Decibels in gain and loss

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Hi, I have a assignment to do and a couple of questions on decibels.

Why are Decibels a convenient unit to measure a gain and loss?

How can decibels be used as a measure of gain and loss?



I understand that a positive decibel value is a gain and a negative decibel value is a loss.

Gain is a power increase and loss is a power decrease.
 

Decibels express the logarithm of a ratio between powers, all multiplied by 10. At the numerator there will be the output power and at the denominator the output power of a device:

dB=10*log10(Pout/Pin)

if Pout > Pin then dB>0 and it will represents a gain
if instead Pout<Pin then dB<0 and it will represents a loss

dB are convenient to measure gain and losses) because you can use the logs properties to translate multiplications to sum, so if all is expressed in terms of dB you can calculate the gain of a cascaded chain simply adding gain and losses of each block.
 
also, if your values span a massive range, then putting it in dB means you can fit it all on to a graph, instead of needing a graph the size of a football pitch to display the data
 

1,000,000,000 times is 180dB of voltage gain or loss. 1,000,000,000,000 is 240dB of voltage gain or loss. With numbers you might not notice that you missed or added a few zeros but it would be obvious with dB's.
 

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