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 magnitudesquared ratio of two different frequency components is 2, then from Eq. (E2),
Likewise, if the magnitudesquared ratio of two different frequency components is 1/2, then the relative power difference is –3 dB because
Table E1. Some seful Logarithmic Relationships
Magnitude ratio 
Magnitudesquared power (P1/P2) ratio 
Relative dB (approximate) 


10–1/2 
10–1 
–10 
P1 is onetenth P2 
2–1 
2–2 = 1/4 
–6 
P1 is onefourth P2 
2–1/2 
2–1 = 1/2 
–3 
P1 is onehalf P2 
20 
20 = 1 
0 
P1 is equal to P2 
21/2 
21 = 2 
3 
P1 is twice P2 
21 
22 = 4 
6 
P1 is four times P2 
101/2 
101 = 10 
10 
P1 is ten times P2 
101 
102 = 100 
20 
P1 is one hundred times P2 
103/2 
103 = 1000 
30 
P1 is one thousand times P2 
Equation E9
Table E1 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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