Jeff Duntemanns Drive-By Wi-Fi Guide

dB, dBi, dBm: The Decibel Family

If you intend to simply buy stock Wi-Fi gear, plug it in, set it up, and go, you don't need to deal with decibels and their children. On the other hand, as soon as you begin to fool with external antennas, coaxial cable, bridge mode, and things like that, power levels, signal levels, and losses begin to loom large. The decibel family of units are ways to get a grip on those things.

Simply put, a decibel (abbreviated dB) is a measure of relative power or signal strength. 'Relative' means it's not a question of absolute units (like watts for power, or volts for signal) but a comparison of two values.

The easiest way to understand the idea of relative power is to think of an amplifier. An amplifier takes a signal of some sort at its input, and reproduces the signal at its output-at greater power. The power of the output signal may be compared to the power of the input signal in terms of decibels. This value in decibels is the gain of the amplifier, and doesn't depend on whether the amp is a small signal amp or a power amp. You can have a 6 dB gain amplifier the size of a matchhead, or the size of a trash barrel. One amplifies signals measured in microvolts; the other amplifies power measured in kilowatts. What matters is the relationship of output to input, expressed in decibels.

Losses in a length of coaxial cable can be expressed in decibels as well. (Especially at microwave frequencies, a length of coaxial cable is like an amplifier in reverse.) The relationship of power levels leaving a cable to the power put into the cable indicates the loss occurring inside the cable. The decibels figure in that case is negative, but it's still the relationship between input and output.

It's not a simple ratio, say, output over input. Decibels express a base-10 logarithmic scale. The relationship between two power levels expressed in decibels is calculated this way:

An amplifier that outputs 32 watts for 2 watts input would have a gain of 10 x log (32 / 2), or 12.04 dB.

For losses, it works the same way. Say you put 5 watts into a run of coaxial cable, and measure 1.8 watts at the other end of the cable. Your cable loss would be 10 x log (1.8 / 5) or -4.43 dB.

Note the x 10 factor in the equation. There is a unit called a Bel (after telephone inventor Alexander Graham Bell) which was developed by telephone engineers seeking to capture the logarithmic nature of human hearing. A Bel is simply the logarithm of a ratio of two signal levels, but the magnitude of the results of the logarithmic equation is smaller than is convenient for most real-world work. So a new unit with one tenth the magnitude of a Bel was defined and named the decibel. Using decibels rather than Bels is simply a mathematical convenience that gives us an appropriate unit of measure; it's very much like choosing to measure the distance from Arizona to Chicago in miles rather than inches.

Eyeballing Gains and Losses

All the math may obscure the real value of decibels: They make it possible to easily calculate (often in your head) combinations of gains and losses as represented by radio amplifiers, antennas, and runs of coaxial cable. The total gain (or loss) of a system may be calculated by simply adding the gains and losses of its various parts, all expressed in decibels. For example, say you have a 6 dBi gain antenna (I'll explain 'dBi' in a moment) fed by a run of coaxial cable that loses 2.7 dB. Adding 6 to -2.7 gives you 3.3 dB, which is the total gain of the system represented by the antenna and the cable.

A convenient rule of thumb is that 3 dB represents a doubling of power, and -3 dB represents a halving of power. 6 dB is thus a doubling of a doubling, or quadrupling (4x) of power, and -6 dB divides your power by 4.

One critical role of gain antennas is to compensate for inevitable losses in coaxial cable. At microwave frequencies, losses in runs of coax longer than a few feet can be crippling, especially if you try to use coax not designed for microwaves. Coaxial cable is rated at loss in dB per 100 feet. (You can calculate shorter runs as simple proportions.) If you intend to use coax in your Wi-Fi installations, you need to be able to calculate the loss that happens inside the cable and make sure that your cables aren't simply eating your power and leaving none for the radios and antennas!

Antennas and dBi

If you shop for commercial Wi-Fi antennas, you'll see most antennas rated for gain in units called dBi. A dBi is not a different unit than a decibel. It's an abbreviation of 'dB gain over an isotropic antenna.' As I explained a little earlier, gain antennas aren't exactly like amplifiers. They don't add power to your signal. They focus your signal, like a lens focuses light. Instead of spraying radio waves equally in all directions, they concentrate radio energy in a particular direction, while reducing energy in other directions.

An isotropic antenna is in fact an antenna that does spray radio waves equally in all directions, including up and down. Such antennas don't really exist in their ideal form, but the uniform theoretical radio field of an isotropic antenna provides an input value for comparison against a gain antenna's output value in the direction of greatest gain. A dBi is a decibel of gain realized by a gain antenna, compared to what that theoretical isotropic antenna would do with the same radio power input. As a unit it actually has more to do with degree of focus of radio energy than gain in the sense that an amplifier provides.

The dBi gain of an antenna tells you, in a sense, how much additional power you would need to get the same performance from an isotropic antenna. The dBi allows you to perform gain/loss calculations that incorporate antennas as well as amplifiers and cables.

Watts and dBm

Unlike dBi, the unit dBm is quite different from the decibel. The dBm unit indicates absolute power levels, not relative power levels. In that it's very much like the watt, and in fact you can convert any dBm value to an equivalent value in watts. So why not use watts? Watt's (sorry) the point?

Just as the dBi unit allows you to easily calculate antenna gain into the total gains and losses in an RF system, the dBm unit allows you to easily calculate absolute power levels into an RF system that includes radio transmitters (which generate RF power) amplifiers, coaxial cables, and antennas.

The term dBm is an abbreviation for 'power relative to one milliwatt.' (A milliwatt is one one-thousandth of a watt, or .001 watts.) The unit dBm assumes one milliwatt of absolute power as a 0-based value, and expresses absolute power values both above and below one milliwatt on a logarithmic scale. (0 dBm is equal to one milliwatt.) The equation for calculating dBm from watts is similar to the first equation I presented for decibels:

This allows you to calculate the equivalent of a power value in watts in dBm units. For example, say the radio output stage of a Wi-Fi client adapter puts out 85 milliwatts of RF power. Plug that value into the Power variable, expressed in watts. That makes the calculation cook down to 10 x log (.085 / .001), or 19.29 dBm. Make sure you express the Power term in watts, not milliwatts!

Think back to the rule of thumb for decibels. The same scale applies here. One milliwatt is 0 dBm. Two milliwatts is 3dBm. Half a milliwatt is -3 dBm.

Learning to think of power in dBm terms allows you to do easy gain and loss calculations that tell you how much absolute power actually comes out of an antenna. This is important, since by the FCC's Part 15 rules, Wi-Fi power is limited to either one watt of actual transmitter output power, or four watts effective radiated power, which depends on the gain of your antenna and the losses in whatever cables links your Wi-Fi device to your antenna.

Calculating that effective radiated power value is much easier when your Wi-Fi client adapter or access point output is expressed in dBm. Here's an example: Say you have a client adapter that puts out 85 milliwatts. As shown above, that's 19.29 dBm. You connect the adapter to an antenna with 14 dBi gain, through a 30' run of cable rated for loss at 8 dB per 100 feet. What is the effective radiated power coming off the antenna?

First figure the total loss in your coaxial cable, in dB. If 100 feet of cable has 8 dB loss, 30 feet has 30/100 x 8 dB, or 2.4 dB. Next, add your radio output power to your antenna gain, and then subtract your cable loss: 19.29 dBm + 14 dBi - 2.4 dB = 30.89 dBm of effective radiated power. How much is that in watts? Converting backward from dBm to milliwatts is done this way:

mw = 10^dBm/10

Divide your 30.89 dBm figure by ten, giving you 3.089, and then raise ten to that power. 10 raised to the power 3.089 equals 1227.4 milliwatts, or 1.23 watts. Your system is thus still on the right side of Part 15!