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  • Pic® Basic


  • 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.

    Effective Isotropic Radiated Power

    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

    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.