RMS Power?
@almargAnd then please where 141 watts comes from. What kind of inbetween power is that to be called? Well its not. We have agreed that a 100 watt RMS amplifier supplies 40 volts peak into an 8 ohm load. 40 x 40 / 8 = 200 last time i checked. As Monty Python says... say no more, say no more. |
@kijanki I often see power specifications like "100W RMS". There is no such thing as RMS power. Of course, you can calculate RMS value from any curve, including power curve, but it won't represent anything. "Real" power representing heat dissipated in resistive load is "Average Power" Pavg=Vrms*Irms. In case of sinewaves Pavg=0.707Vpeak * 0.707Ipeak = 0.5Ppeak, or Ppeak = 2Pavg. Where is the mistake in RMS power? RMS is a measurement that allows one to determine the peak value of a sine wave that will produce the same heating in a resistive load as a DC voltage. So if run a heater or incandecent bulb off 120 DC or 120 RMS AC the heat and light will be the same. The peak voltage of that sine wave will be 1.414 X 120 about 170 volts. By the way the average of a 170 volt sine wave is 0.637 X 170 or 108 volts. This is all well documented and accepted. What is it you are going on about anyway? I make 100 Watt amplifiers and I know how to measure them.They produce 28.28 Volts RMS into a 8 ohm load. Perhaps you missed the fact that at the peak the instaneous power is very large and not related to the average voltage. |
@almarg Hi Roger,
Your first calculations in getting the peak voltage, current and power are indeed correct. 200 watts is the peak power however 100 watts is the RMS power. Thanks for not using the word average which does not apply. I will explain another way. Kijanki needs a math lesson. 0.707 is the proper factor for the voltage and the current as you have demonstrated. One must however use that factor for both voltage and current. If you want to apply it to the already calculated peak power one must multiply that by 0.707 x 0.707=0.5 Correct? Thus RMS power is 0.5 x peak power. It is incorrect to multiply power by 0.707 just once. One has to do it twice If you read the OP’s last line he actually got it the 0.5 right but he called it average. I really dont see what he is going on about. A power amp behaves just like the power supplied to your home. You can use a power amps to run motors at various speeds and all sorts of things. This is basic electronics.. |
@almarg And his point is that strictly speaking what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time. Which would be 141.4 watts in your example, while of course 100 watts (the product of RMS voltage and RMS current) is what is actually being referred to when that phrase is used. First when someone starts an OP with "there is no such thing as RMS power" whats that mean? RMS Power doesn't vary as a function of time, instaneous power does. Im still waiting for the link to Wickipedia. Do you have it. Im just on pins and needles here. |
@kijanki @almarg Like to make it hard done you. I looked at all the references listed in the Wicki article. They can easily be clicked on above. Half of them are referring to average power as a speaker sees it so as not to overheat the voice coil. That is indeed time averaged and all is well there. However a speaker is not an amplifier. If you are betting on reference #8 being valid I will take $100 on that bet. Its pure fiction. http://www.hifi-writer.com/he/misc/rmspower.htm Besides the admission at the top Most of what follows is an edited version of an email sent to me in April 2003 by the editor of Australian HI-FI. It was so well expressed I want to see it published, somewhere. So here it is. Unfortunately the precise authorship has been lost due to rigorous cleaning of computer archives and trashed hard disks. I am told that much of it was probably from ’an electronics professor at Uni of NSW’, originally written as a letter to The Guide, an insert into The Age newspaper. Should the lost electronics professor seek to claim authorship (or even banish his words from this site), I would plead with him or her to email me at scdawson (at) hifi-writer.com. Do you agree with this statement... By contrast, RMS (root mean square) power, would have to be defined as the square root of the time average of the square of the instantaneous power, since this is what ’RMS’ means. FIrst thing wrong with that sentence is that if you take the square root of something you squared you get the same thing back. And what is the square of the instantenous power anyway. Could a math major please come help us out. This is getting no where. Though I love and contribute often to Wickipedia this article needs a lot of help. Did you not read the banner at the top of the article.. This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)This article may require cleanup to meet Wikipedia’s quality standards. (June 2011)This article possibly contains original research. (October 2008) Please read this also. https://en.wikipedia.org/wiki/Talk:Audio_power This is a "start class" article, please read the following https://en.wikipedia.org/wiki/Wikipedia:Content_assessment Evidently you guys have not vetted this article at all. Heres another complaint I found on the talk page.. One thing this article does poorly is differentiate between speaker and amp ratings. Both are given "RMS" and "PMPO" ratings, but the conditions are different. The peak power of an amps is directly limited by their voltage rails and the minimum impedance of the loudspeaker. It is impossible to have a higher peak instantaneous power than this (unless due to reactance?) But for loudspeakers, the peak instantaneous power is not as clearly defined, and has to do with destruction of the speaker. — Omegatron04:48, 25 October 2007 (UTC) |
@almarg To be sure it’s clear, I absolutely did not say that "RMS power" varies as a function of time, although I can see how my statement might have been misread. I said that...... what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time. The paragraph above appears to me contradictory. First you say the waveform defines how power varies as a function of time. That would be instaneous power or instaneous heating, agreed? The RMS also defines how power varies as a function of time and defines its DC heating value. We needed that when Tesla won the "war of the currents" over Edison. How else were we to specify the voltage of the required sine wave. As to the WIckipedia article i did find it and its many flaws. If you have the time, rather than defend kijanki do some reading yourself. There are 18 complaints about this article on the talk page of which 13 and 14 pretty much kill the whole thing. If kijanki learned this from articles like this then he is in the same mistaken camp. Shall we leave him there? Would you care to tell me why an amplifier producing 100 watts RMS is any different than an AC generator producing 100 watts RMS. We are talking about sine waves here, that is all. And then please where 141 watts comes from. What kind of inbetween power is that to be called? |
@kijanki Al, I was right (he is not going to get it). RMS value of ANY sinusoidal waveform, having peak at 200 (of any unit) is 141 (of the same unit). 100W would be an average power value corresponding to VrmsxIrms and equal to half of peak power for sinewave (and equivalent to amount of DC power producing the same amount of heat). Guys, please, this is EE101. Lets be a little careful here for those trying to understand this conversation. "RMS value of ANY sinusoidal waveform, having peak at 200 (of any unit) is 141 (of the same unit). Does that apply to watts? Are 200 peak watts the same heating value as 141 watts. They are the same units? I know you dont think so but one could easily interpret any to mean any. Granted going on its fine. Whats all this about average power? Whats the definition. I saw you 3 step calculus but, sorry I dont get it and I did fine in Calculus. Yes RMS power is half the peak power, but you call it average power without informing us what average power is to you. Al, who you appear to agree with. thinks 141 watts is the average power of 200 watts peak. He has said so. Still what is this average power? We are talking about a sine wave going on and on. Average power as used by most in audio means the average over a long time, playing music and not letting the voice coil get too hot. This is the definition I find most often for average power. I dont see how it applies to amplifiers except for the heat sinking. RMS power is continuous sine wave in this discussion. Why say it is wrong. Whats wrong with it? Come on kijanki, lets get this ironed out for everyone else who by now doesnt know what we are talking about. It is important. The early replies to you OP had no idea what to say. I do think we agree yet use of the term average to describe heating is generally used as RMS. Do you really want to say this. " Prms = 0.61Ppeak "? not 0.5 . P rms= V rms x I rms. does it not. is so .7 x .7 =.5 I am writing a paper on how the FTC got involved, its not the way most people think and its not bad. |
@kijanki @almarg That author’s conclusions:
Why do you quote a paper that is all about square waves when we are talking about sine waves? This is most unscientific. http://eznec.com/Amateur/RMS_Power.pdf I encourage readers, if there are any left over this foolishness, to note all the waves in the picture are square waves. The value of Vp= 1.41 x Vrms applies to sine waves only. Not to square waves where the average is 0.5 and so is the RMS. In this amateur, by its own name, paper, which is highly flawed. In the first step he aready has the average, is correct and done. However he wants to prove something odd. So he applies 1.414 to the already correct answer and gets a new answer which is incorrect. If one stops for a moment and looks at a square wave with at flat top the average and the DC value are both 1/2 the peak. Just cut the wave in half and fill in the hole. Then you get a straight DC line. No problem. But with a sine wave as the voltage peaks and current peaks there is a lot of energy at the top. The use of root 2 or 1/ root 2 ONLY APPLIES TO SINE WAVES, not triangular, not square, not you mothers fancy stiching. TRUE RMS meters actually measure the heating value of nonperodic waves and can even tell you the RMS or heating value of music. That heating value is important to your woofer. So far the author has supported his position with a flawed page from Wickipedia (flawed in their estimation also) and this paper on square waves. There is no point in going further with this. Stating there is no such thing as RMS power is a bold statemtent that has uncountable support for the fact that RMS is real, useful and applies to amplifiers. I did find today a mistake in the authors early math and will present the correct math, I dont know why this author wants to press this most unreasonable theory. As to the authors commment Al (he wont get it) and( he didnt get it.) Rudely said but true. I dont get what you said and I dont know what engineer would. http://www.n4lcd.com/RMS.pdf This is interesting and if all we are actually arguing about is the term "RMS" then we have made a mess of things. Putting the term "RMS" in front of watts is a misnomer. Once you have watts you just have watts. There are no other kind of watts for continuous waves so AVERAGE watts does not apply either. Its just WATTS, AC, DC, any periodic constant value. The RMS I believe is to show that the watts were measured by RMS methods, not peak or peak to peak methods. Perhaps we have argued over nothing but 3 letters of the alphabet, however the OP has cited papers that are incorrect and certainly have muddied the water. Heres you out guys:) We still have to agree on one thing. The heating watts of a 100 watt amplifier is 100 watts. It is measured by V rms sq/R load. The Peak watts is 200 and there are no other meaningful numbers to be stated. Using RMS to mean 'Hey anything with RMS in front of it gets to be multiplied by 1.4"... is a no no. Average watts is generally applied to a signal that is non constant and thus an average is needed. Average is not appplicable to measuring sine waves for power. In fact the average squared comes up low. |
@imhififan https://en.wikipedia.org/wiki/Root_mean_square Thanks, this is most interesting. I note that the coefficient (mulitplier) for peak to peak is 2.8 for the sine, 3.5 for the sawtooth and 1.0 for the square. (divide those numbers in half for the peak, of course) Those are all RMS. So readers might like to know there is not just one RMS in this world. It depends on the waveform. Sines are the best because we have equipment to null out the fundamental and then we can measure and SEE the distortion products on a scope. Do you have a comment to add to our lovely conversation? Recently I have come to the possibiity that the OP decided to apply RMS to power, which I cant imagine anyone doing. There is no RMS of power nor is there average of constant power it is just power. Power determined by RMS voltage. We dont RMS it again. Why go on to use mathmatical arguments to prove or disprove a simple misuse of terms. Thats just grandstanding. If we want to be perfectly clear we should say: 100 Watts (measured by RMS voltage of an undistorted sinewave into a resistive load) .Then then there is no abiguity. Thats all he had to say! At first no one was interested, look at 2nd post. They Ralph properly answered how its done. Then the OP objected to Ralphs answer which happend to be exactly how we do it. Though most of us read it off the Sound Tech which has a watts scale. Just Watts, my hands are steady, the meter is steady, the ship is on course, there is nothing to average. The OP states that the word "average" is appied in ’every textbook". Every is a dangerous word. But im gonna look at a few I have here. |
@almarg Imhififan, thanks for providing the additional link. Al, First please accept my sincere apology for anything I may has said to cause you offence. This has been a muddy thread, made worse by unvetted quotes from poor sources. These I have already cited. The OP pulled much of his argument from this self contradictory paper. And the flawed references in the Wickipedia article Audio Power. http://www.n4lcd.com/RMS.pdf "The FTC also incorrectly assumed that the measurement of the power in Watts would be RMS Watts. It's not. It's Watts. There's no such thing as RMS Watts. In summary, RMS Voltage is correct, but there's no such thing as RMS Power or RMS Watts. Or stated differently, the Voltage that's measured is RMS Voltage, but the resulting power is Average Power and it's measured in Watts." Focusing on the wrong of putting RMS in front of Power and then the word Average the horse took off a running. I dont for a moment believe that the FTC meant to apply any form of root 2 to the aready calculated watts. The were actually trying to get away from Peak watts and Peak to Peak watts which were inflating numbers. Perhaps if they has said Watts (RMS) or more correcty Watts measured by the RMS vaue of a sine wave all would well. Had the OP simply objected to the language instead of coming back with math (some of which is incorrect) we would have been done with the first post by Atmasphere, thanks Raph. However Ralph was ignored. I had my Chinese math guy check the integral also. The answer is 3/8 pi not 3/8, working that out the root the answer is 1.08 as I recall. I dont really care whose math is right or wrong, my question is why throw that out at all? Who on this thread is likely to be a math major? The OP fired all his ammo and I think he's out on this. As to kijanki we are still in a tussle about emitter resistors and losses in amplifiers. I wish we were sitting around a table drinking and having more fun with this. These topics are interesting to discuss, we all learn from those who can best express their ideas calmly and rationally. I would like to have Imhififan at the table. I have enjoyed how he said little but kept coming back a source that cleared it up for me. I was doing repairs in a HI FI store when the FTC rule came around. It uas designed to stop the inflation of power into Peak Watts and Peak to Peak watts (which dont exist). I am writing a paper on the history of that which I hope will extend and clairfy what the FTC was trying to do. In my reasearched no one ever RMSed the Watts in any literature. They used RMS to differentiate real Watts from POP (Peak Output Power) and PPOP (Peak to Peak Output Power) We are all sorry they decided to put RMS in front of watts.I think they has to put something. But I never assumed the meant to RMS the watts. Who would? |
@imhififan Thanks for the nice words, Roger and AL I wish kijanik would join us in laying to rest this matter of three misplaced letters. It appears that three letters misplaced caused all the fuss. I will soon post a paper on my experience of the running up of power numbers that the FTC stepped in to fix a real problem. I dont know which maker started it but Peak to Peak power has no meaning since the load can never see the peak to peak across it. I note some ESL headphone amp makers are using Peak to Peak voltage. That is disappointing. |
