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

• zanner
In summary, the decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. 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
zanner
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.

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

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?

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
analogdesign said:
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 = 100Wyou 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 powerDave

Last edited:
zanner said:
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.

analogdesign

## 1. How does gain relate to dB's?

Gain and dB's are both measurements of the amplification or attenuation of a signal. Gain is a linear measurement of the ratio of output to input signal, while dB's are a logarithmic measurement of the same ratio. In other words, gain is the raw amount of amplification, while dB's provide a more convenient way to express very large or very small ratios.

## 2. Are gain and dB's interchangeable?

No, gain and dB's cannot be used interchangeably. While they both measure the same thing (signal amplification or attenuation), they use different scales. Gain is measured in linear units, such as volts or watts, while dB's use a logarithmic scale. In order to convert between the two, a logarithmic operation must be performed.

## 3. How do I convert gain to dB's?

To convert gain to dB's, you can use the formula dB = 20log10(gain). This formula assumes that the gain is measured in voltage units. If the gain is measured in power units, the formula becomes dB = 10log10(gain). For example, if the gain is 10 volts, the conversion to dB's would be 20log10(10) = 20dB.

## 4. What is the relationship between gain and dB's in terms of sound?

In terms of sound, gain and dB's are used to measure the amplification or attenuation of sound waves. Gain is typically used to describe the raw amplification of a speaker or microphone, while dB's are used to describe the loudness or volume level of a sound. The higher the gain or dB's, the louder the sound will be.

## 5. How do gain and dB's affect audio quality?

Both gain and dB's can affect audio quality in different ways. Too much gain can cause distortion and decrease the overall sound quality. Similarly, too many dB's can result in clipping and distortion. It is important to find the right balance between gain and dB's to achieve the best audio quality.

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