I'm trying to convert dBm to Vrms.
The formula for dBm is
\$ dBm = 10 * log(P1 / P0) \$ where P0 = 1mW
\$ +13dBm = 20mW \$
If I convert this to a voltage using the formula
\$ P = Vrms^2/R \$ where R = 50 ohm, I find that
\$ Vrms^2 = 20mW * 50ohm = 1000mV \$
\$ Vrms = 31.62mV \$
Now if I solve the equation a different way I get a different result.
\$ dBm = 10*log(P1/P0) \$ where \$P0\$ = 1mW
substituting \$P1\$ for \$ Vrms^2/R \$ and \$P0\$ for 1mW we get
\$ dBm = 10*log(Vrms^2/(R * 1mW)) \$
\$dBm = 10*log(Vrms^2/SQRT(R * 1mW)^2)\$
\$dBm = 10*log(Vrms/SQRT(R * 1mW))^2\$
\$ dBm = 20 * log (Vrms/SQRT(R*1mW)) \$
plugging in \$ dBm = +13\$ and \$ R = 50 \$ I get
\$ Vrms = 0.999V\$
This is the correct answer according to some online calculators I've used. But where is the inconsistency in the first solution?