# Decibel Power/Voltage Conversion

#### blah2222

Joined May 3, 2010
582
Something that I had never really received a good answer for and have just taken it for granted is why the input and output resistances used in the gain equation considered equal to make the decibel calculation simplified.

I.E.

$$Gain = 10log(\frac{P_{out}}{P_{in}}) = 10log(\frac{V_{out}^{2}/R_{out}}{V_{in}^{2}/R_{in}}) \approx 20log(\frac{V_{out}}{V_{in}})\ \ \ \ *Rout = Rin$$

Very subtle note, but it is often overlooked. Considering most amplifiers have high input impedance and low output impedance, why do we not take these into account for voltage gain?

#### crutschow

Joined Mar 14, 2008
30,116
Strictly speaking a dB is a ratio of power levels, so it only works properly for voltage if the two voltages are working into the same resistance value. But commonly the voltage ratio is used without regard to resistance level for convenience. Thus one can refer to an amplifier as having a voltage gain of say 20dB (a factor of 10) without knowing (or caring) what the input and output resistance levels are.

But if you want the power gain of an amplifier then you need to include the input and output resistance values. That is commonly done for RF amplifier modules which typically have the same input and output impedance levels matched to the transmission line impedance.

#### bountyhunter

Joined Sep 7, 2009
2,512
The definition of decibel is:

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level
I was taught it's origination was in Bell labs to have a unit for measuring sound levels (which are log scaled) not voltage or current.

To have the unit be meaningful, the parameters units have to be consistent throughout.

many people fail to grasp that dB has to be referenced to something if it is used as an actual measurement. The sound scale often used is dBA which has a reference level (that I don't remember) so that dBA meters can be used to measure actual sound levels. If no reference is built in, then a dB is simply a measurement of a ratio, not a value.