Proton BASIC Compiler - RF Power and the DB

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• # RF Power and the DB

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.

You 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 you 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, you can use simple math in order to manipulate the ratios for the design and assembly of networks. For example, you can apply this basic rule in order to calculate logarithms of large numbers:

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

If you use the formula above, you 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:

 An Increase of: A Decrease of: Produces: 3 dB Double transmit power 3 dB Half transmit power 10 dB 10 times the transmit power 10 dB Divides transmit power by 10 30 dB 1000 times the transmit power 30 dB Decreases transmit power 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 1 W

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.

3. 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).

Note: You can find all values with a little addition or subtraction if you use the basic rules of algorithms.

## Antennas

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

• dBi—For use with isotropic antennas.

Note: 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. (dBi)
Dipole antennas are real-world antennas, dometimes antennas are rated in dBd

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 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 are:

• 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 mW 10 10 3 2 0 1 -3 0.5 -10 0.1 -20 0.01 -30 0.001 -40 0.0001 -50 0.00001 -60 0.000001 -70 0.0000001

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

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