Understanding the deciBel or dB

VHF Marine Band radios, protocol, radio communication theory, practical advice; AIS; DSC; MMSI; EPIRB.
jimh
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Understanding the deciBel or dB

Postby jimh » Thu Jan 10, 2019 11:21 am

Many specifications for VHF Marine Band radio performance include expressions using deciBels. The deciBel is a measure of power ratios using logarithms that evolved from early engineering work for the Bell System at the Bell Telephone Laboratory, and was originally the "Bel" in honor of Alexander Graham Bell. The Bel was often too large to be useful, so it was divided by ten and became the deciBel.

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