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The Decibel
• Subjects Covered
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The bel and decibel units
Relative Power Gain
Relative Voltage Gain
dBm and Absolute Power Gain
• The bel and decibel units
• Derived from how a received signal is perceived
• Specifically by the human ear
• It, the human ear, is logarithmic not linear
• With two sounds, one perceived as being twice as loud
• The louder sound actually has approx. four times the power
• The original unit, the bel, was name in honor of
Alexander Graham Bell
• the decibel = 1/10 bels and is the most commonly used unit
The Decibel
• Relative Power Gain
• Relative Power Gain = (Power Output)/(Power Input)
• Ap = Po /Pi
• Where Po & Pi are specified in Watts
• The gain can be the same for different values of Po & Pi
• Usually expressed in terms of Decibels {AP(dB) }
• AP(dB) = 10 log Ap
or AP(dB) = 10 log (Po /Pi)
• Example Problems
• dB.1
• Given: Amplifier with Po = 2.75W & Pi = 50 mW
• Find: Ap & AP(dB)
• dB.2 -- Second page of the handout
The Decibel
• Relative Power Gain
• Finding Gain from Gain measured in dBs
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• Example Problems
• dB.4 -- Third Page of the handout
• Relative Voltage Gain
• Review of Logarithms
• Fire up the PCs, Click Start, Click Run, Type calc in the text box
• Click View Tab, Click Scientific
• Enter the following numbers click log button & record results
• 10, 100, 1000, 10000
The Decibel
• Relative Voltage Gain
• Review of Logarithms
• Enter 10, the x^y button, the following numbers and record
• 1, 2, 3, 4
• Compare the two sets of results
• Conclusions?????????
• Derivation
• Po = V02/R0
and
Pi = Vi2/Ri
• AP(dB) = 10 log (Po /Pi) = 10log (V02/R0)/(Vi2/Ri )
• If R0 and Ri are equal then they cancel each other
= 10 log {(V0 2 /R)/(Vi 2 /R )} = 10 log{(V0 2)/(Vi 2)}
= 10 log{(V0 )/(Vi)} 2
AV(dB)= 20 log V0/ Vi = 20 log Av where Av = V0/ Vi
The Decibel
• Relative Voltage Gain
• Derivation
• Reverse
• Av = 10 AV(dB)/20 = V0/ Vi
• Example Problems 2.5 and 2.6
• Fourth page of the handout
• Questions
• Absolute Power Gain and dBm
• Previous discussion of dBs were relative measures
• i.e, an infinite sets of powers that can yield a 10 dB change
The Decibel
• Absolute Power Gain and dBm
• Communications industry developed a standard
• Load resistance from the set 50s, 600 s, or 900 s
• Reference power level = 1 mW
• Symbol = dBm
• Formulas
• AP(dBm) = 10log P/(1mW)
• Reverse
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P = 1 mW (10AP(dBm)/10)
• Example Problems
• 2.7 and 2.8
The Decibel
Common
Decibel
Relationships