AVR Freaks

if you calculate the "Area under the curve" for 1/2 a period, or for a full period

You assume OPs signal is periodic, and period can be deduced, which is very optimistic (else, RMS should be calculated explicitely, which takes much more time to converge, if it is possible, i.e if offset is known).

I agree, and the cynical answer would have been : look at the topic title; look at wikipedia : OP lives in England and each and everything -s-he needs is in wikipedia (if bias is known, one just has to substract its square ).

Doc JC and you taught me a lot, as I did not think of floating point errors (would occur, if one waits for convergence) and wide dynamics. Perhaps wide dynamics issue can be solved by buying an external ADC, with 16-24 bits....

Doc JC told, and it is true, that a fast  (an infinite improvement upon waiting until it converges)  and exact solution can be reached quickly if signal is periodic. As some equipments are not linear at all (LCD bulbs, switching power supplies), detecting period (and betting it is 50-60 hz) seemed abnsurd for me. If OP has an optocoupler and is very courageous , he might use the voltage -more sinusoidal than current, except for kettles maybe-  (in UK, except for storms, it may be periodic; cheap generators do not know trigonometry)and detect, after low pass filtering, zero up|down wards crossing might give a good estimation of the period (50 Hz in France can vary by 10%, IIRC : only the daily average  must be 50 HZ, else  some clocks would drift -2hrs/day...- ).

Is my Omericon that good?

If you had asked "Belgium", may be I would have felt insulted (but I know belgien people tell the same funny stories about french silliness), but Belgium makes the same best french    freedom fries in the world (there shoul be a tunnel between Dover and Ostende) and that tobacco is very cheap (when Matesa get deported out of France, they buy cigarettes in Belgien, 150 km away... and come back legally into france to sell them)

OTOH, I asked wikipedia about the greates Scott Iread, RL Stevenson: in Scottland, he suffered from loung disease and boredom, he went to the poorest part of France, Vivarais, and travelled with a 4 legged donkey. He did not suffer from long desease anymore.

Then he went to eden like islands, Samoa, with an  Omerican ... and lost his life.

From http://www.gutenberg.org/files/5... RL Stevenson wrote in Traves with Donkey in the Cevennesl :

I am worthy the name of an Englishman, and it goes against my conscience to lay my hand rudely on a female. 

For 60 Hz, I always use a 4 or 16 point Walsh function. 4 point Walsh functions need 240 Hz sample rate, 16 point Walsh function use a 960 Hz sample rate. These are band pass filters hence any DC offset is automatically removed.  The beauty of Walsh function digital filters is that samples are either added or subtracted. The following equations are for a 4 point Walsh function. 

CAL = x0 - x1 - x2 + x3

SAL = x0 + x1 - x2 - x2

RMS = sqrt(CAL*CAL + SAL*SAL)

The simplicity of the Walsh algorithm described in my previous posting is not realized until you understand the true implications. x0, x1, x2, and x3 are the present and three previous samples of the input signal sampled at a rate of 240Hz. The CAL result is the real part of an complex value and the SAL result is the imaginary part. Taking the arctangent of the SAL/CAL gives the phase of the voltage.  The Vrms and Vphase are updated at the 240Hz sampling rate.  Now this phase is pretty much meaningless UNTIL you apply the same algorithm to the current. Now the phase angle between voltage and current is simply the difference. To compute the real power, P = Vrms*Irms*cos(Vphase - Iphase). To compute the reactive power, just replace cos with sin. Historically, a multi million dollar company (Schweitzer Engineering) got its start in the mid 70's applying this algorithm to power system protective relays. This allowed my friend Ed Schweitzer to not only calculate the magnitude of the fault current but also the distance to the fault location.  Those interested in applications of DSP to power can read my PhD dissertation.

There is even a way to speed up this algorithm.  Just save the present CAL squared value and use it in the next iteration as the SAL squared value. Hence, for the memory of one variable, three add operations and one multiply operation is eliminated.  The reason that this works is that delaying the CAL value by one sample period is essentially the same as a 90 degree phase shift making it the imaginary part of the complex variable. For those who would like to see the ugly math, here is a place to start: http://dergipark.gov.tr/download.... Enjoy!