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Understanding Power Level Calculations: A Comprehensive Guide

Learn how to calculate power level changes and express ratios in decibels (dB). Understand the dB convention and practice conversion exercises. Improve your knowledge of antenna transmission paths and amplifier power levels.

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Understanding Power Level Calculations: A Comprehensive Guide

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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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