I'm a little concerned about the authoritative quotes I've seen lately
which state that the field from a conductor is directly proportional to
the current in the conductor. While true, it's seemingly being used to
support the conclusion that a longer conductor inherently produces a
greater field, and by extension, that a larger antenna fundamentally
radiates more than a smaller one. Those conclusions are false, and I'll
explain why.

It's useful to start with the law of conservation of energy. If an
antenna is lossless, then all the power fed to it must be radiated. This
has to be true regardless of the antenna's size. So how can this be, if
the field is proportional to the conductor length? Are longer conductors
less lossy than short ones?

No, the principle of field being proportional to current and conductor
length assumes zero loss, so it has to apply to small and large antennas
alike. But so does the law of conservation of energy.

The answer to this apparent dilemma is that if you put a fixed *power*
into dipoles, say, of various lengths, the current will increase as the
antenna gets shorter. This keeps the product of length X current
essentially constant, resulting in a nearly constant radiated field for
a fixed power input. Another way of expressing the same thing which
might be more familiar is that the radiation resistance decreases as the
antenna gets shorter. Consequently, the current increases for a given
power input. To look at it yet another way, consider that if all the
power is to be radiated by both a short and long antenna, the current
must be much higher to get the same radiation from a short conductor as
a long one.

This increase in current becomes dramatic when the antenna gets very
small (in terms of wavelength), and that's where one of the problems
lies with short antennas. The I^2 * R conductor loss can become not only
significant but large even with very good conductors, when the antenna
is small. And that's why small antennas are often less efficient than
larger ones. It turns out to be due to the fact that the field is
proportional to the current and conductor length but not for the
simplistic reasons being implied. But the poor efficiency of a small
antenna is a practical matter which can be mitigated, often to a very
great extent, by using large and good conductors for example. It's not
due to any fundamental rule of radiation.

Another reason that looking only at the current - length rule for field
strength can be misleading is that the radiated field is the sum of many
incremental fields from the various parts of the antenna. Some antennas,
such as small loops or a W8JK beam, create fields which fully or
partially cancel in all directions. So the fields generated by the
individual parts of the antennas are greater than they'd otherwise need
to be in order to generate the resulting total radiation field. This
further reduces the efficiency of these antenna types, since higher
currents are being required to generate the larger fields. Still,
though, the law of conservation of energy applies -- except for power
lost to heating, all the power applied ends up in the radiated field,
even if it takes a much larger local (near) field in order to produce it.

There are other consequences of making an antenna small. One is that if
you do succeed in making it efficient by keeping loss very low, the
bandwidth will be very narrow. Another is that the very small radiation
resistance is accompanied by a very high feedpoint reactance. Any
practical network used to match this to the common 50 + j0 ohms required
by most transmitters and receivers will also be likely to be quite lossy
due to very high currents and/or voltages within the network. And, like
the antenna, most reasonably efficient matching networks will tend to be
very narrowbanded when being required to effect such an extreme
impedance transformation.

The considerations above are why small antennas are invariably
narrowbanded, inefficient, or both, and if the matching network loss is
included in the efficiency calculation, virtually never very efficient.
Claims to the contrary are heard all the time. But under scrutiny and
controlled test conditions, they don't fare any better than water dowsing.

Roy Lewallen, W7EL