RMS versus AVERGAGE

Ancient Egyptians calculated the area of a circle with (8d)/9 squared. So, a 1 foot diameter circle has 0.79 square feet of area compared to

0.7854 using a more precise value for pi. Not bad for old timers.

-Bill

"The Journey is the reward"

eff.com

"Bill Bowden"

Ancient Egyptians calculated the area of a circle with (8d)/9 squared. So, a 1 foot diameter circle has 0.79 square feet of area compared to

0.7854 using a more precise value for pi. Not bad for old timers.

** The approximation to " pi " taught to school children in my day was 22/7.

Get your pocket calc out and see how close it is.

.... Phil

---

Assuming a voltage source, 10VDC into a 10 ohm load will dissipate, in the load:

E²d 100 * 1 P = ----- = --------- = 10 watts R 10R

from the same source, 10VDC into a 10 ohm load at 50% duty cycle will dissipate, in the load:

E²d 100 * 0.5 P = ----- = ----------- = 5 watts R 10R

Now, since the RMS value of a waveform is that value which will create the same amount of heat as DC would into an equivalent load, in order to create 5 watts of heat in a 10 ohm resistor, using DC, we can rearrange:

E²d P = ----- R into:

Et = sqrt(PR) = sqrt (5W * 10R) = 7.07VDC.

crosschecking:

E²d 7.07² * 1 50 * 1 P = ----- = ----------- = -------- = 5 watts R 10R 10R

So, a 7.07VDC supply would supply as much power as a 10V square wave into the same load resistance, which would cause the terminal temperature of the load to be equal, in either case, making the RMS voltage of a square wave equal to 0.707 times that of its peak voltage.

--- JF

Well the formula you wrote above is limited only to a half period of a wave... and it applies ONLY to square waves. If you had a Sine wave the Average would be Vin*D[(Cos(w*T/2))] The average value of a periodic function,any kind , square, sinusoidal, etc of voltage, current or whatever is zero in a time interval of 1 period.

Differently from the above formula the rms formula you have written applies to a time interval of 1 period and hence gets you a different result.

Both the rms and averages are a way of determing the mean value of a function.

If you were to find the rms of your periodic function within half a period you'd find it coincides with the "average value". Apart from what others mentioned we use rms because the doesn't give you an accurate mean value when the function becomes negative. Or more like with a zero average you don't go anywhere.

"Jimmy Thumbsun is another trolling Nutter"

** Drivel.

** Total bollocks.

** Must be on drugs, or needs to be.

... Phil

Hog wash.

To understand Electronics you have to understand Math. Prove it to be mathematically wrong if you're capable ... otherwise go back to your tranquilizers.

Average is zero ... if you don't know that ... then get medical help.

Thumbsun

Pi is an irrational number hence cannot be expressed by a fraction.

Interesting link. Alternatively you can do the integration which gives you the average using numerical methods ... the simplest that comes to my mind is Simpson's rule.

22/7 = 3.1428571428571428571428571428571 comes damn close. Pi = 3.1415926535897932384626433832795

So (22/7)/Pi = 99.959766250584330314720471286155 percent for a

00.0402337494156696852795287139% error.

--
For the last time:  I am not a mad scientist, I'm just a very ticked off
scientist!!!

3.1415926536 Or, essentially 3.141593

22/7 = 3.142 pretty much way the f*ck off, with the first error being in the third place after the decimal. That error location is way too soon for some things, but is just fine for many calculations

Hmm. How about the 999/318 = 3.141509 xxxxx

I can remember that because it's just under 1000 HP from a 318 V8

.Now, lets see if a 318 was ever modified to do that! :)

No, Phil is correct that you are wrong.

The average value of a sine wave over a half cycle is Vp*2/pi (where Vp is the peak value of the sine wave). The average value of a sine wave over a full cycle is zero. The rms value of a sine wave over any number of half waves is Vp/sqrt(2). If you need proof and you understand calculus, most participants of this group can oblige you.

Phil is not known for his tactfulness and I don't know him extremely well, but I suspect he knows much more math than you do. If you are patient and read this newsgroup regularly, you could learn a lot from him. It took me two years to understand how to read Phil's responses and glean the valuable information they contained. Lurk a lot, is my advice.

As I said above, the average of a sine wave is zero over a full cycle. So, I guess the power dissipation in a diode over a full cycle is zero since the current reverses every half cycle? The average over a half cycle is Vp*2/pi (considering half-wave) and that is what the experienced designers on this group would use for the calculation. If you design circuits, it becomes second nature to think of the average as Vp*2/pi (in most cases).

Cheers, John

"John - KD5YI"

** Hmmmm.......

** Two whole years ????

That long - to see the obvious benefit of pithy, common sense ??

** Forget it.

The troll is a stupid, literal thinking, utterly autistic maths wanker.

He is just here " coitusing " with us.

.... Phil

Hardly able to be so described, regardless of correctness level.

Phil said _approximation_. And that most certainly can be expressed as a fraction, just as he said. It looks like you missed the word approximation - or that I, and others, are missing your point. So... what is your point?

Ed

Well, he usually seems to be pithed off.

Cheers

Phil "Not Antipodean" Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

That has to be it then.

3 = 3.0... 1 digit (1 kings) 4(8/9)^2 = 3.16... 2 digits (egyptians?) 22/7 = 3.142.... 3 digita (highschool) 355/113 = 3.1415929... 7 digits

cannot be expressed precisely by a fraction.

:) but it's only good to 4 digits.

355/113 is not miraculous in its precision, points like this are common along the continued fraction approximation of a number

--
?? 100% natural

The reason for taking a half cyce is that it gives a good value. Basicly by calculating power is that the current on the negative halve of the sinus is negative too. Negatife multiplied by negative is positive, atleast for an ohms load.

--
pim.