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• Stu WØSTU

# dBi vs. dBd (G9C04)

The 2019-2023 General License question pool wants you do differentiate between dBi and dBd when it comes to antenna gain:

G9C04: How does antenna gain stated in dBi compare to gain stated in dBd for the same antenna?

A. dBi gain figures are 2.15 dB lower than dBd gain figures

B. dBi gain figures are 2.15 dB higher than dBd gain figures

C. dBi gain figures are the same as the square root of dBd gain figures multiplied by 2.15

D. dBi gain figures are the reciprocal of dBd gain figures + 2.15 dB

Antenna gain means that an antenna produces increased signal strength is a particular direction at the expense of signal strength in other directions. Usually, antenna gain is expressed as a comparison with a reference antenna. For instance, a directional antenna such as a 3-element Yagi may provide signal strength in its forward direction roughly 7 dB to 9 dB over common reference antennas that radiate more equally in all directions. This question is all about those common reference antennas and the nature of gain comparisons.

One of the common antenna gain references is the theoretical point source antenna that radiates equally in all spherical directions. Uniformity in all orientations is called isotropy, and this common reference is called the isotropic antenna. When an antenna’s signal strength is compared to the isotropic antenna, any gain in signal strength stated in decibels is denoted with a lower case letter ‘i’ following the unit dB. Hence, dBi. Antenna signal strength patterns: Isotropic, Dipole, and Omnidirectional.

Another common reference antenna is the simple free space dipole antenna. The “free space” terminology means that the dipole reference is the theoretical performance of the dipole if it had no other objects near it, including the earth. The height of a dipole above the earth dramatically affects its radiation patterns, as can other objects (especially conductive objects) near the dipole. But a dipole in free space has none of these RF coupling impacts from other objects and its radiation pattern is a nice, theoretical, toroidal pattern emanating radially from the axis of the dipole radiator. When an antenna’s signal strength is compared to the theoretical free space dipole performance, any gain in signal strength stated in decibels is denoted with a lower case letter ‘d’ following the unit dB. Hence, dBd.

Compare the free space dipole pattern with the isotropic antenna pattern. Notice that the dipole’s pattern produces the greatest signal strength broadside, or radially, to its radiator axis. The increased signal strength in the radial directions comes at the expense of signal strength out the ends of the dipole radiator. Thus, when compared to the isotropic antenna the dipole exhibits gain is its radial directions. We may state the gain of the dipole as compared to the isotropic antenna in units of dB. Further, since this antenna comparison is using the isotropic case as the basis of performance, we should denote the gain units as dBi.

The free space dipole exhibits gain in the radial directions over the isotropic antenna of 2.15 dBi. This is a comparison of one theoretical antenna model (free space dipole) to another theoretical antenna model (isotropic). Now, let’s apply these facts to this specific question pool item.

When you purchase an antenna the gain will often be printed on the packaging or in literature. Gain figures stated on antenna package.

Let’s use a vertical omnidirectional antenna as an example -- this antenna radiates equally in all radial horizontal directions, but not so much in the vertical directions up or down. Here is the packaging for a dual band vertical that I use in my attic. Notice the gain figures are 4.5 dB for the 2-meter band and 7.2 dB for the 70-centimeter band. Ominously missing is the reference antenna denotation. (Shame!) But rest assured, it is dBi. In other words, the antenna produces those stated gain values in the horizontal radial directions as compared to the theoretical isotropic radiator.

Consider what would happen to the stated gain figures for this antenna if they were compared to the dipole reference instead. The dipole already has 2.15 dB gain over the isotropic reference. So, the gain figures must be reduced by 2.15 dB when the higher performing dipole reference is used for comparison. These stated dBi gain figures are 2.15 dB higher than equivalent dBd gain figures. Gain stated in dBi is always a larger number than gain stated in dBd, making an antenna product’s performance sound more impressive, and that’s one reason why most antenna products state gain in dBi even though comparison to a simple dipole is usually a more meaningful and practical comparison.

The answer to this General Class question G9C04, “How does antenna gain stated in dBi compare to gain stated in dBd for the same antenna?” is “B. dBi gain figures are 2.15 dB higher than dBd gain figures.”

-- Stu WØSTU

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