Section E.2. SOME USEFUL DECIBEL NUMBERS
E 2 SOME USEFUL DECIBEL NUMBERS
If the reader uses dB scales on a regular basis, there are a few constants worth committing to memory. A power difference of 3 dB corresponds to a power factor of 2; that is, if the magnitude-squared ratio of two different frequency components is 2, then from Eq. (E-2),
Likewise, if the magnitude-squared ratio of two different frequency components is 1/2, then the relative power difference is –3 dB because
Table E-1. Some seful Logarithmic Relationships
|
Magnitude ratio |
Magnitude-squared power (P1/P2) ratio |
Relative dB (approximate) |
|
|---|---|---|---|
|
10–1/2 |
10–1 |
–10 |
|
|
2–1 |
2–2 = 1/4 |
–6 |
|
|
2–1/2 |
2–1 = 1/2 |
–3 |
|
|
20 |
20 = 1 |
0 |
|
|
21/2 |
21 = 2 |
3 |
|
|
21 |
22 = 4 |
6 |
|
|
101/2 |
101 = 10 |
10 |
|
|
101 |
102 = 100 |
20 |
|
|
103/2 |
103 = 1000 |
30 |
|
Equation E-9
Table E-1 lists several magnitude and power ratios vs. dB values worth remembering. Keep in mind that decibels indicate only relative power relationships. For example, if we're told that signal A is 6 dB above signal B, we know that the power of signal A is four times that of signal B, and that the magnitude of signal A is twice the magnitude of signal B. We may not know the absolute power of signals A and B in watts, but we do know that the power ratio is PA/PB = 4.
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