dB to G relationship

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#### Nezer

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From another thread:

Quote:

Don't you mean:

G = 10^(dB/20)

As I've already got the formula with dB on the LHS.

So, log (x) is just shorthand for (assuming base-10 log): 10^(x)?

Sorry for having to have the math lesson on this board.

Quote:

Originally posted by tangent The inverse of a logarithm is exponentiation. If: X = log_subY_(Z) then: Z = Y^X The subY part is the "base" of the logarithm. Since decibels are figured using base-10 logs, the inverse function is: dB = 10 ^ (G / 20) That is, divide the gain value you calculated by 20, and then raise 10 to that power. Any calculator with a base-10 log function will have a 10^x function as well .... and now you know why! |

Don't you mean:

G = 10^(dB/20)

As I've already got the formula with dB on the LHS.

So, log (x) is just shorthand for (assuming base-10 log): 10^(x)?

Sorry for having to have the math lesson on this board.

#### slindeman

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Here you go: http://et.nmsu.edu/~etti/fall96/comm...ons/db/db.html

So the correct equations are:

dB = 20log(G) [20 multiplied by the base-10 log of G]

G = 10^(dB/20) [10 raised to the power of dB/20]

where G = gain or Vout/Vin

So the correct equations are:

dB = 20log(G) [20 multiplied by the base-10 log of G]

G = 10^(dB/20) [10 raised to the power of dB/20]

where G = gain or Vout/Vin

#### tangent

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Sorry for the confusion, Nezer: I wrote that out on the fly without checking it. Slindeman's got the right equations, and I fixed that other thread.

#### Nezer

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Quote:

I'm just glad to get it cleared-up and have an understanding of what a log is (mathmatically speaking). Like I've said 899+101 times before, math is NOT my strongest subject.

Originally posted by tangent Sorry for the confusion, Nezer: I wrote that out on the fly without checking it. Slindeman's got the right equations, and I fixed that other thread. |

I'm just glad to get it cleared-up and have an understanding of what a log is (mathmatically speaking). Like I've said 899+101 times before, math is NOT my strongest subject.