How can I test if a DMM is reading in true RMS ? - Page 1
Forum section: electronics / general

author: opablo
author_rank: Regular Contributor
timestamp: November 23, 2012, 06:35:06 pm
content: I'm about to buy a ridiculously cheap DMM with true RMS (Uni-T UT61D)It is so cheap that I'm skeptical and want to test if it is really measuring in true rms.How can a create the most simple test without a function generator ?Maybe creating an AC square wave with a 9+9 transformer and checking if the rms meter in ac mode matches the peak voltage and verifying that my other meter has a lower value ?Please don't tell me that it's stupid to buy a measuring device that you don't trust... I know that.I'm on a tight budget.

author: opablo
author_rank: Regular Contributor
timestamp: November 23, 2012, 06:39:21 pm
content: Is there a more simple test like measuring the mains having a diode in series with one of the probes to break the sine wave ? Would that have different reading between an rms vs. non-rms meter ? what should that reading be ?

author: IanB
author_rank: Super Contributor
timestamp: November 23, 2012, 06:45:11 pm
content: Quote from: opablo on November 23, 2012, 06:39:21 pmI think that should work. Wire up a circuit with a bulb to provide a load and measure the voltage across the bulb terminals. Let's say that is 120 V. Now insert a diode in series with the bulb and measure across the bulb terminals again. A true RMS meter should read 84 V more less (which is 120 / sqrt(2) ).To eliminate the effect of the diode drop you could put two diodes back to back in the first circuit and just remove one of the diodes for the second.Obviously this is safer with a low voltage AC supply. Use a transformer and a small bulb for the load. Make sure the diode reverse voltage is rated for at least twice the AC voltage.

author: T4P
author_rank: Super Contributor
timestamp: November 23, 2012, 06:57:47 pm
content: Signal gen in square wave, that should defeat most non-trueRMS meters since they are all sine-calibrated but hey the UT61D uses a AD737J, no worries about not reading TrueRMS because that's a step higher than commonly found industrial standard AD637J TrueRMS convertersIf you are thinking about the UT61D just for the trueRMS, okay. But if you are using it as a all-purposeThe continuity is slow, autoranging is slow but if you need the backlight very badly by all meanscompared to the UT61E which pretty much has the same TrueRMS circuits.

author: opablo
author_rank: Regular Contributor
timestamp: November 23, 2012, 08:04:22 pm
content: Thanks T4P... That information about it's chipset gave me a lot more confidence about it.My other meter is a Mastech MS8229. Not fast refresh rate, fast but not latched continuity test, no analog bar, no rms.The cheap rms meter that I -would- love to buy is the BK 2709BBut I live in Argentina and the only way for me to buy a DMM that matches my budget is through sites like dealextreme, dinodirect, tinydeals, aliexpress, etc. And you have to pick out of whatever happens to be available there.I'm thinking in trying to mod/hack my MS8229 to add latching to it's high responsive continuity tester.

author: iloveelectronics
author_rank: Frequent Contributor
timestamp: November 24, 2012, 04:01:25 am
content: Quote from: opablo on November 23, 2012, 08:04:22 pmTry the Mastech MS8250C, it has an eqivalent chipset as the BK 2709B, and is available at DealExtreme at almost half the price of the BK. It even has a dual display. Main downside is that the Mastech defaults to AC measurements. But thanks to the dual display you would quickly recognize that you are in AC modes as you would see Hz in the secondary display.

author: Lightages
author_rank: Unknown
timestamp: November 24, 2012, 05:09:39 am
content: I can assure you that the UT61D/E will do True RMS properly. They do not like DC offsets of more than around 7.5V however so be aware of that. If you insist on buying a UT61E please read everything available here on the forums about this meter. Yes it is good value for the money but it has its problems. I have one and I still like it but it has many little problems.If you can at all find a way to buy one and you feel it worth the extra money to you then have a look at the Amprobe AM-270. At $90 US it is one of the best deals available in a multimeter. You can get one from ebay from testequipmentdepot and yes they ship worldwide.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 24, 2012, 07:48:08 am
content: They do not like DC offset at all!I've just run a test with oscilloscope and function generator on 61E and 71D on AC+DC.With a 100Hz 5Vpp sine wave or square wave at 50%, the 61E only measures TRMS accurately if there is no DC offset.This is quite normal, since the meter doesn't have the AC+DC feature.If you have tested the 61E yourself, I'd like to hear what your settings were.

author: T4P
author_rank: Super Contributor
timestamp: November 24, 2012, 08:06:01 am
content: The manual didn't explicitly say "NO DC" but they did say "Input Amplitude: (DC electric level is zero)" under voltage measurementwhich doesn't really make sense under the Hz% area for voltage

author: Lightages
author_rank: Unknown
timestamp: November 24, 2012, 12:25:56 pm
content: I did a rough test with my function generator and guestimated where the reading went way off the rail. Yes, any offset starts inducing errors but I was allowing a bit of error before it went way off.

author: tom66
author_rank: Super Contributor
timestamp: November 24, 2012, 01:37:33 pm
content: Why don't they use an ac-coupling cap inside the meter?

author: Lightages
author_rank: Unknown
timestamp: November 24, 2012, 01:47:32 pm
content: Actually, I redid my test using a oscilloscope and I made an error. It was my function generator clipping with the levels I was using. Within the limits of my measurements, my UT61E has no problems with DC offsets.Anyway back to how to test True RMS on a meter. Feed it any logic level square wave of a low frequency, say 100Hz, and the meter should read 1/2 the logic level. It is that easy.

author: Lightages
author_rank: Unknown
timestamp: November 24, 2012, 02:52:27 pm
content: Quote from: tom66 on November 24, 2012, 01:37:33 pmTo get a 6Hz cutoff high pass you need a capacitor of around 2.7 nanofarad and it needs to be very high working voltage, around 3kv? Easily done but it would need to be switched in and out of the circuit. If they had a dedicated position on the selection switch for AC then it would be easy. But because they have a soft switch to AC, it would need a relay.

author: IanB
author_rank: Super Contributor
timestamp: November 24, 2012, 05:23:50 pm
content: Quote from: Lightages on November 24, 2012, 01:47:32 pmIs that right? If you have a positive going square wave with a 50% duty cycle the voltage will be on for half the time, which means it will deliver half the power of a continuous voltage. That means the true RMS voltage should equal the logic level divided by the square root of two.

author: Lightages
author_rank: Unknown
timestamp: November 24, 2012, 05:40:41 pm
content: You are correct if the meter is a True RMS +DC reading meter. If the meter is an AC only reading meter then it effectively shifts the waveform to a bipolar waveform, rectifies it, then measures the resulting "dc" level. I know this is a simplified explanation but it demonstrates the idea.Think of it this way, the meter could be considered as AC coupled.

author: lewis
author_rank: Frequent Contributor
timestamp: November 24, 2012, 07:54:57 pm
content: Quote from: IanB on November 24, 2012, 05:23:50 pmYou're right, RMS voltage of a logic level square wave is Vpk x sqrt(d) where Vpk = logic voltage, d = duty cycle. This holds as long as the square wave does not go negative (ie only between logic high and ground).If the square wave has no DC offset (ie goes above ground then below by the same amount) the RMS value is equal to peak voltage regardless of duty cycle.(Someone can probably tell me what the RMS of a square wave is with an arbitrary DC offset, I don't know off the top of me noggin.)

author: Unknown
author_rank: Unknown
timestamp: November 24, 2012, 11:22:42 pm
content: VAC+DC= sqrt(VAC2+ VDC2) (all RMS voltages, though DC RMS voltage is obviously just the DC voltage). In the case of a 0 to 5 V square wave, this is a square wave with 2.5 V amplitude (2.5 V RMS) plus a 2.5 V DC offset, or sqrt(2.52+ 2.52) V = sqrt(2) * 2.5 V.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 25, 2012, 08:54:48 pm
content: Quote from: opablo on November 23, 2012, 06:35:06 pmBe aware that although the 61E measures true RMS, it is defeated ifanyDC offset is introduced, like most TRMS meters are.If you want to measure true RMS for a waveform with a DC offset, then you need a meter with an AC+DC option, like most bench meters have.Crest factor is also to be considered, with most middle of the road meters giving accurate readings up to a factor of 3.Accuracy gets worse as the signal frequency increases.http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/http://en.wikipedia.org/wiki/Crest_factor

author: Lightages
author_rank: Unknown
timestamp: November 25, 2012, 09:56:51 pm
content: As I have pointed out, my UT61E has no problem with a DC offset up to the limits of my signal generator. When feeding mine a 1V RMS sine wave it stays within 2% up to the 10V offset limit of my function generator, and within 3 or 4% correct with square and triangle waves. I was actually surprised that mine has no real problems after all the reports.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 25, 2012, 09:58:31 pm
content: You're not measuring it right.

author: opablo
author_rank: Regular Contributor
timestamp: November 27, 2012, 07:42:21 pm
content: Wytnucls: I had to do some reading and some googling to fully understand your explanation but now I have a much better understanding of all this.Thanks for taking the time to reply.This means that it's not a good idea to use a 0->5v square logical signal to test it.And it's also not a good idea to use half of the waves of the main using a diode to break the sine wave.I have to really have a non-sine AC signal with a balanced positive and negative stage......... so... what could be the easiest way to create it -without a func gen- ?...what about having the 5v AC sine wave of a transformer passing though 4 diodes connected in parallel with another 4 in the opposite way like this:Code:---+---|>|----|>|----|>|----|>|----+----\--|<|----|<|----|<|----|<|---/thus erasing big/long parts of the wave in which the voltage is low maintaining the balance of the parts untouched.is that a good idea to create a clean non-sine AC wave with no DC offset ?

author: Lightages
author_rank: Unknown
timestamp: November 27, 2012, 09:51:11 pm
content: Quote from: Wytnucls on November 25, 2012, 09:58:31 pmPlease elaborate on how it should be measured.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 27, 2012, 10:13:19 pm
content: I'm glad you asked:Fire up your oscilloscope and make sure the channel trace isDC coupled. Install a BNC T-junction on your function generator and connect both your oscilloscope and the meter under test. The meter should be set on the ACV range.Feed a 5Vpp sine wave at 100Hz to both of them, with 0 DC offset.Note that TRMS is showing correctly on both oscilloscope and meter, namely 1.77VDC.Now, increase the DC offset to 1V. The 61E will show something like 1.7016V, while the oscilloscope will display TRMS at about 2VDC.With 2V DC offset, the 61E shows 1.706V instead of TRMS 2.63V. With 3V offset, it displays 1.705V instead of 3.46V TRMS, and so on.If your oscilloscope doesn't show TRMS, work it out with the formula for a sine wave with a DC offset.If you can, get your 71E out of the cobwebs and it will show the correct TRMS with any offset in the AC+DC mode.This holds true, for any function, as long as the crest factor is kept below 3.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 28, 2012, 12:47:43 am
content: Quote from: opablo on November 27, 2012, 07:42:21 pmWell, as TP4 was saying earlier, the easiest way would be to feed the meter any waveform that is not a sine wave, since the non-TRMS meter is calibrated to give you a voltage based on the sine wave TRMS formula.However, you need to be able to work out the real TRMS of that waveform for comparison, so a square wave or triangular wave would be the easiest.http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/I'm not sure how you would do that with diodes only, but it may be possible.

author: Lightages
author_rank: Unknown
timestamp: November 28, 2012, 03:23:08 am
content: My apologies for confusing people, I was wrong.This is not the first time I have confused myself with this issue.Of course it is not a True RMS reading unless it does account for the DC offset, which the UT61X series does not.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 28, 2012, 05:01:14 am
content: Glad you finally got it. Don't worry, it confuses a lot of people, even professionals.I'm surprised Dave hasn't done a tutorial over this subject, it is so fundamental.Maybe there is too much math involved.

author: Lightages
author_rank: Unknown
timestamp: November 28, 2012, 12:03:36 pm
content: What adds to the confusion is that some multimeters have the option for AC TRMS and AC+DC TRMS.

author: SeanB
author_rank: Super Contributor
timestamp: November 28, 2012, 04:23:46 pm
content: True RMS should not care about DC as long as the peak is within the dynamic range of the converter input. It should give the correct result if you put in pure DC, or with an input of half Dc and AC on top of it. I have some TRMS converter chips around, old AD devices. Need +-15V rails, but do not care as long as the input is in range, crest factor of up to 13 AFAIKR on a 2V pp signal.

author: ejeffrey
author_rank: Super Contributor
timestamp: November 28, 2012, 05:37:00 pm
content: Quote from: SeanB on November 28, 2012, 04:23:46 pmAlmost all hand-held multimeters only use the RMS-DC converter in AC coupled mode. A few offer both AC coupled and AC+DC true RMS. Wytnucls claims that the former is incorrect and means 'it provides incorrect readings in the presence of a DC offset.' I think that is a bit pedantic, but as always it is true that you have to understand what your meter is measuring. It is a true RMS reading with a bandwidth from ~1 Hz up to the BW limit of the meter. That is a perfectly reasonable thing to measure, but it is *not* the heating power of the signal if applied to a resistor, which is a common description of RMS vs averaging.

author: Wytnucls
author_rank: Super Contributor
timestamp: November 29, 2012, 11:01:20 am
content: Quote from: SeanB on November 28, 2012, 04:23:46 pmYou are wrong.Most TRMS converters have the option to take the DC offset into account. The 61E converter has it, but Uni-T elected not to implement it on this particular meter. I'm not sure what converter Fluke uses on the 87V, but the meter also only measures TRMS accurately if there is no DC offset.Few meters have the AC+DC option, which is paradoxically quite common on bench meters.All meters measure TRMS correctly for asine wavewith no DC offset.Meters with the AC+DC option are the only ones giving a correct value for TRMS, if there is the smallest DC offset on the sine wave.All meters measure TRMS correctly for a 50%square wavewith no DC offset, except meters lacking a TRMS converter.Meters with the AC+DC option are the only ones giving a correct value for TRMS, if there is the smallest DC offset on the square wave.With pure DC, with meters set on the AC range, only the meter with AC+DC measures TRMS accurately.

author: Unknown
author_rank: Unknown
timestamp: November 29, 2012, 06:52:03 pm
content: I think you're being pedantic here. RMS voltage is the root mean square of the instantaneous voltage. The RMS of the voltage is the RMS of the whole signal, and the RMS AC voltage is the RMS of the AC (with some lower and upper frequency). It's trivial to add up RMS AC and DC with the formula I gave earlier, AC+DC is just a convenience function, assuming the DC function has a decent NMRR. Some meters even give you the formula in the manual. Are you also going to complain that measuring a 10 MHz RF signal does not indicate the thermal heating power?

author: Wytnucls
author_rank: Super Contributor
timestamp: November 29, 2012, 11:55:56 pm
content: Call me whatever you want, but the problem remains:Your fancy TRMS meter only gives you accurate TRMS readings if the signal being measured has no DC offset, unless it has the AC+DC feature.Anything can be calculated with a formula, TRMS included, but it is not as trivial as you make it out, depending on the shape of the wave. Quite often, you won't even know if the AC voltage or AC current being measured has a DC offset, until you look at it with an oscilloscope.Most people are not aware of the limitations of their TRMS meters, as this thread proves and they seldom have a calculator taped to the back of their Fluke meter for DC offset TRMS calculations.To compound the problem, in the case of the 61E, TRMS measurements for a strictly AC square wave are wrong too!It is only accurate for a duty cycle of 50%. The errors are not trivial either: up to 25% less than TRMS with a 20% or 80% duty cycle (tested at 100Hz 5Vpp). The 71D gives the same wrong readings when in AC mode only, but measures correctly in AC+DC mode.

author: IanB
author_rank: Super Contributor
timestamp: November 30, 2012, 02:53:41 am
content: I don't think it's being pedantic at all. RMS is RMS. There is no "sort of RMS" or "partly RMS". If the meter doesn't measure true RMS correctly, including any DC offset, then it is not a true RMS meter. There is no point calling something what it isn't. Maybe several "true RMS" meters are actually "false RMS" meters, but if so that fact should be publicized. Let's reserve true RMS for those meters that measure the signal many times per second, square it, sum the measurements over an interval, and display the square root of the mean.

author: Unknown
author_rank: Unknown
timestamp: November 30, 2012, 09:38:09 pm
content: RMS(x) is sqrt(mean(x^2)). RMS does not define what this x is: this may be voltage, current, temperature, velocity, only the z component of the velocity or only the 1 Hz - 10 kHz part of the voltage signal. RMS(VAC) is a real RMS value, nothing sort of RMS about it.Just tried an experiment with a function gen, a true RMS DMM without AC+DC feature, and a DMM with. Function gen is set to 1 kHz sine with 200 mV RMS amplitude, 100 mV DC offset. In DC mode, the DMM without AC+DC reads 99.7 mV in DC mode and 200.4 mV in AC mode, or 223.8 mV AC + DC according to the equation I gave. The AC+DC meter reads 0.22375 mV. Could you give an example of a signal where this procedure would fail? It would require two measurements and some arithmetic, that's the only issue.A change in duty cycle from 50% adds a DC offset, it's not a strictly AC signal. Does it show an increase in DC voltage if you increase the duty cycle?

author: Wytnucls
author_rank: Super Contributor
timestamp: December 01, 2012, 12:50:23 am
content: "Let's reserve true RMS for those meters that measure the signal many times per second, square it, sum the measurements over an interval, and display the square root of the mean." IanBI agree with Ian, as this is what the AC+DC meter does, giving you an instant true RMS value on the screen and coping with a small variation in DC offset easily.A change in duty cycle is not a change of DC offset, by the way. The voltage hasn't changed at all.There is a bodge solution, like you describe, but it requires pen and paper and a calculator, exposing the user to mistakes. It is so much easier to use a proper AC+DC meter, since they are available.That is also assuming that the meter AC readings are correct in the presence of a DC offset, which there are not in the case of the 61E, introducing an extra 1% error. This could be insignificant for most applications, but an error nonetheless.So, pedantic or not, iftrueRMS is important to you, buy a meter capable of AC+DC calculations.

author: Unknown
author_rank: Unknown
timestamp: December 01, 2012, 11:22:00 am
content: Quote from: Wytnucls on December 01, 2012, 12:50:23 amThe meters I'm talking about do that, the inputs are just AC coupled, as you would expect in VAC mode. I would be very annoyed if they would respond to DC voltages in VAC mode, this would make them useless for tasks like measuring power supply ripple.Quote from: Wytnucls on December 01, 2012, 12:50:23 amAn AC+DC mode is convenient, I agree that it is annoying to get out your calculator and measure two values, especially for fluctuating signals. AC coupled RMS measurements are not wrong or misleading, however, as you seem to imply. If you're asking for VAC, then it should not take DC voltage into account.Quote from: Wytnucls on December 01, 2012, 12:50:23 amAn AC signal has a mean of zero. What happens to the mean voltage as you change the duty cycle?Quote from: Wytnucls on December 01, 2012, 12:50:23 amThis sounds like a flaw.

author: T4P
author_rank: Super Contributor
timestamp: December 01, 2012, 12:31:58 pm
content: Yes exactly, you expect RMS AC readings when you switch to VAC and not both ... that's proper RMS! You selected VAC so you should get VAC not the other way round! Pfft.

author: Wytnucls
author_rank: Super Contributor
timestamp: December 01, 2012, 02:18:08 pm
content: The AC+DC option is just that, an option. The meters I talk about can give true RMS for AC only, if required, although I hear some Fluke meters are stuck on AC+DC for mV.I never implied that AC coupled measurements are not useful. I just said that working out true RMS for a signal with a DC offset without an AC+DC multimeter or an oscilloscope that doesn't have DC coupling, is a chore.An AC signal has a mean of zero for a sine wave, otherwise it can be any voltage that reverses over time. My function generator certainly doesn't think that the DC offset changes with duty cycle on a square wave. My oscilloscope on the other hand, when AC coupled, moves the base to keep the surface areas in balance (energy?), when the duty cycle changes, so it looks like you are right when it comes to the definition of RMS(AC).Here is a Fluke write-up on the subject:http://www.fluke.com/fluke/usen/community/fluke-news-plus/ArticleCategories/DMMs/True-rms+Facts.htm

author: BravoV
author_rank: Super Contributor
timestamp: December 01, 2012, 02:51:40 pm
content: Quote from: Wytnucls on December 01, 2012, 02:18:08 pmThank you, a really nice reference !

author: The Electrician
author_rank: Frequent Contributor
timestamp: December 02, 2012, 12:22:23 am
content: Quote from: IanB on November 30, 2012, 02:53:41 amThe terms one finds used to describe the capabilities of available meters are "True RMS" and "True RMS AC+DC". Perhaps "True RMS" should be "True RMS AC only", but in the year 2012 it's clear by inference that when they say "True RMS", they really mean "True RMS AC only".There is a point in describing a meter as "True RMS" even if it's not able to include the DC component of a waveform in its measurement when on the AC range of the meter. This because it's possible to get the "True RMS AC+DC" value of a waveform from such a meter by measuring the DC component with a separate measurement and doing the VAC+DC= sqrt(VAC2+ VDC2) computation.If the meter is a "True RMS AC only" (called "True RMS" by manufacturers), this two part measurement is capable of giving the "True RMS AC+DC" value of the waveform. If the meter isn't even "True RMS" (meaning that it's an average responding meter), that measurement won't be possible at all. That's why there's a point in describing a meter as "True RMS"; we need only understand that it's a marketing gimmick.Now, it would be my preference that the very designation RMS should mean a value for a waveform that includes the total waveform in the measurement/computation, AC and DC components both. But, in fact, because of marketing practices, some meters are only capable of measuring the RMS value of the AC part of a waveform when on the AC range. Such a meter can still measure the "True RMS AC+DC" value of a waveform with two measurements, which an average responding meter can't do. The buyer should understand what the manufacturers mean when they describe a meter as "True RMS" or TRMS, without the "AC+DC" addendum.A good example of where it is absolutely necessary to be able to measure an RMS value which includes the DC component of the waveform is determining copper losses in a full wave capacitor input filter power supply, where the transformer secondary is center tapped (a two diode configuration). The current in each half of the center tapped winding has a substantial DC component because there is a single diode in series with the half winding; the current in that half winding is therefore unidirectional. With a "True RMS AC only" (called "True RMS" by manufacturers) you could make the measurement; with an average responding meter, you couldn't.Quote from: opablo on November 27, 2012, 07:42:21 pmSuch a waveform will work just fine; simply put a 1 uF film capacitor in series with it to eliminate the DC component of the waveform.The answer to your original question is that probably the simplest way to determine if a meter is truly responding to the RMS value of the AC part of a waveform is to use a square wave without a DC component. If you have a bipolar square wave, with a positive excursion of 1 volt and a negative excursion of -1 volt, the RMS value of that waveform is 1 volt RMS, regardless of the duty factor. An average responding meter will calculate the average value of the absolute value of that waveform (the full wave rectified version) and multiply by the number 1.1107, which would give the correct RMS value of an undistorted sine wave. That same average responding meter would give a value of 1.111 volts for the square wave I described.If you use a logic square wave with a maximum positive value of V volts (5 volts maybe), minimum value of zero volts, and remove the DC component with a capacitor, you will have a DC free square wave with a peak value of V/2 volts (2.5 volts maybe). A "True RMS AC only" meter will read that waveform as 2.5 volts; an average responding meter will read 2.5*1.111 = 2.777 volts.You could even use the CAL output from a scope. Put a big film cap in series with it and measure with your meter. If the P-P voltage of the calibrator output (as measured by the scope) is V volts, then a "True RMS AC only" meter will read V/2 volts, but an average responding meter will read V/2*1.111 volts.NOTE WELL. This assumes that the duty factor of the calibrator out is a 50% duty factor square wave. If it's not, use the following to compensate. (When you remove the DC component of a square wave, the positive and negative excursions change with changes in duty factor.)Assume we have a square wave with a positive excursion of 1 volt and a negative excursion of -1 volt, with adjustable duty factor. If the DC component is removed with a capacitor, and the RMS value of the DC free waveform and the average of its absolute value (what a non RMS meter would measure) are calculated, we would get table shown in the first image. The first column is the duty factor in percent. The second column is the RMS value and the third column is the average of the absolute value. If you have a square wave with peak values other than 1 volt, use numbers in the table as compensating factors.The second image shows the same information in graphical format with the duty factor along the horizontal axis. The red curve is for the RMS value and the blue curve is for the averaged absolute value.