# Question of the Day, 1/26/07

#### mbenonis

##### Wireless Guy
What does RMS stand for, and what is it? Why do we use it instead of a straight average? What other methods do we use to measure voltage, current, and power? What is the formula to calculate the RMS value? For the last part, provide a general formula that applies to non-sinusoidal signals as well.

#### bahaha

##### Member
I know the first part and a half. RMS stands for root mean square. I don't entirely remember why it's used instead of an average, but it has something to do with the graph of an absolute value not having a derivative in the middle...at least that's why RMS is used in statistics. I guess i know the general formula also. Square all the numbers and take the average, then take the square root.

#### ship

##### Senior Team Emeritus
Why does an analog meter not have this problem.
Part B' why is an analog meter less used?

#### mackem_techie

##### Member

RMS is, im presuming the root mean square as said above. The forumal for sinusoidal (or other periodic) functions is:

√((Integral[f(t)², Lims: T1, T2])/(T1-T2)) where T1≤t≤T2 (the time T1-T2 should be a whole number of cycles of the function), f(t) is the function being investigated.

EDIT after some investigation: it appears in electronics that the function is generally for ac power, in which case:

RMS= √((Integral[(Imax sinωt)², Lims: T1, T2])/(T1-T2)) where Imax is the amplitude of the fluctuations, ω is the angular frequency (radians per second)

EDIT after some more investigation and some subsequent algebra (gotta love calculus):

RMS=(Imax)/√2

The formula for non-sinusoidal functions is:

√((Σxi²)/n) where xi is a value of x, n is the number of items (obviously Σ is the summation sign).

RMS and other such measures, are only likely to be used if they are BLUEs (Best Limit Unbiased Estimators), which to the best of my knowledge they arent, the average (officially, mean (of the sample)) is the BLUE of the mean (of the population). However, your statement "provide a reference... for non-sinusoidal signals" suggests to me that the RMS is used to estimate the average voltage coming from an ac power supply, which if i understand correctly tends to be more towards one of the two limits rather than being completely in the middle of the limits.[EDIT: the stuff in edits above was obviously added after this comment, i feel a bit silly now]

Presumably, other methods of investigating the power, voltage and current are to investigate the maximum, which is useful so you dont blow fuses etc, or the minimum, so you get at least a certain voltage all the time. IEDIT: apparently the peak voltage is given by Vpeak= Vrms x √2, which it seems could be as high as 339V in the UK!
I cant think of any other stuff to put here at the moment, so i will go off for an investigate...

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