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The Decibel The Decibel

The Decibel - PowerPoint Presentation

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Uploaded On 2016-03-15

The Decibel - PPT Presentation

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

decibel gain log power gain decibel power log relative dbm click amp problems voltage page bel handout absolute results

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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