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

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• dB.1

• Given: Amplifier with Po = 2.75W & Pi = 50 mW• Find: Ap & AP(dB)

• dB.2 -- Second page of the handout

Data Acquisition ET 228The Decibel

• Relative Power Gain• Finding Gain from Gain measured in dBs

• Third Page of the handout• 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

Data Acquisition ET 228The 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 = Vi

2/Ri

• AP(dB) = 10 log (Po /Pi) = 10log (V02/R0)/(Vi

2/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

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

Data Acquisition ET 228The Decibel

• Absolute Power Gain and dBm • Communications industry developed a standard

• Load resistance from the set 50s, 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)

Semi-Log Graph Paper

handout – page 4 )

Semi-Log Graph PaperFrequency Scale

• There are eight additional lines in between the ones with numbers• The first line to the right of 1 is 2, 10 is 20, 100 is 200, etc.• The marked numbers could have any scalar multiplier, i.e., 10, 100, 1k

Semi-Log Graph PaperGain

• Gain as a ratio on the left – same gain in dB or dBm on right• Notice that the dB gain is linear and Gain as a ratio isn’t.• The start and stop points of the scale could be different