<P> The power gain can be calculated using voltage instead of power using Joule's first law P = V 2 / R (\ displaystyle P = V ^ (2) / R); the formula is: </P> <Dl> <Dd> gain - db = 10 log ⁡ V out 2 R out V in 2 R in d B . (\ displaystyle (\ text (gain - db)) = 10 \ log (\ frac (\ frac (V_ (\ text (out)) ^ (2)) (R_ (\ text (out)))) (\ frac (V_ (\ text (in)) ^ (2)) (R_ (\ text (in))))) ~ \ mathrm (dB).) </Dd> </Dl> <Dd> gain - db = 10 log ⁡ V out 2 R out V in 2 R in d B . (\ displaystyle (\ text (gain - db)) = 10 \ log (\ frac (\ frac (V_ (\ text (out)) ^ (2)) (R_ (\ text (out)))) (\ frac (V_ (\ text (in)) ^ (2)) (R_ (\ text (in))))) ~ \ mathrm (dB).) </Dd> <P> In many cases, the input impedance R in (\ displaystyle R_ (\ text (in))) and output impedance R out (\ displaystyle R_ (\ text (out))) are equal, so the above equation can be simplified to: </P>

1. why is it convenient to measure gain in db