Data Acquisition ET 228 The Decibel

1
Data Acquisition ET 228The 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 unit

2
Data Acquisition ET 228The 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
• 2.1
• Given Amplifier with Po 2.75W Pi 48 mW
• Find Ap AP(dB)
• 2.2 -- Second page of the handout
• 2.3 -- Third Page of the handout

3
Data Acquisition ET 228The Decibel

• Relative Power Gain
• Example Problems
• 2.4 -- Third Page of the handout
• In Class Pencil and paper Exercise
• Problems 1 2 on handout
• Solutions to be presented to the class by each
  Lab group
• 15 Minutes to solve problem
• then a 5 minute break
• Presentations
• Questions
• 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

4
Data Acquisition ET 228The Decibel

• Relative Voltage Gain
• Review of Logarithms
• Enter 10, the xy 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

5
Data Acquisition ET 228The 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

6
Data Acquisition ET 228The 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 Problems
• 2.7 and 2.8