Estoy tratando de derivar la conversión de dBm a dB \ $ \ mu \ $ V. Por lo tanto, corríjame si me equivoco.
\ begin {align} \ textrm {dBm} & = 10 \ log_ {10} \ left (\ frac {P} {1 \ textrm {mW}} \ right) = 10 \ log (P) + 30 \\ & = 10 \ log_ {10} \ left (\ frac {V ^ 2} {Z} \ right) + 30 \\ & = 10 \ log_ {10} \ left (V ^ 2 \ right) - 10 \ log_ {10} (Z) + 30 \\ & = 20 \ log_ {10} \ left (V \ right) - 10 \ log_ {10} (Z) + 30 \\ & = 20 \ log_ {10} \ left (\ frac {V} {1 \ mu V} 10 ^ {- 6} \ right) - 10 \ log_ {10} (Z) + 30 \\ & = \ underbrace {20 \ log_ {10} \ left (\ frac {V} {1 \ mu V} \ right)} _ {\ textrm {dB} \ mu V} + \ underbrace {20 \ log_ {10 } \ left (10 ^ {- 6} \ right)} _ {- 120} - 10 \ log_ {10} (Z) + 30 \\ & = \ textrm {dB} \ mu V -120 - 10 \ log_ {10} (Z) + 30 \\ & = \ textrm {dB} \ mu V -90 - 10 \ log_ {10} (Z) \\ \ Leftrightarrow \\ \ textrm {dB} \ mu V & = \ textrm {dBm} + 90 + 10 \ log_ {10} (Z) \ end {align}