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Voltage to Power Conversion in a 50 Ω System
(with no DC component)

A lot of people have a hard time converting between power and voltage in 50 Ω systems. The full derivation requires a little extra work because of the use of the root-mean-square value of a sinewave, based on its peak voltage value. Here's how it's done.

The Table of Equivalent Voltages & Powers was generated using an Excel spreadsheet. Equations for the cells are shown at the bottom of the table.

Voltage to Power (for a sinewave with no DC component) in a 50 Ω System

Volts to milliwatts in 50-ohm system equation forumla - RF Cafe

Volts-to-power dBm in 50-ohm system equation forumla - RF Cafe

where Vpk is the peak (not pk-pk) voltage in units of volts
Power to Voltage (for a sinewave with no DC component) in a 50 Ω System

Power -to - volts voltage equation forumla - RF Cafe
Table of Equivalent Voltages & Powers in a 50 Ω System
Vpeak(V) Vrms(V) Vavg(V) P(W) P(mW) P(dBm)
10 7.07107 6.36620 1.00000 1000.00000 30.00000
9 6.36396 5.72958 0.81000 810.00000 29.08485
8 5.65685 5.09296 0.64000 640.00000 28.06180
7 4.94975 4.45634 0.49000 490.00000 26.90196
6 4.24264 3.81972 0.36000 360.00000 25.56303
5 3.53553 3.18310 0.25000 250.00000 23.97940
4 2.82843 2.54648 0.16000 160.00000 22.04120
3.162278 2.23607 2.01317 0.10000 100.00000 20.00000
3 2.12132 1.90986 0.09000 90.00000 19.54243
2 1.41421 1.27324 0.04000 40.00000 16.02060
1 0.70711 0.63662 0.01000 10.00000 10.00000
0.9 0.63640 0.57296 0.00810 8.10000 9.08485
0.8 0.56569 0.50930 0.00640 6.40000 8.06180
0.7 0.49497 0.44563 0.00490 4.90000 6.90196
0.6 0.42426 0.38197 0.00360 3.60000 5.56303
0.5 0.35355 0.31831 0.00250 2.50000 3.97940
0.4 0.28284 0.25465 0.00160 1.60000 2.04120
0.316228 0.22361 0.20132 0.00100 1.00000 0.00000
0.3 0.21213 0.19099 0.00090 0.90000 -0.45757
0.2 0.14142 0.12732 0.00040 0.40000 -3.97940
0.1 0.07071 0.06366 0.00010 0.10000 -10.00000
0.09 0.06364 0.05730 0.00008 0.08100 -10.91515
0.08 0.05657 0.05093 0.00006 0.06400 -11.93820
0.07 0.04950 0.04456 0.00005 0.04900 -13.09804
0.06 0.04243 0.03820 0.00004 0.03600 -14.43697
0.05 0.03536 0.03183 0.00003 0.02500 -16.02060
0.04 0.02828 0.02546 0.00002 0.01600 -17.95880
0.031623 0.02236 0.02013 0.00001 0.01000 -20.00000
0.03 0.02121 0.01910   0.00900 -20.45757
0.02 0.01414 0.01273   0.00400 -23.97940
0.01 0.00707 0.00637   0.00100 -30.00000
0.009 0.00636 0.00573   0.00081 -30.91515
0.008 0.00566 0.00509   0.00064 -31.93820
0.007 0.00495 0.00446   0.00049 -33.09804
0.006 0.00424 0.00382   0.00036 -34.43697
0.005 0.00354 0.00318   0.00025 -36.02060
0.004 0.00283 0.00255   0.00016 -37.95880
0.003162 0.00224 0.00201   0.00010 -40.00000
0.003 0.00212 0.00191   0.00009 -40.45757
0.002 0.00141 0.00127   0.00004 -43.97940
0.001 0.00071 0.00064   0.00001 -50.00000
Formulas Vpk/SQRT(2) Vpk*2/PI() V2pk/(2*50) PW*1000 10*log(PmW)
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About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2024

Webmaster:

    Kirt Blattenberger,

    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

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