RF power unit conversion

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W to dBm

$$P[dBm] = {10 · log_{10} (P[W] · 10^{-3})} = {10 · log_{10} (P[W]) - 30dB}$$

dBm to W

$$P[W] = {10^{0.1 · P[dBm]} + 30}$$

W to dBµV

$$P[W] = {(V[V])^2 \over Z_0[Ω]} = {(V[µV] · 10^6 )^2 \over Z_0[Ω]} \Rightarrow {P[dBµV] = 20 · log_{10}(\sqrt{P[W] · Z_0[Ω]})} + {20 · log_{10}(10^6)}$$

$$P[dBµV] = {10·log_{10}(P[W]·Z_0[Ω]) + 120 dB} = {10·log_{10}(P[W])} + {10·log_{10}(Z_0[Ω])} + {120 dB}$$

So, if Z0 = 50 Ω:

$$P[dBµV, 50 Ω] = {10·log_{10}(P[W])} + {136.99 dB}$$

If Z0 = 75 Ω:

$$P[dBµV, 75 Ω] = {10·log_{10}(P[W])} + {138.75 dB}$$

W to dBmV

$$P[W] = {(V[V])^2 \over Z_0[Ω]} = {(V[mV] · 10^3 )^2 \over Z_0[Ω]} \Rightarrow {P[dBmV] = 20 · log_{10}(\sqrt{P[W] · Z_0[Ω]})} + {20 · log_{10}(10^3)}$$

$$P[dBmV] = {10·log_{10}(P[W]·Z_0[Ω]) + 120 dB} = {10·log_{10}(P[W])} + {10·log_{10}(Z_0[Ω])} + {60 dB}$$

So, if Z0 = 50 Ω:

$$P[dBmV, 50 Ω] = {10·log_{10}(P[W])} + {76.99 dB}$$

If Z0 = 75 Ω:

$$P[dBmV, 75 Ω] = {10·log_{10}(P[W])} + {78.75 dB}$$

W to dBpW

$$P[dBpW] = {10 · log_{10}\left( {P[W] \over 10^{-12}W} \right)} = {10 · log_{10}\left( {P[W]} \right)} + 120dB$$

Summary

from \ to W dBm dBµV (Z0=75 Ω) dBmV (Z0=75 Ω) dBµV (Z0=50 Ω) dBmV (Z0=50 Ω) dBpW
W $$10 · log_{10}(P[W]) + 30$$ $$10 · log_{10}(P[W]) + 138.75$$ $$10 · log_{10}(P[W]) + 78.75$$ $$10 · log_{10}(P[W]) + 136.99$$ $$10 · log_{10}(P[W]) + 76.99$$ $$10 · log_{10}(P[W]) + 120$$
dBm $$10^{0.1 · P[dBm]} - 30$$ $$P[dBm]+108.75$$ $$P[dBm]+48.75$$ $$P[dBm]+106.99$$ $$P[dBm]+46.99$$ $$P[dBm]+90$$
dBµV (Z0=75 Ω) $$10^{0.1 · P[dBµV]} - 138.75$$ $$P[dBµV]-108.75$$ $$P[dBµV]-60$$ $$P[dBµV]-1.76$$ $$P[dBµV]-61.76$$ $$P[dBµV]-18.75$$
dBmV (Z0=75 Ω) $$10^{0.1 · P[dBmV]} - 78.75$$ $$P[dBmV]-48.75$$ $$P[dBmV]+60$$ $$P[dBmV]+58.35$$ $$P[dBmV]-1.76$$ $$P[dBmV]+41.25$$
dBµV (Z0=75 Ω) $$10^{0.1 · P[dBµV]} - 136.99$$ $$P[dBµV]-106.99$$ $$P[dBµV]+1.76$$ $$P[dBµV]-58.35$$ $$P[dBµV]-60$$ $$P[dBµV]-16.99$$
dBmV (Z0=75 Ω) $$10^{0.1 · P[dBmV]} - 76.99$$ $$P[dBmV]-46.99$$ $$P[dBmV]+61.76$$ $$P[dBmV]+1.76$$ $$P[dBmV]+60$$ $$P[dBmV]+43.01$$
dBpW $$10^{0.1 · P[dBpW]} - 120$$ $$P[dBpW]-90$$ $$P[dBpW]+18.75$$ $$P[dBpW]-41.25$$ $$P[dBpW]+16.99$$ $$P[dBmV]-43.01$$
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