If two power levels, P1 and P2, are to be compared with deciBels, the relationship is defined as
(1) dB = 10 × log(P1/P2) where log is to Base-10
Here is an example: how much stronger in deciBels is a power of 25-Watts compared to 7-Watts?
- Given:
P1 = 25-Watts
P2 = 7-Watts
dB = 10 × log(P1/P2)
dB = 10 × log(25/7)
dB = 10 × log(3.57)
dB = 10 × 0.553
dB = 5.53
If we reverse the power ratio comparison, and ask how much weaker in deciBels is a power of 7-Watts compared to 25-Watts, the same formula is used:
- Given:
P1 = 7-Watts
P2 = 25-Watts
dB = 10 × log(P1/P2)
dB = 10 × log(7/25)
dB = 10 × log(0.28)
dB = 10 × -0.553
dB = -5.53
If a power ratio is stated in deciBels and we want to find the numerical ratio, we can manipulate equation 1 to solve for P1/P2. This gives:
(2) (P1/P2) = 10(dB/10)
For example, if a power ratio is expressed in deciBels to be 5.53 dB, what is the numerical ratio (P1/P2):
- Given:
dB = 5.53
(P1/P2) = 10(dB/10)
(P1/P2) = 10(5.53/10)
(P1/P2) = 10(0.533)
(P1/P2) = 3.57