# How do these both relate to one another? (Gain and dB's)

## Main Question or Discussion Point

I have tried to look at how these, gain and dB's, relate to one another, but there seems to be nothing solid on the Internet. Perhaps I am looking in the wrong places.

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Just a thought: Could it perhaps relate to the gain or loss in power?

jack action
Gold Member
Decibel:
The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. One of these values is often a standard reference value, in which case the decibel is used to express the level of the other value relative to this reference.
Gain:
In electronics, gain is a measure of the ability of a two port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port to the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units ("dB gain").A gain greater than one (zero dB), that is amplification, is the defining property of an active component or circuit, while a passive circuit will have a gain of less than one.

The term gain alone is ambiguous, and can refer to the ratio of output to input voltage (voltage gain), current (current gain) or electric power (power gain).
Was that clear enough?

analogdesign
Jack is correct. But even simpler, dB is just a relative shorthand that is often used to describe gain. Nothing more. It is often used instead of the linear value because it leads to smaller numbers (instead of dealing with numbers like 1000 or 1 million you have 60 dB or 120 dB) and it makes certain mathematical operations simpler to do in your head.

Keep in mind that dB doesn't inherently have anything to do with gain, it is just a shorthand. People use dBs for other things with wide spreads in value for example isolation, noise, or relative level of harmonics in a signal.

• davenn
davenn
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But even simpler, dB is just a relative shorthand that is often used to describe gain. Nothing more. It is often used instead of the linear value because it leads to smaller numbers (instead of dealing with numbers like 1000 or 1 million you have 60 dB or 120 dB) and it makes certain mathematical operations simpler to do in your head.
taken a little further, there is ....
voltage gain = VoltageGain = 20 Log10 x Vin /Vout in dB
and
Power gain = Power in WattsGain = 10 Log10 x Pin /Pout in dB

note voltage is 20 x Log10 and power is 10 x Log10

for power gain and particularly when working with RF and amplifiers gain is usually related to a standard level ( a reference level)

this may be 0dBm = 1 mW or say 0dBW = 1W
so if using the 0dBm reference, a gain of 10dBm = 10mW, a gain of 20dBm = 100mW, a gain of 30dBm = 1000 mW (1W), a gain of 50dBm = 100,000 mW = 100W

you quickly see that this is a logarithmic scale

analogdesign's example of 1000 = 60dB is for a voltage remembering it is 20 x Log10 and not 10 x Log10 that is used for power

Dave

Last edited:
jim hardy
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but there seems to be nothing solid on the Internet.
Sometimes it's tricky to get all the way down to the basics. Computers are just too nitpicky ...

Do you understand that "gain" implies a ratio ?
Alexander Graham Bell used the ratio 10 to 1 in his work and got a unit named after him, the "Bel" with just one "l" .
It stands for a power ratio of ten and is basic to sound measurement. We measure intensity of sound with logarithms because the ear is capable over such a wide range of loudness.

Try a search on that term, maybe it'll cement the idea in place for you.
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