equation: dBm to mW/cm^2

The equation I cited Friday afternoon from:

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..Provides an example of a 100 W transmitter radiating anisotropically at a distance of 100 feet from the receiver, which is on axis with the main radiated lobe of the transmitter's 10 x gain antenna.

I misremembered the example as being isotropic instead so let me rephrase my question:

I tried different numbers for antenna gain in his equation.

In his example, his equation appeared to indicate that if this transmitter were radiating isotropically instead of anisotropically, we can reasonably expect to see the point of constant power density (0.0086 mW/cm^2) to be 1/10 the distance (or only 10 feet) from the transmitting antenna rather than 100 feet, given that the receiving antenna is on-axis with the main lobe in the anisotropic condition.

Is this correct?

I'm just checking my basic understanding here.

--Winston

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Winston
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Good. Thanks!

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the

OK, but can we talk about electric power density as isolated from the magnetic density or voltage density?

At what distance does electric power density stop falling as the inverse of distance and begin to fall as the square of distance? (This is the definition of 'near field' / 'far field', yes?)

My current misunderstanding is that for an (admittedly theoretical) isotropic radiator, that distance is 'several wavelengths'.

If that is true, can we reasonably expect to see the shape of the near field be the same as the shape of the far field in the radiation pattern of an anisotropic transmitting antenna, though the *sizes* of those fields be quite different.

Is this correct?

My bad. I meant to say W/cm^2 not W/cm.

Even within the near field? (Electric power density only)

You reveal the reason behind my original smiley. :)

I'm equally happy with an answer expressed in W/m^2 or W/cm^2.

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Cool! Thanks!

--Winston

Reply to
Winston

No, because the "near field" component *does not radiate power*.

A theoretical isotropic radiator, by definition, has no near field. It's a radiator only.

Near field boundary is determined by physical dimensions, not theoretical gain.

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"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
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Reply to
Fred Abse

At a quick glance, your quoted reference says not much more than I've been saying. I suspect you're not understanding some of the basics, especially the terminology.

--
"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
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Reply to
Fred Abse

Your terminology is confusing. Power has density (per unit area), electromagnetic fields (voltage and magnetizing force) have intensity or strength (per unit length). Consider a simple example: a capacitor has two parallel plates, separated by one meter. The PD between the plates is one volt, hence the field between the plates is one volt per meter intensity.

Power density *always* follows an inverse square law. Field intensity follows a first power law.

See below.

No, see below

There's no such thing as electric power density. Get these things straight in your mind, I think you're getting confused, there is:

Electric field intensity - B Volts per meter. Magnetic field intensity - H Amps (or amp turns if you like) per meter. Power density - Watts per square meter.

All three are inseparable, and are linked by the intrinsic impedance of free space = 377 ohms. It's just like Ohm's Law.

The near field has two components.

Firstly, an inductive component, which merely stores energy, returning it to the antenna each half cycle. Analogous to a resonant circuit. The inductive field *does not radiate power*, hence does not contribute to power density. Its electric and magnetic components are antiphase.

Secondly, a component which radiates power as a field having an electric (E) component, and a magnetic (H) component, mutually at right angles in space, and in phase.

Energy flow (the Poynting vector) is at right angles to both E and H, and flows away from the antenna, into space, and is equal to the vector product of E and H.

In the far field, only the radiation component exists.

Kraus gives the near field boundary as R=2L^2/lambda (meters), where L is the antenna physical length.

The electric and magnetic components of the *inductive* field have different spatial patterns. The electric component is concentrated around the open end (where voltage is maximum), while the magnetic component is concentrated around the point of maximum current.

The radiating field has both components spatially co-located.

Hence, the near and far field polar patterns are not the same.

Definitely get a copy of Kraus, and bone up on cylindrical and spherical coordinate systems.

--
"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
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Reply to
Fred Abse

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I was referring to S, the power density.

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Ah! This puts that boundary at ~ 0.6 m for the system I'm looking at. So that removes near field / far field from 'things I should be concerned about', no matter what.

That is extremely good news and I appreciate it.

The equation I cited earlier yields results that are very close to the actual readings taken from a live system, so I am happy to use it to check on the data I'll eventually gather.

Thanks again, Fred.

--Winston

Reply to
Winston

OK. Got it! Thanks.

Excellent news!

Thanks for helping me limit my ignorance. :)

--Winston

Reply to
Winston

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