# Why I use dBi - Mostly

### L. B. Cebik, W4RNL

Although current commercial practice is to specify antenna gain in dBd, I tend in my modeling work to use dBi. It is reasonable to ask why, if for no other reason than to understand better the other entries in this collection of notes. So I shall explain why. My object is not to get anyone to change their preferred ways, but only to make a little clearer my preference for specifying gain in dBi.

### dBi

Every measure in decibels, or dB, is ultimately a relative power measurement (with some defined relative voltage and current measures having been derived from the basic power measure). Decibels are defined this way:
Relative power in dB = 10 log (base 10) P1 / P2,

where P1 and P2 are two power levels measured in the same units (e.g., watts).

Since we may pick any two powers for P1 and P2, power gain or loss is strictly relative.

However, we have found it useful to select--for specific purposes--certain baseline power levels. One such level is whatever power there might be in the radiation far field of an isotropic radiator. An isotropic radiator is a lossless dimensionless point in free space that radiates equally well in all directions. Although some say this is a absolutely theoretic concept only, Brian Beezley, K6STI, has established that a pretty good approximation of an isotropic radiator can actually be constructed.

Using this radiator as the baseline and taking measurements at the same far field distance from the antenna, the power received from the antenna will have a certain relative level in comparison to what would have been received from the isotropic radiator. What that level is depends on the characteristics of the test antenna and the direction in which we choose to take the readings, using a full 3-dimensional sphere as the possible directions for readings. In some directions we may get more power; in others we may receive less.

One of the chief advantages of the isotropic radiator is that its field never changes, so that it functions as an agreed upon constant against which every antenna may be measured in every direction.

Every antenna measurement referenced to a P2 that is the far field power from an isotropic radiator has a positive or negative gain in dBi.

### Gain

When we casually refer to antenna gain, we do not normally mean the gain in any haphazard direction from the test antenna. Nor do we mean all the possible gain numbers we might gather from a systematic tour around the surface of our far field globe surrounding the antenna. Gain in every direction is important, for it defines the antenna pattern and tells us where the far field is strongest and weakest and in the middle--and by how much.

However, when we casually mention gain, we are usually interested in the direction(s) of maximum gain from a given test antenna. Then we rotate the antenna to present that antenna direction to the receiving station. For satellites, we may rotate in 3 dimensions, but for HF, 2-dimensional rotation usually suffices (unless we must somehow compensate for a bit of tricky terrain and have the wherewithal to do so).

We can specify maximum antenna gain in terms of dBi. Then we can compare maximum antenna gains from 2 or more antennas by citing their gains in dBi and merely comparing numbers.

This practice is perfectly reasonable so long as we do not make it a fetish; that is, so long as we do not use this number exclusively in our gain considerations. Horizontal beamwidth is also important and is usually defined in terms of the number of degrees between half-power or -3 dB points where the direction of maximum gain is the center. Vertical beamwidth is also important in estimating the success of a potential path. We also want to know, in conjunction with vertical beamwidth, the elevation angle of maximum radiation. Together, these numbers give a more complete picture of antenna performance in a desired direction than raw gain alone.

I have modeled an array with a 21 dBi gain figure. However, the horizontal beamwidth is only about 17 or 18 degrees wide, making it unsuited for general amateur operation. However, we often assume that competing antennas have the same beamwidth and that all we need to know in making our selection is the maximum gain. Good practice calls for making no such assumption. Rather, before we focus on maximum gain, we should establish that all other factors are equal.

### dBd: a warm but fuzzy concept

The concept of dBd was formed to capture the gain of an antenna relative to a dipole. A dipole is considered the standard basic horizontal antenna, and comparisons to it seemed to some folks to be more meaningful than comparisons to the isotropic radiator.

Unfortunately, the concept of dBd has become a cluster of concepts. Here are some of them. The notation is my own, since few folks are anxious to distinguish the individuals in the cluster.

1. dBd-I: dBd ideal compares the gain of an antenna to an ideal dipole in free space. An ideal dipole uses infinitely thin lossless wire and is resonant at the frequency of interest. In this application, the ideal dipole has a gain of about 2.15 dBi, that is, 2.15 dB over an isotropic radiator. All measurements are thus arithmetically transportable between dBi and dBd-I by adding or subtracting 2.15, as appropriate.

dBd-I is of limited utility, since my backyard dipole may have a gain of 7.15 dBi and 5 dBd. Some folks become confused by the idea that a dipole has gain over a dipole. We then have to explain that the real wire dipole has gain over the perfect dipole in free space. That rarely helps a lot. And it does not tell us until we do some arithmetic how much gain some other antenna has over a real dipole.

2. dBd-RM: dBd can be expressed as the gain over a real dipole modeled at the same height as the test antenna. For studies that are strictly modeling investigations, this measure is sometimes useful. However, it requires that we further specify the construction of the dipole in terms of element diameter and element material. Using the same material, dipole gain will vary with element diameter. It will also vary inversely with the loss of the material used for the dipole.

Both these constraints apply within the further rule of keeping the dipole resonant. If we make measurements across a ham band, we shall find that the dipole gain varies with frequency unless we re-resonate it for each readout frequency. Actually, we are usually more careless than this and take one resonant reading and apply it across the band without checking. And we tend to use fairly loose standards of resonance rather than converging the results. We may more precisely say that an antenna is resonant when the reduction of feedpoint reactance results in no further changes in gain to the number of significant digits that apply to the test.

As one more qualification, we should note that dipoles and other antennas may have different elevation angles of maximum radiation over the same type of ground. When we cite dBd-RM, we must also say whether we are giving the figure for the dipole at its angle of maximum radiation or at the angle chosen for the test antenna. To avoid confusion, it is usually better to give details about the differing elevation patterns.

3. dBd-RR: dBd can be expressed as the gain over a real dipole set in the same position as the test antenna, where both antennas are oriented for maximum gain relative to the far field receiving site of the test range. For fairness, one should specify the construction of the dipole to ensure that the materials are comparable to those of the test antenna.

However, there are a number of variables that occur within this way of handling dBd. First, range conditions vary considerably from one site to another. Second, some testers take the average of a number of readings in various directions, while others take readings along a single line defined as the best test line. Third, different ranges may use different test heights. The importance of this factor stems from the fact that many antennas that might be tested have different elevation angles of maximum radiation than a dipole, and this variance may introduce differences in readings as we change test antennas and as we move from range to range with different test antenna heights.

Good testing and modeling protocols would specify all of the relevant factors applying to the comparisons involved. We sometimes do find these specifications. Unfortunately, we often don't. Without the specifications, comparisons in dBd-R (either M or R) are quite difficult to make. If we could only bring all antennas to a single test range with a single (large) set of dipoles and standardized conditions, we could likely establish the gain of each antenna over its standard dipole and then have truly precise comparisons among antennas. Someone has noted to me that the odds of the earth being struck by a meteor like the one which ended the reign of the dinosaurs are higher than the odds of the emergence of a universal test range. I really wish I could have disagreed with this individual.

For additional pitfalls of careless dBd-ing, see the next item on the Index.

### Why I tend to stick to dBi

My antenna work includes the building of test models of antennas that are feasible to construct, but is devoted predominantly to modeling all sorts of antennas for all sorts of purposes. This factor alone suggests the use of a single standard for all comparisons, such as dBi. However, there are a number of reasons I tend not to use dBd except in special circumstances.

1. The relevant comparisons are not with a dipole. Very often, antenna comparisons are among antennas that do not include dipoles. In such cases, simply comparing gain figures in dBi tells us all we need to know and can know about the relative maximum gains of the antennas. For example, in comparing the gains of self-contained 1 wl wire-loop antennas, the best designs for a given purpose are the ones that are best within the group, and the group does not include a horizontal dipole.

Likewise, when contemplating whether it is worthwhile to increase the size of a Yagi for 20 meters from 3 to 4 elements, the dipole is not relevant. Rather, the relevant gain comparison is between both models and real antennas of 3 and 4 element design. The gain advantage is derived as easily from dBi as from any other system of gain numbers.

2. The relevant comparisons have only passing reference to maximum gain. Additional factors, such as elevation angle, beamwidth, etc., may be far more important than gain itself. For some applications, good antennas do not need gain relative to a dipole. But they may require close specification of other antenna properties. Gain becomes a secondary specification for which dBi suffices nicely.

### Range tests are another matter

If my work were primarily with real antennas, then dBi would become a problematical term. A test range approximation of an isotropic radiator is an unlikely event anytime soon. Hence, antennas on test ranges must be compared to some standard, and the dipole is the most likely simple horizontally polarized candidate. If we accept this premise, then it is unreasonable to expect range testers to then correlate their results to a scheme of modeling in which the gain is converted to a value in dBi.

However, this situation makes it imperative that range testers specify a test protocol and comparison antenna for the evaluation of the procedure against good engineering practice. In many instances, the comparison antenna will not be a dipole (although amateurs often think only in terms of Yagi tests). Verticals require specification of a vertical standard of the appropriate class. Nothing substitutes for the revelation of detailed test protocols where range testing is at stake.

Conversion of the test situation to models--like any other case of modeling--is at best the most reasonable approximation we can develop. Absolute precision is unlikely in most instances. Hence, the conversion of range test results to modeling results--with the accompanying conversion of dBd-RR (with a clear specification of the standard dipole used) to dBi--is not an automatic process and is subject to varying degrees of adequacy.

Modeling of detailed test protocols, on the other hand, can yield some correlation factors among different test protocols. A model may substitute one standard dipole for another, may insert or remove test range objects affecting results, may change antenna heights with ease, etc. As a simple example, if Smith tests his antenna at 60' up and Jones tests his at 85' up, the differences in test results (all other factors being equal or equalized) can be at least tentatively resolved with effective modeling.

Whatever the prospects for such work in the future (for we have just begun to scratch the surface of effective modeling in antenna work), those who predominantly model will likely stick to dBi as the basic measure of maximum gain. Range testers will likely stick to dBd-RR, where the range test is a comparison to a dipole or other relevant standard.

Since I am mostly a modeler, I use dBi---mostly.

Updated 6-23-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.