Okay...let me make the best sense of this I can...and see if we can get something useful.

micael said:

Ok perhaps is a little bit confusing...

Using Berkeley Mica2 motes as an example, the transmission power is 10dBm (10mW).

Okay...never heard of these until just now, but I found the spec sheet on the MICA2 MPR410CB data transceiver. 433 MHz transceiver for short-range data links, right?

RF power is programmable from -20 to +10dBw.

With you so far.

micael said:

The antenna gain varies depending on the length, size and shape of the antenna.choose a typical 5/8-wavelength monopole antenna . According to the manufacturer(Chipcon,Application Note AN003), the gain of the antenna is 8.2dB.

Chipcon Application Note AN003 that I've tracked down is a paper on antenna design theory for Short Range Devices (SRDs).

It does discuss some theoretical directivities of some antenna designs, including a 5/8-wavelength monopole, which it says has a theoretical directivity of 8.2dBi, or 6 dBd (that last d being a dipole in free space).

There is a good deal of discussion in that paper on efficiency of a tuned radiator (an antenna), where efficiency is expressed as a ratio of radiation resistance to dissipation resistance. [Radiation resistance being the load apparent to a generator contributed by the energy used to create the electromagnetic field emissions, while dissipation resistance is the apparent resistance to a generator contributed by heating/resistance losses in the antenna that is not being used to radiate a field.]

Okay...that's the part I'm roughly following along with.

micael said:

Considering environmental issues, choose 8dB as the transmitting antenna’s gain and 6dB as the receiving antenna’s gain. They correspond to numerical values of 6.31 and 3.98 ,for Gs and Gr respectively. The wavelength for 433MHz is 0.69m.With the distance, D, assigned a value of 3 meters, the received power is found to be 0.084mW.

Here's where you lose me, I'm afraid. I'm not sure what equation you're referencing here, or how the resulting calculation is derived.

There seem to be some references to another paper or source here. I can't locate these variables in the technical note, nor an equation that would derive to these terms.

An equation relating terms like these would have to reference a specific system under specific conditions, such as orientation of the antennas, the environmental issues you mention, and antennas of known efficiency (which we haven't addressed here).

It seems as though you're using an equation here and treating directivity gain as a circuit gain or loss, and then using some derivation of typical field propagation as a measure of induced current and voltage into a receiving element of some specified efficiency.

(I'm assuming that because the units you derive aren't correct for expressing field strength, which would be expressed as power per area or Gauss (volts/unit lenth)--somebody check me on this, okay?)

micael said:

The voltage at the receiving antenna Vin=sqrt(0.084mW*Rs)

Rs is the internal resistance of the receiving antenna which if assumed to be 9Kohm, then

Vin=0.87V

So what i am trying to figure out here is how i can actually get an antenna with > 9Kohm intenal resistance working.

It sounds like you've made the conclusion that the expression of radiation resistances or dissipation resistances yeild an inherent "internal resistance" to an antenna, and that is somehow a property you could manipulate or design by adding simple resistance to the antenna.

Adding resistance in the way you describe will not increase the received power in any circumstance.

I'm afraid that's just not how it works. If you were to add internal resistance to the antenna in some fashion, it would add to the dissipation resistance of the system, which would lower the efficiency of the system considerably. There's not really a way to increase radiation resistance--which is really just a way to describe the energy losses from an antenna system in creating the field it's radiating.

Any added resistance, whether it's at the bottom of the antenna or distributed throughout the antenna, will reduce the voltage and power presented to the receiver.

And we'll not even go into how the characteristic impedance of a reactive circuit is changed when we add resistance.

Does that help?