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
Units of Power
(absolute)
watt (W)
Units of Comparison
(Relative)
decibel (dB)
milliwatt (mW)
dBi
dBm
dBd
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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
101=10
Log10(10)=1
102=100
Log10(100)=2
103=1000
Log10(1000)=3
104=10000
Log10(10000)=4
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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 Gain
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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
3
+
X 2
10
-
/
dBm
0
10
mW
1
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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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