Chapter 2: Introduction to Radiation Patterns

October 11, 2023

ABSTRACT
There are three important terms that we hear all the time when it comes to antennas– directivity, gain and efficiency. These three concepts are linked together along with the concept of an isotropic radiator. The detailed definitions of these terms require some amount of math to support them. I will explain these terms in more detail so that you can have a working definition of each one.

Stephen V. Saliga, Ph.D.
Vice-President, Engineering

I want to start with the concept of an isotropic radiator or isotropic antenna. An isotropic antenna is an ideal lossless element that radiates energy equally in all directions. From this description, it is easy to draw out its radiation pattern – it’s a simple sphere and the 3D radiation pattern and elevation and azimuth plane patterns are shown below. No real antenna does this, but we use an isotropic antenna as a comparison standard to assess how actual antennas perform.

The term “directivity” is defined as the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions. Therefore, the directivity of an antenna is the ratio of its radiation intensity in a given direction over the radiation intensity of an isotropic antenna. Note that directivity is a dimensionless quantity since it’s the ratio of two radiation intensities and the result of this definition is that the directivity of an isotropic antenna is equal to one. Directivity can certainly be greater than one if the antenna radiates more energy in a particular direction than an isotropic element (many antennas do this).

Now for the term “gain”. It is unfortunate that the word “gain” is used because antennas don’t create any energy. There is no amplification, just redistribution. Even if an antenna has a gain greater than one, it does not imply that there is amplification or that somehow, we have created energy. Gain (in a given direction) is defined as the ratio of the radiation intensity to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. Here we are again, comparing to an isotropic antenna. This is quite similar to “directivity” so what is going on here?

Notice that in the definition for directivity, there is no mention of power at the input of the antenna. It is all power radiated from the antenna. An isotropic antenna radiates all its power – it is lossless. So, directivity does not take into account any losses at the input or through the antenna. Gain on the other hand, depends on the power accepted (input) by the antenna, and therefore gain is implicitly dependent on losses incurred in radiating the energy. Notice that gain is dependent on the direction at which you look. But frequently we refer to “the gain” of antenna and by that we typically mean the “maximum gain” or “peak gain”.

As a simplification, you can think of directivity as a description of how an antenna should radiate energy and then the gain is a description of how an antenna does radiate energy, including losses. In fact, the relationship is G = εD where G is the gain, ε is the antenna’s radiation efficiency and D is the Directivity. This radiation efficiency is related to the total radiated power and the total input power by the simple equation Prad = εPin. The total radiated power is always smaller than the total input power – always – antennas don’t create energy (or power), they are a loss mechanism.

One more point on efficiency. There are wonderful antenna measurement systems on the market today that will make measurements of “efficiency”, but these measurements are not quite the same as the definition of radiation efficiency. These measurement systems make direct measurements of “total efficiency” since the VSWR (related to impedance mismatch) is included in the measurement. Radiation efficiency does not include impedance mismatch losses. These are the same, however, if the antenna is perfectly matched, as in the case of an isotropic antenna (it is lossless). Impedance mismatches are often the most important loss mechanism and the most controllable.

In this short post, we’ve covered the basics of gain, efficiency, and directivity. You will see these concepts frequently when you encounter antennas and hopefully now you have a better feeling for their meaning.

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