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Restricted Space Antennas

by Walt Fair, Jr., W5ALT

Basics Concepts II

In this section we will continue our review of basic concepts important to the understanding of antennas in general, and small antennas in particular.

Skin Effect. When I started messing with antennas I took an ohm-meter and measured the resistance of copper wire. It was pretty low, of course, and hard to measure. Unfortunately the resistance that we are interested in for antenna work is not the resistance that you can measure with a DC ohm-meter. The reason is called skin effect.

Because an alternating current causes an electromagnetic field to form around a conductor and conversely a changing magnetic field causes a current to flow in a conductor, there is a tendency for the current to flow on the outside surface of a conductor. The magnitude of the effect depends mainly on frequency.

The skin effect has two main consequences for us in antenna work. First, since the current flows mainly on the outside of the conductor, there is no advantage to using solid conductors. It is just as efficient to use tubes or pipes that weigh a lot less for large diameter conductors. That certainly makes things easier for us.

The other effect is that the resistance to current flow of the wire will be more than we would normally estimate from DC current measurements. This will impact the antenna efficiency, because the skin effect does indeed cause real losses and heat. To estimate the resistance of copper wire, the following equation can be used, where the resistance is in ohms/ft, frequency is in MHz and diameter in inches.

R = 0.000996 F0.5 / d
For aluminum, the resistance will be about 1.5 times greater

Gain. Gain is one of those confusing things that says a lot and doesn't tell you much. Basically gain is defined as a power ratio and is usually expressed in decibels, abbreviated "dB". The definition of decibels is dB = 10 log(P1/P0), where P1 is the power being compared to the reference power, P0.

Now the advantage of reporting gain figures is that it allows a direct comparison of powers. If you have 3 dB of gain, the power is doubled, 10 dB means there is 10 times more power, etc. The problem is you have to define P0, the reference power, or you have no way of knowing what the figure really means.

So, if an antenna has 3 dB of gain over a reference antenna, that means you can get the same signal strength at the receiving end by using the antenna you are evaluating, or by doubling the transmitter power to the reference antenna. At the receiving end there's no way to tell which really occured.

Another important concept concerning gain is that gain always is accompanied by directivity. If an antenna radiates power equally in all directions, then the gain is 0 dB with respect to any direction or with respect to an isotropic radiator. (See next section.) The only way to get more power radiated in one direction is to have less radiated somewhere else. Therefore, if an antenna shows gain in some particular direction, you can rest assured that it worse in other directions.

dBi and dBd. In antenna work there are 2 commonly used gain references: an isotropic antenna (dBi) and a dipole antenna (dBd).

An isotropic antenna is a fictional antenna that radiates equally in all directions in 3D space. It's fictional because no one can actually build one, but the mathematical properties are easily calculated. If an isotropic antenna would yield a certain power density, P0, while an real antenna shows P1, then the antenna gain is 10 log(P1/P0) dBi. The advatage is that it is easily defined and easily calculated and there is no ambiguity to the use of dBi. However, since there is no real isotropic antenna, it's not so easily visualized.

A dipole antenna is a real antenna and they have been built, so a direct comparison to a dipole is possible and the gain in terms of dBd can indeed be measured. Unfortunately, real dipoles are affected by lots of factors, as we shall see later, but gain in terms of dBd is normally referenced to a perfect dipole in free-space. So once again, we're not quite sure what we are comparing. When one takes into account ground reflections, a real dipole often shows gain "relative to a dipole." Talk about confusing!

To avoid confusion once and for all, all gain figures in these notes will be expressed in dBi - relative to an isotropic antenna. If you want to convert the figures to dBd, just subtract 2.14 dB, which is the free-space gain of a dipole in dBi.

Next - Antenna Scaling