# RF Power Values

Radio frequency (RF) power levels and the most common measure, the decibel (dB).

Power Level

The dB measures the power of a signal as a function of its ratio to another standardized value. The abbreviation dB is often combined with other abbreviations in order to represent the values that are compared.

Here are two examples:

• dBm The dB value is compared to 1 mW.
• dBw The dB value is compared to 1 W.

We can calculate the power in dBs from this formula:

Power (in dB) = 10 * log10 (Signal/Reference)

This list defines the terms in the formula:

• log10 is logarithm base 10.
• Signal is the power of the signal (for example, 50 mW).
• Reference is the reference power (for example, 1 mW).

Here is an example. If we want to calculate the power in dB of 50 mW, apply the formula in order to get:

Power (in dB) = 10 * log10 (50/1) = 10 * log10 (50) = 10 * 1.7 = 17 dBm

Because decibels are ratios that compare two power levels, we can use simple math in order to manipulate the ratios for the design and assembly of networks. For example, we can apply this basic rule in order to calculate logarithms of large numbers:

log10 (A*B) = log10(A) + log10(B)

If we use the formula above, we can calculate the power of 50 mW in dBs in this way:

Power (in dB) = 10 * log10 (50) = 10 * log10 (5 * 10) = (10 * log10 (5)) +

(10 * log10(10)) = 7 + 10 = 17 dBm

These are commonly used general rules:

 Increase Of Decrease Of Produces 3dB Double Transmit Power 3dB Half Transmit Power 10dB 10 times the Transmit Power 10dB Divide Transmit Power by 10 times 30dB 1000 times the Transmit Power 30dB Divide Transmit Power by 1000 times

This table provides approximate dBm to mW values:

 dBm mW 0 1 1 1.25 2 1.56 3 2 4 2.5 5 3.12 6 4 7 5 8 6.25 9 8 10 10 11 12.5 12 16 13 20 14 25 15 32 16 40 17 50 18 64 19 80 20 100 21 128 22 160 23 200 24 256 25 320 26 400 27 512 28 640 29 800 30 1000 or 1W

Here is an example:

1. If 0 dB = 1 mW, then 14 dB = 25 mW.

2. If 0 dB = 1 mW, then 10 dB = 10 mW, and 20 dB = 100 mW.

Subtract 3 dB from 100 mW in order to drop the power by half (17 dB = 50 mW). Then, subtract 3 dB again in order to drop the power by 50 percent again (14 dB = 25 mW).

3. We can find all values with a little addition or subtraction if we use the basic rules of algorithms.

Antennas

We can also use the dB abbreviation in order to describe the power level rating of antennas:

• dBi_For use with isotropic antennas.

Isotropic antennas are theoretical antennas that transmit equal power density in all directions. They are used only as theoretical (mathematical) references. They do not exist in the real world.

• dBd_With reference to dipole antennas.

Isotropic antenna power is the ideal measurement to which antennas are compared. All FCC  calculations use this measurement (dBi). Dipole antennas are more real−world antennas. While some antennas are rated in dBd, the majority use dBi.

The power rating difference between dBd and dBi is approximately 2.2_that is, 0 dBd = 2.2 dBi. Therefore, an antenna that is rated at 3 dBd is rated by the FCC (and Cisco) as 5.2 dBi.

The radiated (transmitted) power is rated in either dBm or W. Power that comes off an antenna is measured as effective isotropic radiated power (EIRP). EIRP is the value that regulatory agencies, such as the FCC or European Telecommunications Standards Institute (ETSI), use to determine and measure power limits in applications such as 2.4−GHz or 5−GHz wireless equipment. In order to calculate EIRP, add the transmitter power (in dBm) to the antenna gain (in dBi) and subtract any cable losses (in dB).

Path Loss

The distance that a signal can be transmitted depends on several factors. The primary hardware factors that are involved:

• Transmitter power
• Cable losses between the transmitter and its antenna
• Antenna gain of the transmitter
• Localization of the two antennas

This refers to how far apart the antennas are and if there are obstacles between them. Antennas that can see each other without any obstacles between them are in line of sight.

• Receiving antenna gain
• Cable losses between the receiver and its antenna

Receiver sensitivity is defined as the minimum signal power level (in dBm or mW) that is necessary for the receiver to accurately decode a given signal. Because dBm is compared to 0 mW, 0 dBm is a relative point; much like 0 degrees is in temperature measurement. This table shows example values of receiver sensitivity:

 dBm mW10 10 10 3 2 0 1 -3 .5 -10 .1 -20 .01 -30 .001 -40 .0001 -50 .00001 -60 .000001 -70 .0000001

The receiver sensitivity of the radios in Aironet products is −84 dBm or 0.000000004 mW.

Estimate Outdoor Ranges

Cisco has an Outdoor Bridge Range Calculation Utility to help determine what to expect from an outdoor wireless link. Because the outputs of the calculation utility are theoretical, it is helpful to have some guidelines on how to help counteract outside factors.

• For every increase of 6 dB, the coverage distance doubles.
• For every decrease of 6 dB, the coverage distance is cut in half.

In order to make these adjustments, choose antennas with higher (or lower) gain. Or use longer (or shorter) antenna cables.

• If we change to 100−foot cables instead of 50−foot (which adds 3 dB of loss on each end), the range drops to 9 miles.
• If we change the antenna to 13.5−dBi yagis instead of the dishes (which reduces gain by 14 dBi overall), the range drops to less than 4 miles.

Estimate Indoor Ranges

There is no antenna calculation utility for indoor links. Indoor RF propagation is different than outdoor propagation. However, there are some quick calculations that we can do in order to estimate performance.

• For every increase of 9 dB, the coverage area doubles.
• For every decrease of 9 dB, the coverage area is cut in half.