## Tuesday, October 18, 2011

### What does the ‘dBi’ mean when used to rate an antenna

Q Jerry, KC8OTH, asks, “What does the ‘dBi’ mean when
used to rate an antenna

A I will presume that you are somewhat familiar with the decibel. If not, at least a few numbers will put it into perspective. Decibel is a term that can compare two powers or voltage levels. The formulas are:

dB = 10log (P1/P2) where P1 and P2 are two power levels.

It can also compare voltages, if the voltages are at the same impedance. The formula is:

dB = 20log (V1/V2) where V1 and V2 are the two voltage levels.

(For “extra credit,” if the resistances are not equal, you can
use the formula dB = 10log ((V12/R1)/(V22/R2)).

Now, in antenna gain, there are two common references. The first is an imaginary antenna called an “isotropic” radiator. This is an antenna that radiates equally in all directions. An isotropic radiator placed at the center of a sphere would illuminate the sphere equally. No such antenna exists in real life. A practical example of what is nearly an isotropic radiator is a light bulb.

When gain is expressed in dBi, it indicates how much louder a signal from that antenna will be in the main beam of the antenna than it would be if the same amount of power were applied to an isotropic radiator in free space. The thing to remember about gain is that an antenna develops gain by concentrating energy in one direction and not radiating energy in other directions. Two examples of gain are flashlights, and the technique of cupping your hands when you shout to make the sound louder in the desired direction.

A directional antenna such as a Yagi can have considerable gain. Typical HF Yagi beams can have 8 dBi gain or more; a large VHF or UHF beam can have 20 dBi gain, or even more. Some easy numbers to remember are:

1 dB = 1.25 × power
2 dB = 1.6 × power
3 dB = 2 × power
10 dB = 10 × power

A 20-dBi-gain antenna would have 10 × 10 or 100 times the power gain of an isotropic radiator. One watt fed into a 20-dBi gain antenna would be as loud as 100 W fed into an isotropic source, but only in the direction the antenna is beaming.

Decibels also work in the other direction, too. An antenna with –3 dBi “gain” actually has a loss of 3 dB—it will lose half of the power applied to it. An antenna that is –10 dBi is radiating 1/10 the signal of one with 0 dBi gain; one that is –20 dBi is radiating 1/100 the signal and so on. A –20 dBi gain antenna with 1 W fed to it would sound as loud as an isotropic antenna being fed with 10 mW

Most H-Ts have antennas that are not very efficient. A gain of –10 dBi would be about typical. This can work very well if you are near a repeater, but if you are right at the edge of a repeater’s range, or operating simplex over a few miles, this will not give a very good signal; it will sound “scratchy” on the receiving end.

Another reference point is dBd, or referring the gain to a half-wave dipole in free space. The half-wave dipole in free space has a gain of 2.15 dBi, so gain expressed in dBd is always 2.15 dB less than gain expressed in dBi. Don’t worry, the gain of the antenna is the same in both cases, only the reference has changed. If you want to compare an antenna whose gain is in dBd to one whose gain is in dBi, add 2.15 to the gain of the antenna in dBd.

I don’t want to make it too complicated, but I will add that most antenna gain figures tell you what the antenna would be if it were in free space—infinitely far away from the Earth. In the real world, the ground affects the antenna performance by reflecting signals upward. This actually adds up to about 5 dB to the gain of an antenna. So, a half-wavelength dipole over ground can actually have about 5 dBd of gain! Slick, eh? The half-wavelength dipole over ground has 5-dB gain over a halfwave dipole in free space.

From QST April 2001