RE: [SI-LIST] : RMS Definition, clarification

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From: Zabinski, Patrick J. (zabinski.patrick@mayo.edu)
Date: Tue May 29 2001 - 12:59:37 PDT


Vrms = Sqrt[ Integral (V(t)^2) ] / T

Where:

        V(t) = Voltage with respect to time
        T = one period of time = boundaries of integral

Simply insert the equation for V(t) into the integral,
integrate over one period, and you can figure out Vrms
for any (deterministic, periodic) waveform.

In terms of a table of values, you've got the most
common ones already listed. Sorry, I don't have
any handy-dandy, all-inclusive chart.

One point to keep in mind, though, is that you should
be clear in what "V" represents in your table. Some folks
assume "V" means Vpeak-to-peak, while others assume "V"
means Vpeak-to-ground. Similarly, don't forget to take into
account DC offsets (some folks assume "square wave"
means Zero to V, not -V to +V; etc.).

Pat

>
>
> Sorry if I wasn't clear. I know what RMS means. What I am
> looking for is an
> equation of the form
>
> RMS = sqrt[integral(V^2Sin^2(theta))/n] with the correct integration
> boundaries.
>
> The table I am looking for might have entries like this:
> sine Vrms = V/.707
> Square Vrms = .5*V (If symmetrical around zero axis,
> then Vrms = V)
> DC Vrms = V
> Triangle Vrms = ?*V
> Saw Tooth Vrms = ?*V
> etc
>
> Sorry for any confusion
>
> Doug
>
>
>
> Hi Gurus
>
> I am looking for the mathematical formula for RMS voltage. I seem to
> remember that it can be expressed as an integral of a squared
> function. I
> can almost fake it(!) but I'd like to see the real thing! I
> would also like
> to see a table of RMS values for different types of (non-sinusoidal)
> waveforms (such as triangular, saw tooth, etc.) Can anyone
> point me to a
> web page where this info might exist. Or perhaps, might
> someone create the
> formula in an equation editor and e-mail it to me as an attachment.
>
> Thanks for any help
>
> Doug Brooks
>
>
>
> ***********************************************************
> Doug Brooks' book, "Electrical Engineering for the
> Non-Degreed Engineer is
> now in its 3rd printing. Learn about it at www.ultracad.com
>
>
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>
> ***********************************************************
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> Non-Degreed Engineer is
> now in its 3rd printing. Learn about it at www.ultracad.com
>
>
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