| I've seen a few comments lately that show there is a bit of confusion out there with regards to the meaning of 'RMS' when it comes to waveform measurements. RMS stands for Root Mean Square and would more accuratley be described as the 'square root of the mean of the squares'. Rms measurements apply to varying waveforms and can be measured by dividing the periodic time interval up so that the voltage/current changes very little from division to division, taking the square of the measurment over each division, calculating the mean of the squared values then calculating the square root of that mean. This calculated value gives you the equivalent DC measurement which would dissapate the same power across a given resistance as the waveform measured. For example if Vrms of a particular waveform is 10V then 10Vdc would dissapate the same energy across a given resistance. The rms measurement applies to any waveform, not just sine waves. It just so happens that most (cheap) multimeters expect all AC waveforms to be a sine wave and estimate the rms value based on this assumption (0.707 * Vpeak for instance). This will give you unreliable measurements when the waveform varies significantly from a sine - such as the current in a phase of an alternator charging a battery through a rectifier. Meters that are 'true rms' should calculate the rms value based on the actual waveform measured and thereby give meaningful information regardless of the waveform.
I have put together a spreadsheet that (hopefully) illustrates the value of rms measurements. The spreadsheet compares a 50Hz sine wave with an arbitary (random) waveform. A new random waveform can be generated for comparison by clicking the 'Regen' button at the top of the sheet. You can also specify the peak voltage and the resistance across which the output of both waveforms will be compared. Both waveforms are divided up into 200 divisions over a 0.02S interval (1 cycle @ 50Hz). For each waveform the energy dissapated across the specified resistance is calculated along with the rms voltage. The total energy dissapated is then compared using the two methods at the bottom of the table. As you can see, the calculation using the rms value gives the same energy dissapation for both methods. The ratio of Vrms/Vpeak is always 0.707 (1/2^0.5) for the sine wave but varies for the arbitary wave.
http://www.otherpower.com/images/scimages/2210/RMSComparison.xls |
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