[HCARC] 10 meter Loop

[Kerry Sandstrom]

Actually, Gary, its not exactly either.  The best way to think about it is 
the antenna is completely enclosed by a sphere of a certain radius.  For a 
half wave dipole the radius of the sphere is a quarter of a wavelength, for 
40 m , thats about 33 feet.  The antennas 'physical aperture' is the cross 
sectional area of the sphere in the favored direction.  For a dipole, this 
cross sectional area is the area of a circle of a quarter wavelength radius. 
The second thing to consider is the 'aperture efficiency' of the antenna. 
The aperture efficiency is basically an indication of how uniform the the 
illumination of the aperture is.  For a dipole its pretty bad, the 
'illumination' is just a single wire accross the diameter of the aperture. 
The result is that the 'effective aperture' of a dipole is much less than 
its physical aperture.  Antennas such as parobolic reflectors illuminated by 
a horn have effective apertures that are ~70% of their physical aperture. 
For a Yagi, the effective area is the area of a sphere whose radius is the 
turning radius of the Yagi.  A yagi, however, doesn't have a very high 
aperture efficiency.  A stacked array of shorter yagis, does have a higher 
aperture effiency.  Many years ago large VHF stations usually used 2 or 4 
short yagis rather than one long one.  Why not now you might ask?  I think 
it is because it is difficult to have stacked antenna arrays for several 
bands.  Today's VHF/UHF ops are apt to be on half a dozen bands while years 
ago most were only on one or two bands.

There are a couple simple formulas that relate the aperture size to the 
approximate beamwidth and gain.  The beamwidth in radians is approximately 
the inverse of the diameter of the effective aperture measured in 
wavelengths.  For a uniformly illuminated aperture, the gain is 
approximately 4 * Pi * A where A is the area of the aperture in wavelengths. 
These formulas work best for antennas with uniformly illuminated apertures.

Bottom line:  For a high gain antenna you need the largest aperture you can 
get and you need to 'illuminate' that aperture as uniformly as possible.

The metal does make a difference.  The metal needs to be a good conductor, 
at least on the surface.  If the metal has a high resistance, the antenna 
will have losses do to that resistance.  Because RF doesn't penetrate into a 
conductor very far, 'skin depth', copperweld wire with a steel center and a 
copper jacket will work as well as solid copper and be mechanically much 
stronger.  That is also why silver plating various microwave things works, 
although the thickness of the plating is very small, it contains essentially 
all of the RF current.

There are two quantities that are important to losses in antennas.  One is 
the radiation resistance and the other is loss resistance.  The radiation 
resistance is the part of the total antenna input impedance that contributes 
to actual radiation.  The loss resistance is the part of the antenna input 
impedance that leads to heat.  There is also an 'imaginary' part of the 
input impedance which leads to the energy stored in the antennas 
non-radiating near fields.  For an efficient antenna you want the ratio of 
the radiation resistance to the loss resistance to be as large as possible. 
The radiation resistance goes as the square of the antennas length while the 
loss resistance goes as the length directly.  as you can see, for very small 
antennas, the loss resistance is a larger part of the input impedance and 
the the antenna generates more heat and less radiation.  Most small antennas 
use much heavier conductors to try to control the losses.  Thats why you 
should use as close to a full size antenna as you can.

In order to have an intelligent discussion about loop antennas I need to 
introduce the concept of duality.  Maxwell's equations have the property of 
duality.  If you exchange every quantity in Maxwell's equations for its dual 
quantity, you get the same equations back.  The electric field and the 
magnetic field are duals of each other.  What this means to us is that a 
dipole and a loop are duals of each other.  The same equations describe the 
performance of both antennas.  a dipole is called an electric antenna 
because the near field is dominated by the electric field components.  A 
loop is a magnetic field antenna because its near field is dominated by 
magnetic fields which have the same mathematical description as the elctric 
fields of a dipole.  Of course, in the far field the electric and magnetic 
field components are related by a constant, the impedance of free space, so 
the far field performance of a loop antenna and an equivalent size dipole is 
identical.  What are the reasons for choosing on type over the other?  In 
the case of loop antennas, the performance of a small loop antenna is easier 
to predict and loop antennas are often used for instrumentation where a 
small calibrated antenna is needed for LF and VLF measurements.  I think 
dipoles are easier to build mechanically than similar size loops.  Loop 
antennas are often easier to rotate and work better close to the ground than 
dipoles.  Some people just like to be different!  As you can see there isn't 
a real reason to choose one over the other for far field radiation.  The 
coice is made for other reasons.

I hope you didn't get too confused.  Believe me it all works and the common 
antennas all are based on these considerations.

Kerry