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| Power vs. Voltage in a 50 Ω System |
 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) in a 50 Ω System |
where v is in volts
| | Power to Voltage (for a sinewave) in a 50 Ω System |
 Volts
| | 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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Kirt
