1. COMT 3911 Power Level Calculations COMT 391

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

3. COMT 3913 Power Level Change Reduction: 1/100 Reduction: 1/10000 Reduction: 1/100 Increase: 1000/1 0.010.0000010.000000010.00001 Cumulative Change: 10 -2 10 -6 10 -8 10 -5 Better:

4. COMT 3914 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. COMT 3915 Definition A ratio is expressed in Decibels (dB) by computing Ratio(dB) = 10log 10 (Ratio) 0.00000000000000000001 equals -200dB If a signal is amplified 100-fold, the gain equals 20dB

6. COMT 3916 Back to the Example Reduction: 1/100 Reduction: 1/10000 Reduction: 1/100 Increase: 1000/1 10 -2 10 -4 10 -2 10 3 Signal Change: -20dB-40dB-20dB30dB Signal Level: -20dB-60dB-80dB-50dB

7. COMT 3917 Try it Convert the following to dB: 0.1.001 100000 10 20 Convert to fractions: 30dB -50dB

8. COMT 3918 Answers: Convert the following to dB: 0.1 = -10dB 0.001 = -30dB 100000 = 50dB 10 20 = 200dB Convert to fractions: 30dB = 1000 -50dB = 0.00001

9. COMT 3919 A complication What if we want to work with actual power levels (in watts)? Can I express 0.003W in dB?

10. COMT 39110 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. COMT 39111 The dB(something) convention 0.003W - remove the unit 0.003 = -25.2dB Place the reminder: 0.003W = -25.2dBW So: 0dBW = 1 W, -20dBW = 0.01 W Also common: –dBm = power relative to 1mW