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Data Acquisition ET 228 The Decibel

Data Acquisition ET 228 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

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Data Acquisition ET 228 The Decibel

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  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 • dB.1 • Given: Amplifier with Po = 2.75W & Pi = 50 mW • Find: Ap & AP(dB) • dB.2 -- Second page of the handout

  3. Data Acquisition ET 228The 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, 10000

  4. 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 = 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 Avwhere 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

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