the nature of the radiating structure, and
is nebulous anyway.) The FCC addresses this issue for Part 15 somewhat
in section 15.31(f).

Roy Lewallen, W7EL