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?
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?