Units of Power and Comparison• Key ideas for wireless are

coverage and performance• To measure power, we can

measure absolute or relative power– Absolute is compared to a

known scale– Relative is to another signal

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Units of Power and Comparison• Comparative units can help:

– compare coverage areas for different signals– Measure gain or loss

• Measure the change in power

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Units of Power and Comparison

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Units of Power (absolute)

Units of Comparison (Relative)

watt (W) decibel (dB)

milliwatt (mW) dBi

dBm dBd

Watt• Basic unit of power

– 1 ampere of current at 1 volt• Volts x Amps• Ability to move/push/etc

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MilliWatt (mW)• 1/1000 th of a watt• Most 802.11 equipment is measured in

milliwatts– Usually 1 to 100 mw

• FCC may allow up to 1 W in some cases, but it isn’t usually needed except in point to point.

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Decibel (dB)• Base unit of comparison, not of power• Represents the difference between two

values• Compare the power of two transmitters• Compare the output of a transmitter and

received at the receiver• From the term bel

– Bell Labs– 10 to 1 ratio

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Decibel (dB)• Bels are logarithmic

– Use the log10 to calculate

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101=10 Log10(10)=1

102=100 Log10(100)=2

103=1000 Log10(1000)=3

104=10000 Log10(10000)=4

Decibel (dB)• Decibels are 10 x a bel• bel=log10(P1/P2)

• decibel= 10Xlog10(P1/P2)

• No log math on the test!• We use decibels instead of watts as it is

easier to write in many cases.

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Decibel (dB)

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dBi• Antennas are compared to isotropic radiators• The difference between the theoretical isotropic

radiator and the actual antenna can be measures in decibels isotropic (dBi)– Relative measurement– Change in power relative to an antenna– Measure of antenna gain

• Measured at focus point– Always a gain, not a loss– No-gain or unity gain (0 dBi)

• Think antenna GainPg 73

dBd• A second relative measure of strength• Decibel dipole

– Decibel gain relative to a dipole antenna• Can also compare to dBi

– Standard dipole is 2.14 dBi– If an antenna is 3 dBd the total is additive

• 2.14+3=5.14 dBi

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dBm• Absolute measurement

– Decibels relative to 1 mw of power• So 100 mW= +20dBm• Can also calc from a dBm value• PmW=log-1(PdBm/10)• 1 mW is reference and 0 dBm is 1 mW

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dBm• Why use dBm?

– Easier to grasp -100dBm than .0000000001 mW• Also, the 6dB rule

– If you double the distance between a received and transmitter, the received signal will decrease by 6 dB.

– Also, every 6dBi of gain will double the usable distance of the RF signal

• Also helps when adding units– If transmitter is +20dBm and the antenna is 5 dBi, the

EIRP is 25 dBm

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Inverse Square Law• The 6 dB rule is based on Isaac Newton’s inverse

square law.– Change in power is equal to the

square of the change in distance– If you double the distance, the power will change by (2xD)2

• FSPL = 36.6 + (20log10(f)) + (20log10(D))– FSPL = path loss in dB– f = frequency in MHz– D = distance in miles between antennas

• FSPL = 32.4 + (20log10(f)) + (20log10(D))– FSPL = path loss in dB– f = frequency in MHz– D = distance in kilometers between antennas

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RF Math• No need for LOG on test.• Rules of 10s and 3s

– Provide for approximate values• For every 3 dB of gain (relative), double the

absolute power (mW).• For every 3 dB of loss (relative), halve the

absolute power (mW).• For every 10 dB of gain (relative), multiply the

absolute power (mW) by a factor of 10.• For every 10 dB of loss (relative), divide the

absolute power (mW) by a factor of 10.

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RF Math• For every 3 dB of gain (relative), double

the absolute power (mW).– For example, if your access point is

configured to transmit at 100 mW and the antenna is rated for 3 dBi of passive gain, the amount of power that will radiate out of the antenna (EIRP) will be 200 mW

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RF Math• For every 3 dB of loss (relative), halve the

absolute power (mW).– Conversely, if your access point is configured

to transmit at 100 mW and is attached to a cable that introduces 3 dB of loss, the amount of absolute amplitude at the end of the cable will be 50 mW

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RF Math• For every 10 dB of gain (relative), multiply

the absolute power (mW) by a factor of 10.– In another example, if your access point is

configured to transmit at 40 mW and the antenna is rated for 10 dBi of passive gain, the amount of power that radiates out of the antenna (EIRP) will be 400 mW

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RF Math• For every 10 dB of loss (relative), divide

the absolute power (mW) by a factor of 10.– Conversely, if your access point is configured

to transmit at 40 mW and is attached to a cable that introduces 10 dB of loss, the amount of absolute amplitude at the end of the cable will be 4 mW.

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RF Math• dBm is a measure of power• dB is a unit of change• dB can be applied to dBm• So, if you have +10dBm and increase by 3

dB, you have +13 dBm

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Step by Step Exercise

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3 + X 210 - / 10

dBm

mW

0 1

RF Math Summary• Log Functions

– dBm =10 × log10(mW)– mW = log–1 (dBm ÷ 10) = 10(dBm ÷ 10)

• Rules of 10 and 3– 3 dB gain = mW × 2– 3 dB loss = mW ÷ 2– 10 dB gain = mW × 10– 10 dB loss = mW ÷ 10

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RF Math Summary

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