Confusion between Voltage gain & Voltage gain in decibels (dB)
The definition of the Voltage Gain is \$ V_{out} \over V_{in} \$.
However, I read some articles about the gain in decibels, and I have a confusion now.
Here is an article about it: https://en.wikipedia.org/wiki/Gain#Voltage_gain
Here, I understand the definition of Power gain in decibels, which is \$ Gain = 10 \log ( {P_{out} \over P_{in}} ) dB \$.
However, I can't understand why Voltage gain in decibels is \$ 20 \log ( {V_{out} \over V_{in}} ) dB \$.
If \$ 20 \log ( {V_{out} \over V_{in}} ) dB \$ is derived from \$ 10 \log {( {V_{out}^2 \over R_{out}}) \over ({V_{in}^2 \over R_{in}}) } dB \$, then this is the power gain, not the voltage gain, isn't it? However, the Wikipedia says it is a formula for the Voltage gain in decibels. I thought the voltage gain in decibels would be \$ 10 \log ( {V_{out} \over V_{in}} ) dB \$. Actually, the example section in that linked page uses voltage gain \$ V_{out} \over V_{in} \$.
Why suddenly \$ V^2 \over R \$ came out from the voltage gain in decibels?
The definition of the Voltage Gain is \$ V_{out} \over V_{in} \$.
However, I read some articles about the gain in decibels, and I have a confusion now.
Here is an article about it: https://en.wikipedia.org/wiki/Gain#Voltage_gain
Here, I understand the definition of Power gain in decibels, which is \$ Gain = 10 \log ( {P_{out} \over P_{in}} ) dB \$.
However, I can't understand why Voltage gain in decibels is \$ 20 \log ( {V_{out} \over V_{in}} ) dB \$.
If \$ 20 \log ( {V_{out} \over V_{in}} ) dB \$ is derived from \$ 10 \log {( {V_{out}^2 \over R_{out}}) \over ({V_{in}^2 \over R_{in}}) } dB \$, then this is the power gain, not the voltage gain, isn't it? However, the Wikipedia says it is a formula for the Voltage gain in decibels. I thought the voltage gain in decibels would be \$ 10 \log ( {V_{out} \over V_{in}} ) dB \$. Actually, the example section in that linked page uses voltage gain \$ V_{out} \over V_{in} \$.
Why suddenly \$ V^2 \over R \$ came out from the voltage gain in decibels?
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