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Back to Basics: What is dBi?

Decibels often make our students' eyes glaze over...

The question:

B-006-009-010 The gain of an antenna, especially on VHF and above, is quoted in dBi. The "i" in this expression stands for:

   A. isotropic
   B. ideal
   C. Ionosphere
   D. interpolated

There are a couple of questions in the Basic Question Bank that relate to decibels and to antenna gain measurements. This specific question involves two concepts, measurement in decibels and isotropic antennas.

The decibel (symbol: dB) is a logarithmic unit used to express the ratio of one value of a physical property to another, and may used to express a change in value (e.g., +1 dB or -1 dB) or an absolute value. In the latter case, it expresses the ratio of a value to a reference value; when used in this way, the decibel symbol should be appended with a suffix that indicates the reference value or some other property. For example, if the reference value is 1 volt, then the suffix is "dBV" (i.e., "20 dBV"), and if the reference value is one milliwatt, then the suffix is "dBm" (i.e., "20 dBm"). For Basic exam purposes, it is important to know that +3dB is a doubling and –3dB a halving of a value. For example, question B-006-009-011 asks about the front-to-back ratio of a beam antenna.

The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth (deci-) of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, antennas, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

An isotropic radiator [pictured on the left] does not exist, it is a theoretical point source of electromagnetic or sound waves which radiates the same intensity of radiation in all directions. It is a point in space. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centered on the source. Isotropic radiators are used as reference radiators with which other sources are compared, for example in determining the gain of antennas. 

In electromagnetics, an antenna's power gain or simply ‘gain’ is a key performance number which combines the antenna's directivity and electrical efficiency. In a transmitting antenna, the gain describes how well the antenna converts input power into radio waves headed in a specified direction. In a receiving antenna, the gain describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, "gain" is understood to refer to the peak value of the gain, the gain in the direction of the antenna's main lobe. A plot of the gain as a function of direction is called the radiation pattern.

Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi). An alternative definition compares the received power to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd. 

Directive gain or directivity is a different measure which does not take an antenna's electrical efficiency into account. This term is sometimes more relevant in the case of a receiving antenna where one is concerned mainly with the ability of an antenna to receive signals from one direction while rejecting interfering signals coming from a different direction.

The answer to our initial question therefore is 1. isotropic.

~ John VE7TI

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