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# 6dB/octave

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#### Electronman

##### New Member
Somewhere I read that 3dB is where that the power is reduced by half which is right, but again I read that 3dB is where the power reaches to 70% or 0.707 of its max!
What does the second means really??
It is not matched with the first sentence!?

The other question is that what is the meaning of 6dB per octave?
I even do not know what octave means there?

An octave is a doubling of frequency; 1kHz,2kHz,4kHz,8kHz,16kHz,32kHz,....

A decade is an increase by a factor of 10; 1kHz, 10kHz,...

half power is a 3db reduction; 10log(P1/P2) = 10log(0.5) = -3.0101999

half voltage is a 6db reduction; 20log(V1/V2) = 20log(0.5) = -6.0205999

Oh ok, thanks,
So it means 6db per doubling the freq, makes sense, thanks

What about my first question? what 0.707 refers to?

No, when the power reaches half, the voltage reaches 0.70710678 of its former value.

P = E²/R, assuming R unchanged, P1/P2=0.5 = (E1²/R)/(E2²/R) = E1²/E2².

Rearranging, and solving for E1/E2 = √0.5 = 0.70710678

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When the power is -3dB (half), the voltage is reduced 0.707 times and the current is also reduced 0.707 times. Power equals voltage times current so 0.707 voltage times 0.707 current= 0.5 times the power.

Just to enforce:

-3dB = 20*log(V1/V0)
V1/V0 = 0,707945784

-3dB = 20*log(I1/I0)
I1/I0 = 0,707945784

Or, if you use power proportinal to the voltage squared: .707^2 = .5 watts/watts.

Same for current.

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