COMT 391

1

Power Level Calculations

COMT 391

COMT 391

2

Example

Trans-mitter

Antenna

Transmission Path

Amplifier

Antenna

Reduction:1/100

Reduction:1/10000

Reduction:1/100

Increase:1000/1

COMT 391

3

Power Level Change

Reduction:1/100

Reduction:1/10000

Reduction:1/100

Increase:1000/1

0.01 0.000001 0.00000001 0.00001

Cumulative Change:

10-2 10-6 10-8 10-5

Better:

COMT 391

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....

COMT 391

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

COMT 391

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

COMT 391

7

Try it

• Convert the following to dB:0.5290.5

• Convert to fractions:12dB-39dB

COMT 391

8

Answers:

• Convert the following to dB:0.5 = -3dB2 = 3dB9 = 9.54dB0.05 = -13dB

• Convert to fractions:12dB = 15.8-39dB = 1.26x10-4

COMT 391

9

A complication

• What if we want to work with actual power levels (in watts)?

• Can I express 0.003W in dB?

COMT 391

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

COMT 391

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