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Tweakers' Asylum Tweaks for systems, rooms and Do It Yourself (DIY) help. FAQ. |
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Tweakers' Asylum Tweaks for systems, rooms and Do It Yourself (DIY) help. FAQ. |
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In Reply to: Re: Check your log scale Math... posted by Jon Risch on March 23, 1999 at 10:39:25:
The DeciBel is a ratio of power, by definition.The definition is dB = 10 log(base 10) ( Power_1/power_ref)
One can assume that measurements made in a given circuit (for instance) or in a given digital domain are all going to reflect signals that are going into the same impedence (although is is not always true, naturally). As such, one can make an equation that says:Power_1 = alpha * voltage1 * voltage1.
Likewise
Power_ref = alpha * voltage_ref * voltage_ref
When the ratio is taken, the alpha (that's the assumption on impedence) divides out, leaving us with voltage squared on top and bottom...So the ratio of the squares of the voltage * 10 can also be used.
Bear in mind that log(x*x) = 2* log(x). Ergo, that works out to
dB = 20 log(base 10) v_1/v_ref
Just being pedantic, but the ratio is really of energy, it's just that under most circumstances one can replace energy by voltage (or current, intensity, etc) squared, and get the same result.
Why do I mention this? Knowing the rule and the derivation often makes one able to figure out the need for 10* vs. 20* much more easily. :_)
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Follow Ups
- Not that this is disagreeing, BUT - jj 11:18:45 03/23/99 (0)
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