|
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.
|
where Vpk is the peak (not pk-pk) voltage in
units of volts
|
|
|
| 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 |
|
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