# Explain: "Antenna gain" in dB?

I was speaking to an EE who couldn’t explain why antenna gain (in an RF signal) is measured in dB. He says “because it’s sound”. But, I had to point out it’s NOT sound, RF is part of the electromagnetic spectrum, i.e.: light! What’s up with that? - Jinx The decibel is a unit of power (strictly speaking, of power ratio). It’s applicable to any sort of power, electrical, acoustic, or otherwise.

Gain is measured in dB because you’re usually interested in the ratio between the input and output power, rather than (say) the voltage of the signal, which will depend on the impedance of the receiver.

Antenna gain is a power ratio. It is the ratio of the power that must be supplied to the test antenna in order to get a particular field strength at some location relative to the antenna to the power that must be supplied to an isotropic antenna to get the same field strength at the same location.

It is a power ratio so expressing it in dB seems quite in order.

Example. Take the test antenna, apply a signal of 1 Watt to it and measure the field strength at Location A. Replace the antenna with an isotropic antenna and increase the power to it until you get the same field strength as before at Location A. Suppose that power is 100 Watts. The antenna gain in dB is 10log(P1/P2) which in this case is 20 dB.

To be more exact the gain in the direction of Location A is 20 dB.

Cripes. Someone wasn’t paying much attention in EE school.

The “gain” of an antenna comes from the fact that the antenna in question focuses its energy more in one direction than another. If you grab your handy dandy field strength meter and walk around the isotropic antenna that David mentioned, you’ll find that as long as you keep the same distance away from the antenna, you will read the same signal strength no matter what direction you are away from the antenna.

Now take a directional antenna. You’ll find that on the front side of the antenna, it may boost the signal by a factor of 100. As David said, this is going to be a “gain” of 10log(100/1), or 20 dB. But, if you walk around to the sides of the antenna, you’ll find that the signal there is much smaller than it was before when you were using the isotropic antenna.

The important concept here is that the antenna isn’t amplifying the signal, it’s just focusing it. Even though there is a “gain”, you aren’t getting more power out of the antenna than you are putting into it. You are just focusing it in one direction.

Here’s a graph showing the radiation pattern of a typical directional antenna:
http://www.astronwireless.com/images/Understnd_fig4.gif
Note that most of the signal is directed towards the front of the antenna. Down on the sides (at 90deg and 270 deg) the signal is reduced to almost zero.

In contrast, an antenna with a pattern like this one is going to have a much lower gain, because it spreads its energy out in a much wider pattern:
http://www.hp.com/rnd/images/pdf_html/antennas_figure5.jpg

I can sorta understand why it’s a logarithmic ratio without knowing much about the subject, but why a factor of 10?

To convert from Bels to decibels. In the same way that you’d put in 100 to convert from metres to centimetres.

One will commonly see antenna specs listed with dBi measurements, indicating decibel gain referencing an ideal isotropic antenna. There are other reference antennas, too. dBd is a dipole. Simply saying dB may lead to misunderstood or, worse, dishonest ratios. For example, my new Jngl-modified yagi design might boast a 20 dB gain. However, if I bury in the fine print the fact that the reference antenna is a q-tip, my antenna doesn’t look so hot.

Saying ‘20 dB gain’ is like saying cucumber is 100x better.

The Bel was considered an inconveniently large unit for most purposes, which lead to the creation of the decibel.

Im Horrified that anyone could obtain a EE degree, yet be so clueless .

Respondants have been mostly correct so far. dB indicates a ratio, so you need to know what the reference standard is. dB is a valid way to express any power ratio. dBm is frequently used as an absolute measure of power, the “m” meaning that 0dBm = 1 milliwatt.

Back to antennas: “Gain” of one antenna over another comes from two sources. First, some antennas are quite lossy, converting RF to heat rather than EM at the input frequency.
The larger factor is directionality. Consider how the reflector on a spot-light creates a lot of “gain” over a bare bulb…not a bad analogy when you consider that parabolic reflecting dishes used at microwave frequencys are some of highest gain antennae extant.

An Omni-directional antenna can still have some gain, because it is only an “omni” in one plane. By directing more power to the horizon, and less toward the sky and ground.

The two common standards of comparison for antennas (dipole and isotropic) are mentioned in a previous response. The isotropic antenna is discribed as “ideal”, which is an accurate, but possibly confusing adjective.

An isotropic antenna isn’t “ideal” in the sense of being ezpecially useful, or a goal a designer seeks to attain, but “ideal” in the sense that it is next to impossible to actually build one. An antenna that radiates equally well in every direction is in many ways a sensible standard of reference, but since you can’t make one, it is impossible to actually use one for comparison when making the measurements. Thus a dipole antenna, or even a two dipole array which IS very easy to make, and has predictable and repeatable performance is often used for the actual measurements.

You only get to dBi figures (decibels with respect to an isotropic antenna) by adding the theoretical gain of your actual reference antenna over an isotropic…in layman’s terms, you take what you measured, and add a “fudge factor” to get to what you wished you had a way to measure. Not really dishonest, but it is the reason you occassionally see dBd (gain with respect to a dipole) figures, which will be a few dB lower than dBi figures for a given antenna…When a company publishes that, it usually means “here is our raw data without the dBd-dBi fudge factor that the marketing department wanted us to add”… You will only see dBd figures when marketing is directed toward engineers, never on a consumer oriented product.

The next question will be “Why not express the ratio as a ratio instead of messing about with logs?”

The first answer is that when designing or analyzing a communication system, the engineers can just add up all the gains, and subtract all the losses, and come up with a net gain figure in a minute or so. Absent the logs, this would require a lot of tedious and mistake prone multiplying.

The second answer is that a huge range of power levels can be accomidated with a fairly compact range of numbers. A communicaions engineer may be dealing with Kilowatts of power at the transmitter, and micro- or even nanowatts at the receiver. Eleven or twelve orders of magnitude compress to less than a 150 dB range, which makes it much less likely to screw the pooch by misplacing a decimal point.

Sound is measured in dB for an entireley different reason. Human hearing response is approximatly logarithmic, thus the dB scale tracks well with how loud things “seem”.

QUOTE=Kevbo]Im Horrified that anyone could obtain a EE degree, yet be so clueless .

Respondants have been mostly correct so far. dB indicates a ratio, so you need to know what the reference standard is. dB is a valid way to express any power ratio. dBm is frequently used as an absolute measure of power, the “m” meaning that 0dBm = 1 milliwatt.

Back to antennas: “Gain” of one antenna over another comes from two sources. First, some antennas are quite lossy, converting RF to heat rather than EM at the input frequency.
The larger factor is directionality. Consider how the reflector on a spot-light creates a lot of “gain” over a bare bulb…not a bad analogy when you consider that parabolic reflecting dishes used at microwave frequencys are some of highest gain antennae extant.

An Omni-directional antenna can still have some gain, because it is only an “omni” in one plane. By directing more power to the horizon, and less toward the sky and ground.

The two common standards of comparison for antennas (dipole and isotropic) are mentioned in a previous response. The isotropic antenna is discribed as “ideal”, which is an accurate, but possibly confusing adjective.

An isotropic antenna isn’t “ideal” in the sense of being ezpecially useful, or a goal a designer seeks to attain, but “ideal” in the sense that it is next to impossible to actually build one. An antenna that radiates equally well in every direction is in many ways a sensible standard of reference, but since you can’t make one, it is impossible to actually use one for comparison when making the measurements. Thus a dipole antenna, or even a two dipole array which IS very easy to make, and has predictable and repeatable performance is often used for the actual measurements.

You only get to dBi figures (decibels with respect to an isotropic antenna) by adding the theoretical gain of your actual reference antenna over an isotropic…in layman’s terms, you take what you measured, and add a “fudge factor” to get to what you wished you had a way to measure. Not really dishonest, but it is the reason you occassionally see dBd (gain with respect to a dipole) figures, which will be a few dB lower than dBi figures for a given antenna…When a company publishes that, it usually means “here is our raw data without the dBd-dBi fudge factor that the marketing department wanted us to add”… You will only see dBd figures when marketing is directed toward engineers, never on a consumer oriented product.

The next question will be “Why not express the ratio as a ratio instead of messing about with logs?”

The first answer is that when designing or analyzing a communication system, the engineers can just add up all the gains, and subtract all the losses, and come up with a net gain figure in a minute or so. Absent the logs, this would require a lot of tedious and mistake prone multiplying.

The second answer is that a huge range of power levels can be accomidated with a fairly compact range of numbers. A communicaions engineer may be dealing with Kilowatts of power at the transmitter, and micro- or even nanowatts at the receiver. Eleven or twelve orders of magnitude compress to less than a 150 dB range, which makes it much less likely to screw the pooch by misplacing a decimal point.

Sound is measured in dB for an entireley different reason. Human hearing response is approximatly logarithmic, thus the dB scale tracks well with how loud things “seem”.
[/QUOTE]
Good post. One small nitpick. I object to calling the conversion of an actual antenna gain to that of an isotropic antenna a “fudge factor.”

This correction factor is derived as a result of calibration of your actual antenna and isn’t in any sense just something thrown in to make things look good.

There is also a “fudge factor” in the measurement with an actual dipole. The theoretical gain of an ideal, isolated half-wave antenna is 1.64 or 2.148 dB. In order to make actual measurements with a real half-wave antenna in an anechoic chamber you have to calibrate the antenna in that chamber to get a “fudge factor” that you can apply to all of your measurements. That is, you set up your actual antenna and measure the field power at various places. Then you compute what the field intensity would be for an ideal half-wave antenna. This gives you the actual gain of your real antenna taking into accounts its losses and the losses in the chamber.

This explanation that dB measures power is not true, at least with acoutsical phenomena. dB is a measure of sound pressure <> wattage, although there is a relationship to equate the two. If dB= power, wouldn’t that simplify everything? But, IIRC, to increase a sound by 3 dB, it would require double the wattage.

Maybe someone can provide more to the story, regarding dB for sound vs. dB for RF antenna gain?

Thanks,

• Jinx Yes - 3dB gain is equal to doubling the power, approximately.

Gain (db) = 10 log[sub]10[/sub] (P[sub]out[/sub]/P[sub]in[/sub])

If P[sub]out[/sub] = 2 * P[sub]in[/sub]

Gain = 10 log[sub]10[/sub] (2) = 3.0103 dB

Wikipedia has an excellent article on the decibel.

For those who don’t want to follow a link, here’s some tidbits off the top of my head answering some questions:

• A Bel is the common logarithm of a power ratio. A tenth of a Bel is a decibel, or dB.

• Telephone technicians in the olden days found that one dB was about the smallest change in signal level that they could perceive, so that’s why dBs are more popular than Bels.

• To answer Jinx’s question, a dB is unambiguous - it’s the ratio of two signal levels. If you want to talk about the power in the signals, then 3 dB is double the power, and 10 dB is 10x the power. If you need to talk about the amplitudes (sound pressures, voltages, currents), then 6 dB is double, and 20 dB is 10x. A dB is 10log(power ratio) or 20log(ampl ratio), but by saying that one level is 20 dB more than another, you don’t have to say whether you’re talking power or voltage - it’s 10x the voltage and 100x the power.

• Often dBs are used relative to some fixed standard. Common are dBspl for ratios relative to a certain sound level, and dBm for ratios relative to one milliwatt.

Yes there is no confusion about the meaning of dB. Tevildo’s first post was the only one that spoke of dB as a unit of power and he corrected it immediately to a power ratio and should have corrected it to 10 times the common log of a power ratio.

As to the 10log for power ratio and 20log for amplitude ratio, they are only equivalent under special circumstances. In electrical power the two voltage amplitudes must be measured across the same resistance. The derivation of 20log for voltage ratios is straightforward.

P1 = E1[sup]2[/sup]/R1
P2 = E2[sup]2[/sup]/R2

10log(P1/P2) = 10log(E1[sup]2[/sup]R2/E2[sup]2[/sup]R1)

if, and only if, R1 = R2 the above becomes 10log(E1[sup]2[/sup]/E2[sup]2[/sup]) or 20log(E1/E2)