Subjects Covered 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 ID: 257176
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Slide1
The Decibel
Subjects Covered
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 unitSlide2
The Decibel
Relative Power Gain
Relative Power Gain = (Power Output)/(Power Input)
A
p
= P
o
/P
i
Where P
o
& P
i
are specified in Watts
The gain can be the same for different values of P
o
& P
i
Usually expressed in terms of Decibels {A
P(dB)
}
A
P(dB)
= 10 log
A
p
or A
P(dB)
= 10 log (P
o
/P
i
)
Example Problems
dB.1
Given: Amplifier with Po = 2.75W & Pi = 50
mW
Find:
A
p
& A
P(dB)
dB.2 -- Second page of the handoutSlide3
The Decibel
Relative Power Gain
Finding Gain from Gain measured in
dBs
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, 10000Slide4
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?????????
DerivationPo = 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 Slide5
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 handoutQuestionsAbsolute Power Gain and dBm Previous discussion of dBs were relative measuresi.e, an infinite sets of powers that can yield a 10 dB changeSlide6
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 P = 1 mW (10AP(dBm)/10)Example Problems2.7 and 2.8Slide7
The Decibel
Common Decibel Relationships