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Power Level Calculations

Power Level Calculations. COMT 391. Example. Reduction: 1/100. Reduction: 1/10000. Reduction: 1/100. Increase: 1000/1. Antenna. Antenna. Transmission Path. Trans- mitter. Amplifier. Power Level Change. Reduction: 1/100. Reduction: 1/10000. Reduction: 1/100. Increase: 1000/1.

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Power Level Calculations

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  1. Power Level Calculations COMT 391

  2. Example Reduction:1/100 Reduction:1/10000 Reduction:1/100 Increase:1000/1 Antenna Antenna Transmission Path Trans- mitter Amplifier

  3. Power Level Change Reduction:1/100 Reduction:1/10000 Reduction:1/100 Increase:1000/1 Cumulative Change: 0.01 0.000001 0.00000001 0.00001 Better: 10-2 10-6 10-8 10-5

  4. Working with the Exponents • In power level computations, we always multiply and divide • If all factors are powers of ten, we can simply add and subtract exponents • In general, we have to use logarithms to get that advantage, therefore....

  5. Definition • A ratio is expressed in Decibels (dB) by computing • Ratio(dB) = 10log10(Ratio) • 0.00000000000000000001 equals -200dB • If a signal is amplified 100-fold, the gain equals 20dB

  6. Back to the Example Reduction:1/100 Reduction:1/10000 Reduction:1/100 Increase:1000/1 10-2 10-4 10-2 103 Signal Change: -20dB -40dB -20dB 30dB Signal Level: -20dB -60dB -80dB -50dB

  7. Try it • Convert the following to dB: 0.5 2 9 0.5 • Convert to fractions: 12dB -39dB

  8. Answers: • Convert the following to dB: 0.5 = -3dB 2 = 3dB 9 = 9.54dB 0.05 = -13dB • Convert to fractions: 12dB = 15.8 -39dB = 1.26x10-4

  9. A complication • What if we want to work with actual power levels (in watts)? • Can I express 0.003W in dB?

  10. Not Really... • You cannot take the log of 0.003W • You can take the log of 0.003 • Therefore • “Remove” the unit • Convert the remaining number to dB • Place a “reminder” on the answer, so we can replace the unit later

  11. The dB(something) convention • 0.003W - remove the unit • 0.003 = -25.2dB • Place the reminder: • 0.003W = -25.2dBW • So: 0dBW = 1 Watt -12dBW = 0.063 Watts

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