A few questions about TRUE RMS - Page 1
Forum section: electronics / testgear

author: zapta
author_rank: Super Contributor
timestamp: September 21, 2013, 04:17:35 pm
content: 1. What is true RMS? My understanding is that it is DC voltage that will result with same power when applied to same resistance but am not sure. (I do understand the mathematical definition of RMS, I wonder what it means and why it is important).2. Why multimeters provide RMS measurement for AC only? I would think it would be useful for DC voltages as well, for example PWM.3. When dealing with household electrical projects, is true RMS really required or an average measurement is sufficient? (what can be the error between them in % in common house hold scenarios?)4. How true RMS meters work? (I think I understand how average measurement works, e.g. by a rectifier and some low filter).Thanks,Z.

author: c4757p
author_rank: Super Contributor
timestamp: September 21, 2013, 04:39:20 pm
content: You are correct, power from 120 V RMS = power from 120 V DC. It just comes from Ohm's law and P=VI.A true RMS DMM should have no trouble responding to pulsed DC, though you will have to manually add the offset. Some have an AC+DC mode that does this.I can't really think of a reason why you would need one for household electrical work.They literally compute sqrt(mean(v^2)). Some use an analog circuit making use of a logarithmic amplifier. Some newer ones sample the voltage and compute digitally. It is also possible to actually measure power delivered thermally, but that is uncommon.

author: PA4TIM
author_rank: Super Contributor
timestamp: September 21, 2013, 04:44:01 pm
content: AC in Volt is allway RMS except when stated that it is not.It is the same Voltage that you need for heating up a resistor when using DC.Everey meter should be able to measure the correct AC voltage, but to bad, that never was the reality. The meters that did this were called RMS meter or later under marketing pressure TRMS meters.But then the cheapys allso started to make TRMS meters. To bad many have a very narrow bandwidth, crestfactor.There are AC coupled TRMS meters and TRMS meters that also have a AC +DC mode. (I haver 4 meters who do that and two upto 1 MHz and high crest factors)You can however measure AC and DC separate and do the math if your meter does not do it for you.There are several ways. Today most times this is done by special IC's. Look at the site of Analog Devises. They have a (very) thick pdf only about measuring TRMS. In the earley days they often used a measurement based on heating.

author: Lightages
author_rank: Unknown
timestamp: September 21, 2013, 04:47:06 pm
content: Quote from: zapta on September 21, 2013, 04:17:35 pmRMS is Root Mean Squared. There are better resources to explain the math than I can provide here. Yes, it basically means the equivalent power into a resistive load. This can be measured by applying the voltage to a known nonreactive load and measuring the heat produced.Quote from: zapta on September 21, 2013, 04:17:35 pmMany multimeters do provide AC+DC True RMS. Some provide a way of switching from AC only to AC+DC.Quote from: zapta on September 21, 2013, 04:17:35 pmIt depends. If you are just trying to get a rough measure of the output of a transformer, then an averaging meter will do. If you are trying to measure a reactive load or trying to determine things like power factor or measure music waveforms then True RMS is a must.Quote from: zapta on September 21, 2013, 04:17:35 pmTrue RMS calculations are done a few different ways. Most meters use a chip that is made specifically to do the calculations and then pass on the equivalent DC voltage to the main meter processor.Here are a couple of resourceshttp://en.wikipedia.org/wiki/Root_mean_squarehttp://www.analog.com/en/special-linear-functions/rms-to-dc-converters/ad636/products/product.html

author: zapta
author_rank: Super Contributor
timestamp: September 21, 2013, 09:31:13 pm
content: Thanks guys for the informative answers. I think I get it now. I have two follow up questions if I may1. The true RMS meters that use heat, do they take the heat from the input signal (effecting the measurement and difficult to have multiple ranges) or do they have high impedance and internal buffer that feed the heat load?2. I tried to make sense of the match of measuring true RMS by adding the DC bias to the true RMS of the AC decoupled signal but could not make it to work. Here is an exampleLet S0 be the measured signal: 10% duty cycle pulse between 0V and 10V.AverageDC(S0) = 1v.TrueRMS(S0)=sqrt(0V*0V*0.9 + 10V*10V*0.1) = 3.3VLet S1 be S0 after AC coupling. S1 = AcCoupling(S0) = S0 - AverageDC(S0) = S0 - 1V. This is 10% duty cycle pulse between -1V and 9V.TrueRMS(S1) = Sqrt(-1V*-1V*0.9 + 9V*9V*0.1) = Sqrt(9VV) = 3V.If we add the AverageDC(S0) to TrueRMS(S1) we get 3V + 1V = 4V which is not the same as TrueRMS(S0) = 3.3V.I think that the problem is that we are mixing average measurement (the AC decoupling which subtracts the average DC level) with RMS measurement.

author: c4757p
author_rank: Super Contributor
timestamp: September 21, 2013, 10:26:12 pm
content: I misspoke when I said "add" the offset, I should have said "consider" or "adjust for" or something like that. You're right, it doesn't quite work that way.If I'm not mistaken:

author: macboy
author_rank: Super Contributor
timestamp: September 21, 2013, 10:44:34 pm
content: Quote from: zapta on September 21, 2013, 09:31:13 pmWe are measuring voltage not power. Generally, they have a high input impedance (unless it is an RF range instrument, which might have a 50 ohm input). The input voltage is buffered and fed to a resistor to generate heat. This has a temperature sensor. Usually what is done is that there is an identical resistor and temperature sensor which is fed by an internally generated DC voltage and controlled by a control loop which balances the two; it makes the power dissipated in the DC-fed resistor equal to the power dissipated in the (external signal) AC-fed resistor. Then the DC voltage is measured and displayed. It's simple really but very difficult to pull off.

author: c4757p
author_rank: Super Contributor
timestamp: September 21, 2013, 11:22:45 pm
content: Even better, if you'd rather be convinced that it holds true forallAC waveforms:Edit: Fixed a missing factor of two. Thanks, zapta!

author: G0HZU
author_rank: Super Contributor
timestamp: September 22, 2013, 12:38:36 am
content: I have an old school Racal 9300 true rms meter here that has a very elegant method of measuring true rms.It operates from about 5Hz to 20MHz and uses a series of precision attenuators followed by a multiplier stage (squared) followed by an integrator (mean) and then a final stage to display rms. It also has a complex 'offset error' cancelling system and I have used one of these as my gold standard true rms meter here and at work for many years.I think my Fluke 45 bench DVM uses an AD637 chip for the true rms function but I think it only works up to about 100kHz and I would always trust the 9300 more than the Fluke for signals that contain noise.

author: zapta
author_rank: Super Contributor
timestamp: September 22, 2013, 12:58:35 am
content: Quote from: c4757p on September 21, 2013, 11:22:45 pmHi cp. I am not a math wiz but tried anyway to follow your formulas and got stuck at line 7. When you go from line 6 7o line 7, do you say that (AC + DC)^2 = AC^2 + AC*DC + DC^2 ? Is there a 2 missing somewhere?

author: c4757p
author_rank: Super Contributor
timestamp: September 22, 2013, 01:04:26 am
content: Ah, yes! Thank you, I missed that.It doesn't make a difference, though, since the integral of AC is zero and that whole term drops out, so don't worry about it.Edited above.

author: zapta
author_rank: Super Contributor
timestamp: September 22, 2013, 05:06:22 am
content: Thanks cp. So the way to combine the DC level and the AC RMS is a geometric mean of the two. Makes sense. I plugged it in my example above and it gave the correct answer. Mystery solved ;-)

author: mikes
author_rank: Regular Contributor
timestamp: September 22, 2013, 04:57:48 pm
content: Quote from: PA4TIM on September 21, 2013, 04:44:01 pm"True RMS" is not a marketing term, it's a feature. Many meters which claim simply "RMS" are only accurate for sine waves, and that's good enough for many uses. With a true RMS meter, the shape of the waveform doesn't matter, and that may be needed in some cases.

author: Dave
author_rank: Super Contributor
timestamp: September 22, 2013, 05:56:58 pm
content: Quote from: mikes on September 22, 2013, 04:57:48 pmThe waveform shape matters even with true RMS meters.The key here is crest factor. If your meter has a poor crest factor, you may get incorrect readings with waveforms that have large, but short spikes.

author: Robomeds
author_rank: Frequent Contributor
timestamp: September 22, 2013, 06:51:03 pm
content: Perhaps I'm wrong but I have assumed that RMS and True RMS were marketing terms for the same things. IE they don't assume a sign wave when reporting AC voltage. I think the cheap meter just rectify and average the AC wave and assume a scaling factor that results in the same value as the ideal true RMS value.My understanding of all RMS meters is they effectively integrate the voltage over time (either via heating or sampling or charging etc) and again report the voltage with out needing to assume a sinusoidal wave form.Finally, there are the AC+DC RMS meters which add both the AC and DC wave forms just in case there is a DC offset.

author: PA4TIM
author_rank: Super Contributor
timestamp: September 22, 2013, 07:47:11 pm
content: Quote from: mikes on September 22, 2013, 04:57:48 pmThe wave form does matter: crest factorAnd it is a marketing term because AC volt is defined as RMS. So if a meter has a reading in AC Volt, it is rms, there is no other way. If the volt has no extra like peak-peak, avarage, mean etc it is volt and so by nature rms.An example: The HP3400 maual states it is a rms meter, this to differentiate it from meter that only have an ACV scale but measure f.i. avarage or peak. So that was a form of marketing (not in a negative way )

author: mikes
author_rank: Regular Contributor
timestamp: September 22, 2013, 09:59:11 pm
content: Quote from: Dave on September 22, 2013, 05:56:58 pmIf crest factor matters, then it's not true RMS.

author: c4757p
author_rank: Super Contributor
timestamp: September 22, 2013, 10:01:03 pm
content: Sure it is. Even a true RMS meter will have a bandwidth, and anything approaching that will be measured incorrectly. That's like saying your DMM doesn't really measure voltage because it can't measure megavolts, or your spectrum analyzer doesn't really measure RF because it doesn't measure terahertz...

author: macboy
author_rank: Super Contributor
timestamp: September 23, 2013, 12:11:09 am
content: Quote from: PA4TIM on September 22, 2013, 07:47:11 pmYou are neglecting the fact that cheap meters that are not "True RMS" are in fact average-responding (average of rectified voltage input), but calibrated to the RMS of a sine wave. So the displayed reading will be the correct RMS value for a pure sine, but way off for a triangle, saw-tooth, or most real-life waveforms.

author: PA4TIM
author_rank: Super Contributor
timestamp: September 23, 2013, 06:35:14 am
content: No, I'm not neglecting that. I wrote that before and that does not change it. AC Volt is always RMS if not stated that it is not. Just because people do not read manuals or manufacturers lie they invented the term TRMS. Most cheap meters today are no meters, they are indocators. And that does not justify the fact that Vrms is double up. It is like saying 1 kilo kOhm, or . This is becoming a just as stupid discussion as audio people can have over RMS Power, or writing VSWR as 1:1.5 instead off VSWR = 1.5, or Return Loss as -25dB instead of 25dB. This are all double statements.

author: nctnico
author_rank: Super Contributor
timestamp: September 23, 2013, 04:42:46 pm
content: To add to the confusion:When measuring DC its custom to use the average value. All analogue DC panel meters will show the average value (current or voltage). Now it gets interesting when DC isn't DC but it consists of pulses. In that scenario any attempt to calculate the power will be wrong. So even when measuring DC (be it pulsating) you'd need a true RMS meter to be able to calculate the power dissipated in the load / drawn from a source.I wouldn't rule out the cheap meters. Maybe in the old days those cut corners but my cheap VC8145 bench multimeter can show DC, AC or true RMS for pulsating currents and voltages.

author: PA4TIM
author_rank: Super Contributor
timestamp: September 23, 2013, 05:27:28 pm
content: http://vicimeter.en.alibaba.com/product/518095781-212886966/VC8145_4_7_8_bench_digital_multimeter_DMM_80000_digit.htmlAre you kidding, it only goes up to 50 kHz and no crestfactor given !. Even my old PM2505 does better as 50 kHz. (my Keitley 2000 was still accurate at 1 MHz !!!! Not that I care much, I rarely measure AC with a meter.

author: zapta
author_rank: Super Contributor
timestamp: September 25, 2013, 07:19:28 am
content: The RMS thing good be a good topic for an EEVBlog video. Explaining what it is, why we care about it (sometimes), and comparing average and TRMS meters with various signals shapes.

author: KedasProbe
author_rank: Frequent Contributor
timestamp: September 25, 2013, 09:05:55 am
content: If you want to see RMS values of different signals you can see them here:The scope screen shows DC, RMS DC+AC and RMS AC (assume -10mV DC is actually 0V)

author: perkabrod
author_rank: Contributor
timestamp: December 31, 2016, 10:47:44 am
content: Why does my Brymen BM257 multimeter read 2.5 V when I measure a 5V PWM signal at 50% duty cycle?According to theory and simulation it should read 3.54 Vsqrt(0.5 * (5^2 + 0^2)) = 3.54 VMy meter reads 2.5 V both when dialed to AC and DC

author: PA4TIM
author_rank: Super Contributor
timestamp: December 31, 2016, 12:39:38 pm
content: Because that is what it is.A 5V squarewave with a 2,5V DC offset, flip the tops down and you have 2,5V DC signal

author: tszaboo
author_rank: Super Contributor
timestamp: December 31, 2016, 01:09:21 pm
content: Quote from: perkabrod on December 31, 2016, 10:47:44 amYou are right, that is how you calculate RMS.The meter will measure RMS AC, which means it is AC coupled, so the measured signal is plus and minus 2.5V.

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 02:45:02 am
content: So RMS AC would be 2.5V, RMS AC + DC (offset) would be 3.54V - that's the confusion here?

author: oldway
author_rank: Super Contributor
timestamp: January 01, 2017, 11:54:40 am
content: QuoteThe mains voltage is sinusoidal and for this reason it is not necessary to use a true rms multimeter.But with regard to current measurements, this is different because there are many non-linear loads and the currents therefore do not have a sinusoidal waveform.For example, the simple magnetization current of a transformer is strongly distorted and its measurement with a non-true rms multimeter will give an erroneous value.But we must avoid using the multimeter to measure currents on mains.For safety and convenience reasons, use a true rms current clamp.

author: cs.dk
author_rank: Unknown
timestamp: January 01, 2017, 12:04:04 pm
content: Quote from: NANDBlog on December 31, 2016, 01:09:21 pmsqrt(0.5 * (2,5^2 + -2,5^2)) = 0,000 VWhat is RMS then? I can see the logic behind, avarage of 0-5V DC is 2,5V when the high and low times are equal. ie. 50% duty cycle.I don't get it

author: oldway
author_rank: Super Contributor
timestamp: January 01, 2017, 12:31:38 pm
content: QuoteBack to school(-1)^2=+1sqrt(0.5 * (2,5^2 + -2,5^2)) = 2.5V

author: cs.dk
author_rank: Unknown
timestamp: January 01, 2017, 12:39:27 pm
content: My TI-89 gives me 3,06 on that.

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 12:51:25 pm
content: Quote from: perkabrod on December 31, 2016, 10:47:44 amBecause it's reading the 2.5V DC (50% pulse width 5V peak signal) in DC mode, and it's reading 2.5V AC in AC mode because the meter is measuring the voltage as an AC signal - the center of the signal becomes zero and there's 2.5V above and 2.5V below that artificial "zero." If you use your oscilloscope to measure the same PWM signal, it will show the same result - as long as you set it correctly! When measuring DC you need to DC couple the vertical channel. When measuring AC you need to AC couple the vertical channel. Both will show 2.5V. An RMS measurement (depending on your scope) will usually show RMS AC + DC - which will give you your 3.54V.sqrt[(2.5²(this is RMS AC)+2.5² (this is DC)]=3.54VRMS AC is good for measuring irregular waveforms - RMS is used to calculate the area of these irregular shapes. When we talk about DC there shouldn't need to be an RMS because DC is defined as a steady voltage. There is a third option which is a DC signal with an AC component (like pulsed DC) - and this is what is measured by meters with a TRMS AC + DC setting. On my scope this is just labeled as RMS - but there's a twist - if the scope is DC coupled you'll get the RMS AC + DC voltage (DC voltage with AC component) and if it's AC coupled you'll get RMS AC voltage only.This is pretty easy to demonstrate/view on any scope with probe compensation and it's 50% pulse width 0.5V (or whatever) pulsed DC squarewave signal even if you don't have a function generator.

author: perkabrod
author_rank: Contributor
timestamp: January 01, 2017, 01:41:33 pm
content: Happy new year!Thanks eKretz for a great writeup, amazing how many replies I've gotten, I signed up to ask this question and seems to be an amazing group of peopleYes I used a DIY scope and swapped between DC and AC coupling and noticed how in AC it looks like a 2.5 V amplitude square wave centered around 0 V.If I have a 1 volt sine wave that has a 1 volt DC offset,typey=1+sin(x)in google search to see a graph of what signal I meanWill the multimeter in DC-mode give me the DC equivalent, and in AC mode the meter would read .707 V, from the 1V/sqrt(2) equation, because the 1 V DC offset can't pass the AC ”capacitor coupling”I don't have a signal generator to try this but am interested in finding out what the meter would show in DC mode for a 1 V DC offset 1 V sine signalWould clear things up in terms of measuring techniques.

author: perkabrod
author_rank: Contributor
timestamp: January 01, 2017, 01:48:48 pm
content: Quote from: cs.dk on January 01, 2017, 12:39:27 pm(0.5*2.5^2+2.5^2)^.5 = 3.06Problem is the bold part needs to be within parentesis because we're using HALF of 2.5^2 + -2.5^2(0.5*(2.5^2 + -2.5^2))^.5 = 2.5

author: cs.dk
author_rank: Unknown
timestamp: January 01, 2017, 01:52:28 pm
content: Quote from: perkabrod on January 01, 2017, 01:41:33 pmHave a look in this thread - It's more complicated then so;https://www.eevblog.com/forum/testgear/brymen-multimeters-fault/

author: cs.dk
author_rank: Unknown
timestamp: January 01, 2017, 02:04:17 pm
content: Quote from: perkabrod on January 01, 2017, 01:48:48 pmThanks..Well, my math is not used everyday - But something seems wrong, have a look at the attached photos. (Sorry for crappy quality)EDIT: Welcome to the community btw.

author: slicendice
author_rank: Frequent Contributor
timestamp: January 01, 2017, 04:16:14 pm
content: LOL! Sorry for laughing but that is what happens when relying on calculators too much.Try typing in this:sqrt(0.5*(2.5^2+(-2.5)^2))and you get your 2.5Vif you type:sqrt(0.5*(2.5^2+ -2.5^2))you get sqrt(0.5*(2.5^2+ -(2.5)^2))which is 0Please see attached screenshotEdit: added a second calculation where you actually divide by 2 instead of multiplying by 0.5Edit2: something was wrong with the second image, uploaded again

author: perkabrod
author_rank: Contributor
timestamp: January 01, 2017, 04:41:34 pm
content: Thanks for the Brymen link, interesting info there about autoranging etc.Will update here with actual readings on a DC offset sine wave when I get time.Attached a photo from the Casio fx9860, been very happy with it, coming from a TI82.Some features I miss (or don't know how to do) but overall a very nice calculator, with BACKLIGHT and nice input/output in terms of fractions, etc.Here's a graphing speed test of the Casio vs TI82 I didhttps://youtu.be/lYE8YmZ4yoc

author: cs.dk
author_rank: Unknown
timestamp: January 01, 2017, 04:45:46 pm
content: Quote from: slicendice on January 01, 2017, 04:16:14 pmYou are absolutely correct - Just tested it. It gave me 2,5Laugh all you want to, i take it as a "lesson learned".. Its many years since i used calculus for anything serious (In school as marine engineer), and haven't touched it since.

author: HKJ
author_rank: Super Contributor
timestamp: January 01, 2017, 04:50:35 pm
content: Quote from: perkabrod on December 31, 2016, 10:47:44 amEven true rms meters uses average on DC

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 05:24:34 pm
content: Quote from: perkabrod on January 01, 2017, 01:41:33 pmYes there are a bunch of great guys here, it is a good place. Here is a link that might help you further understand:http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 06:16:40 pm
content: Oh, and for the y=1+sin(x) question, I believe the meter on RMS AC would read .707V; on DC would read 1.0V (the offset - the AC "ripple" cancels out); and on RMS AC + DC would read 1.225V.

author: perkabrod
author_rank: Contributor
timestamp: January 01, 2017, 06:26:11 pm
content: Quote from: eKretz on January 01, 2017, 06:16:40 pmInteresting. Curious, why not 1.707 V for AC+DC? Not that I have ever come across a multimeter that had a setting for AC+DC.I noticed something on the brymen bm257 but it may be applicable to other DMM, just in case anyone has wondered about why the Hz not always working. I ”discovered” I had to be in AC when entering Hz mode, at least for a pwm signal. Maybe certain signals will trigger also in DC mode when trying to read the frequency.

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 06:53:23 pm
content: Quote from: perkabrod on January 01, 2017, 06:26:11 pmDid you forget your earlier lesson already? I will answer a question with a question: why on a 50% pulse width 5VDC signal did your meter read 2.5V RMS AC and on DC read 2.5VDC but measured 3.54V RMS AC + DC? Why shouldn't it have read 5V?BTW for the fun of it and to check myself I just went ahead and set up a 2V peak to peak sinusoidal wave with +1VDC offset - DC coupled, my scope showed 1.22V RMS (AC + DC) and AC coupled measured 0.707V. My multimeter read 0.707V on AC (TRMS) and 1.0V on DC.

author: slicendice
author_rank: Frequent Contributor
timestamp: January 01, 2017, 07:57:25 pm
content: The RMS for a AC voltage (sinewave) of 1V with an offset of 1V we put in this formula:SQRT(^2 + ^2 / 2)which becomes:SQRT(1^2 + 1^2 / 2)that equals 1.2247.....If we have a voltage of 2V and an offset of 1V it would become this:SQRT(1^2 + 2^2 / 2) = 1.732...With a voltage of 3VAC and offset of 2VDC we get:SQRT(2^2 + 3^2 / 2)--> SQRT(4 + 9 / 2 )--> SQRT(4 + 4.5)--> SQRT(9.5) = 2.915...

author: rrinker
author_rank: Super Contributor
timestamp: January 01, 2017, 08:07:31 pm
content: Quote from: cs.dk on January 01, 2017, 04:45:46 pm"Knowing" -2.5^2 is +6.25 (also known as, I haven't used this calculator in ages and couldn't find the negate button), I got the right answer with my TI-83. Once I figured out the negate key though - the answer it returns if typed in as originally specified is 0, because it applies the negation AFTER the exponent. So the extra set of parentheses is necessary and typing it in as (-2.5)^2 results in the same final answer of 2.5Potential trap for young players as these sort of calculators allow you to type in equations as written and will apply correct order of operations and result in the correct answer. MOST OF THE TIME!I usually prefer Casios, but I sort of inherited the TI plus it reminds me of my old TI-57 I wish I could find.

author: perkabrod
author_rank: Contributor
timestamp: January 01, 2017, 10:22:57 pm
content: Quote from: eKretz on January 01, 2017, 06:16:40 pmOn a 50% 5VDC signal I measured 2.5V in AC and 2.5V in DC on the multimeter. I never measured 3.54V (only in ltspice simulation), though I did the math and got confused as to why in DC mode my multimeter didn't read 3.54V. You saidWhen we talk about DC there shouldn't need to be an RMS because DC is defined as a steady voltage.which makes sense.Why I was thinking 1.707 for 1+sin(x) was because if a 1 VAC sine reads 0.707 and I offset that with 1 V I thought it would just become 1+0.707 but maybe not that easyDo you know the math for AC+DC situation? For the example with 1 V offset and 1 VAC sine

author: eKretz
author_rank: Frequent Contributor
timestamp: January 01, 2017, 10:28:00 pm
content: Yes I posted it in my answer to you earlier in this thread. Your meter won't read the 3.54V unless it's RMS AC + DC. It will read 2.5V RMS AC and 2.5V DC (averaged). RMS AC+ DC would read 3.54V. The equation to figure it is RMS AC + DC = sqrt[(RMS AC)² + (DC V)²].So for the y=1+sin(x) example:sqrt [.707VAC² + 1.0VDC²] = 1.225VYour pulsed waveform example is not straight DC - it is DC with an AC component - so to correctly measure it you need to use RMS AC + DC. Your scope simulation is measuring RMS AC + DC because you had it set to DC coupling. When the scope is DC coupled it passes all signals, so you get RMS AC + DC when you measure RMS. When the scope is AC coupled it will only pass the AC component of the signal - so you get RMS AC when you measure RMS.

author: slicendice
author_rank: Frequent Contributor
timestamp: January 02, 2017, 07:38:02 am
content: All these calculations are actually integrals (calculating areas below any curve within a certain range) with a lot of variables, but if you read the text in the link, posted by eKretz, that talk about how to derive from the original formula, you can clearly see that most components cancel out. This is why the formulas become what they are.About graphing calculators...I bought a TI-85 when I was in high-school. Many of my friends had HP or Casio, except one who also had TI-85. We were the only ones who could calculate any problem that was given to us, using the calculator only. All others had issues because there was something always missing. :-) TI series calculators are really good, and they have pretty much everything, but the formulas and constants for certain things can be found under unexpected menus. But once you understand how the calculations are done, one can find everything needed to get the right answer from one single equation. :-)Love TI, and don't like the other brands that much. Not bad calculators, but for me they just don't make any sense at all. Casio and HP had a lot of features that TI did not have, but for pure Math, Chemistry and Physics problems those features were of no help to solving the problem.

author: eKretz
author_rank: Frequent Contributor
timestamp: January 02, 2017, 08:58:37 am
content: I have a TI-89 and a TI-92 - I love them -except the battery life. They eat batteries like crazy even when powered off - lots of parasitic draw. I actually installed isolation switches on mine - now the batteries last a couple years.

author: slicendice
author_rank: Frequent Contributor
timestamp: January 02, 2017, 11:30:29 am
content: Quote from: eKretz on January 02, 2017, 08:58:37 amYes, because they are powered on by a soft switch (button) they draw a bit of current all the time. Try overclocking your TI's and you will witness HUGE power drains. I did OC on my TI-85 because some calculations simply took too long to complete. The speed was incredible, but batteries ran out within a few weeks.Been long planning on buying a TI-NSpire CX CAS. But for the moment I don't need such power. Once I dig deeper into engineering I will certainly buy one.

author: R_G_B_
author_rank: Frequent Contributor
timestamp: January 04, 2017, 11:02:46 am
content: Take a look here for a detailed look at measuring true RMS power in detailhttps://youtu.be/UGfLMHTpPCY