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**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 Pg 69

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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 Pg 69

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**Units of Power and Comparison**

Units of Power (absolute) Units of Comparison (Relative) watt (W) decibel (dB) milliwatt (mW) dBi dBm dBd Pg 69

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**Watt Basic unit of power Volts x Amps Ability to move/push/etc**

1 ampere of current at 1 volt Volts x Amps Ability to move/push/etc Pg 70

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**MilliWatt (mW) 1/1000 th of a watt**

Most 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. Pg 70

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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 Pg 70

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**Decibel (dB) Bels are logarithmic 101=10 Log10(10)=1 102=100**

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 Pg 70

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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. Pg 70

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Decibel (dB) Pg 72

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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 Pg 73

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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 Pg 73

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**dBm Absolute measurement So 100 mW= +20dBm**

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 Pg 74

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**dBm Why use dBm? Also, the 6dB rule Also helps when adding units**

Easier to grasp -100dBm than 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 Pg 74

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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 = (20log10(f)) + (20log10(D)) FSPL = path loss in dB f = frequency in MHz D = distance in miles between antennas FSPL = (20log10(f)) + (20log10(D)) D = distance in kilometers between antennas Pg 76

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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. Pg 77

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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 Pg 77

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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 Pg 77

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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 Pg 77

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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. Pg 77

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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 Pg 77

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Step by Step Exercise 3 + X 2 10 - / dBm mW 1 Pg 78

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**RF Math Summary Log Functions Rules of 10 and 3 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 Pg 85

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RF Math Summary Pg 86

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