[ Copied from another newsgroup.]

While I'm in the mood, the following little calculation may assist in
understanding what goes on in an antenna. Suppose we wish to know the
radiating efficiency of a resonant half-wave dipole fed at its center.


When at exact resonance we are concerned only with pure resistances.


For calculating convenience, we assume the radiation resistance, Rrad, is
uniformly distributed along the length of the wire and is 140 ohms which has
been calculated from its dimensions. It only has two - Length and
Diameter. But for a half-wave dipole it is always about 140 ohms. Wire
diameter has a relatively small effect on Rrad.


Frequency, F = 10 MHz.
One wavelength = 300/F = 30 metres.
Overall dipole length L = 15 metres.
Copper wire diameter D = 2mm.


Calculate Rloss, the end-to-end wire loss resistance -


Rloss = 0.0833 * Sqrt( F ) * Length / Diameter ohms, which takes skin
effect with copper wire into account.


Rloss = 1.976 ohms.

Insofar as the current flow is concerned, the total resistance in the
antenna wire is 140 + 1.976 = 141.976 ohms. But only Sqr( Amps ) * Rloss
watts is lost.


So antenna efficiency = (Power radiated) / (Power input) = Rrad / ( Rrad +
Rloss )


Effncy = 140 / ( 140 + 1.976 ) times 100 percent.


Effncy = 98.6 percent.

Note that we have taken care to place both the radiation and loss
resistances at the same place in the system so that they can be properly
compared. It is usual to locate the radiation resistance at the dipole
centre as one lump when it then becomes 70 ohms. But a slightly different
efficiency calculation is then needed to provide the same correct answer.


Almost certainly there will be an appreciably greater loss in the
transmission line to the transmitter and in the coupling/impedance
transforming coil and capacitor networks.


If you are interested in numerical quantities without tedious arithmetic,
download in a few seconds one or two simple programs from the following
website and run immediately. Amuse yourself.
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Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
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