# A power amplifier with a 10-dB gain has an input power of 0.5-W. What is the output power? ( in watts)?

So i figured out the answer is 5 watts, by multiplying the gain (10db x 0.5 watts); but I'm sure that's not the way to go about solving this decible problem. Can someone guide me in the right direction?

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• Anonymous
1 month ago

A 10dB increase would be 10^, +dB, +10, or 5+5dB.

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• The formula to calculate the multiplier for a DB increase is 10^(dB/10).

+10dB would be 10^(10/10), or

10^1, or just 10. So 1/2w would increase to 5w if dB s increase by 10.

You can verify that by knowing a 3dB increase doubles power. So 1/2w +3db is 1w, +3 more db is 2w +3 more is 4w +1 more would end up at 5.

Simply multiplying by 10 happened to work because it's a logarithmic relationship - with a base of 10.

9, for example is not 4.5. It's 3.97.

11 isn't 5.5, it's 6.29.

• N2Audio
Lv 7
1 month agoReport

I see there are 4 idiots thumbing down good answers.  Way to go YA!

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• Just buy a DMM...it's only about \$5-10 dollars and everybody should be able to afford it. Do some calculating math work and you will know how much power to output at wherever you want it to be. You will need a 50-60hz test tone and disconnect ALL your speakers and subwoofers.

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• An increase of 10 dB will be a 10-fold increase in power, but your method was wrong.  You got the right answer the wrong way, as you suspected.

P[i] * 10^(d/10) = P[o]

That's the formula

P[i] is the input power

d is the change in decibels

P[o] is the output power

0.5 * 10^(10/10) =>

0.5 * 10^(1) =>

0.5 * 10 =>

5

If you increased it by 20 dB, it'd be:

0.5 * 10^(20/10) =>

0.5 * 10^2 =>

0.5 * 100 =>

50

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