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

Well, let's see. We can start with an isotropic antenna, which
distributes its power equally in all directions. I did that one three
days ago on this newsgroup, in the thread "Theoretical antenna
question". The result is that the power density from an isotropic source
at any distance r is

PD = P / (4 * pi * r^2)

where P is the total power radiated. Power density PD will be in
watts/square meter if P is in watts and r is in meters.




That's just the power divided by the surface area of the outwardly
traveling EM wave that is a perfect sphere in the case of an isotropic
raditator.

Right.


In the far field, the field strength E from any antenna is sqrt(PD *
Z0), where Z0 is the impedance of free space, very nearly 120 * pi ohms.
E is in volts/meter if PD is watts/meter^2 and Z0 is in ohms.
Substituting in the first equation gives

E = sqrt[(P * Z0) / (4 * pi * r^2)] ~ sqrt(30 * P) / r




This is more proof that the "transformer" action between two
antennas is highly dependant on the impedance of the medium between
them.

There's no doubt, and certainly no disagreement from me, that the mutual
coupling or "transformer action" between two antennas is strongly
affected by the medium between them.

Roy, i don't mean to be an overly inquisitive laid-off engineer
with too much time on my hands, but how was E = sqrt (PD * Zo)
derived exactly? This is really the key equation.

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.

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.

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.

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.

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