What is the r.m.s. value of a current? 10

[davrom]

I responded to a question of this forum (cable selection based on duty cycle) where I afirmed that the r.m.s. value is similar to the thermal equivalent current. I realized this may be a stupidity (in fact, I am pretty sure).

I analyzed the problem and now I believe that the r.m.s. value of a current is the so called "effective" value of the current (for ac currents).

I.e. for an ac current i(t) = I*sin(omega*t - fi), the effective value is sqrt(2)*I, where I is the amplitude.

Can anyone explain me what the r.m.s. value is?

 

[allmend]

Just imagine an experiment:

You have a generator which can generate a voltage with different frequencies (from zero Herz , i.e. DC, to 100 Giga-Herz). You have a device, that can measure the RMS-Value of the current. You have a real resistor and you can measure the temperature on this resistor.

1) You generate DC-Voltage and measure the RMS-Value of the DC-Current and the temperature on the resistor.

2) You generate 100-GHz-Voltage and measure the RMS-Value of the DC-Current and the temperature on the resistor.

In this case you will measure the same RMS-Value of the current (you can adjust your generator), but the temperature on your resistor will be different, because there is no pure resistance in this resistor. There is also a L and C resistance. Then you have to take into account the skin effect (you cannot ignore this phenomenon!) and the electromagnetic radiation in a 100-GHz-circuit.

As you see, only in and ideal circuit with an ideal resistance is the RMS-Value of a current an equivalent of the temperature on this resistance.

 

[ScottyUK]

Hi Allmend,

I'm a power engineer posting in a power engineering forum. This sounds like microwave engineering, where the conductors are replaced with pipes, and the 'normal' electrical laws get mixed in with waveguide theory and the like.

However, the thermal losses are still determined by the RMS value of current passing through the resistance.

The capacitance and inductance of the resistor do not dissipate energy as heat, although I agree that current may be shunted through a capacitance and therefore not pass though the resistor. The shunted current will not contribute to the heat loss.

Skin effect (and proximity effect) are relevant to the thermal calculations, but as noted by [blue]electricpete[/blue] on Dec 15th are an entirely different subject to calculation of RMS, and only have practical significance to conductors which are 'large', although large is a somewhat loose term as it is frequency-dependent. Skin effect does not magically add L and C to the 'pure' resistance, it just makes the effective resistance, still pure, higher than its DC value. The effective resistance still dissipates energy as heat; the heat loss may be calculated as (RMS current)^2 x (effective R). The only change is that the effective resistance is substituted for the DC resistance normally used in the calulation.

 

[allmend]

„However, the thermal losses are still determined by the RMS value of current passing through the resistance.“


Hi ScottyUK,

RMS means Root-Mean-Square, that indicates that we are talking about a mathematical model.

Can you understand the difference between a mathematical model and a real circuit?


RMS-model works with a DC-Current or with a Sine-Current, but only approximately.

If there is a “distorted” current, you have to represent this current as a mix of different sine curves with different frequencies (Fourrier Analysis).

You can calculate the RMS-Value of a sine current as:

I rms = squ(sum( In mom ^2)/n); n- number of the instant-currents

As you see, you have to split your real current curve into n instant-currents to find out your “root mean square”, which means that you can only find out an approximate value of the real current curve, because you are operating with a limited number .

If your current is “ugly”, you have to do your calculation with a limited number of sine curves and then find the total RMS of the sine-mix.

I rms-total = squ(sum Im rms ^2 ); m – the number of sines

As you can see, there is a big fault in this model. You cannot take into account the phase-displacement of different frequencies.

In circuits with “ugly current” you have to distinguish between DPF (displacement power factor) and TPF (true power factor).

The term “effective current” refers to a low-frequency-sine-current that causes the same thermal “effect” in a resistor as a DC-Current. You just measure the temperature in this resistor and if the temperatures are equal, you can say that the “effective” values of these currents are equal.

As you see, the “Effective Value” (heating effect in a resistor) and the “RMS-Value” of a current are different things. "Effective value" can be measured with a thermometer, the "RMS-Value" can be calculated, but only approximately, not taking into account many important things.

Have you got my drift, ScottyUK?

 

[jghrist]

Allmend,

You don't have to do a Fourier analysis to determine the rms value of the current. If you can define the current as any function of time, you can do the integration on that function. If you can't define the current as a function, but can measure it with a digital meter and capture the sample values, you can square each sample, sum the squares, take the square root, and divide by the number of samples. You could even develop a digital meter that does this automatically and market it as a "true rms" DMM. Your accuracy would be limited by the sample rate.

I guess you could measure the "effective value" with a thermometer by measuring the temperature rise of a "real resistor" with the test current passing through it, then run dc current through it and adjust the current until the temperature rise was the same for the same period of time. You could call the resultant dc current level the "effective value" of the test current. This would make current measurements a little more time consuming than using a "true rms" DMM.

The normal way to account for the frequency effects is to adjust the resistance to get an "effective resistance" instead of using dc resistance and developing an "effective value" of current. But hey, if you want to market your method of current measurement, go ahead. I'll try to get a patent on my "true rms" DMM and we can compete in the marketplace. Hope I'm not too late.

 

[allmend]

„You could even develop a digital meter that does this automatically and market it as a "true rms" DMM. Your accuracy would be limited by the sample rate.“

Precisely that is the problem! There are no true rms current meters!

The first digital rms-meters just measured the amplitude of the current and multiplied it with the factor 1/1,4142... (1/squ(2)). The manufacturers assumed that the current is a pure sine. The old-fashioned electromagnetic meters were more accurate than the firs digital meters.

Most modern digital meters make use of numerical sampling and Fourier Analysis.

 

[Laplacian]

allmend-

As ScottyUK said, this is a power engineering topic at the 50-60Hz level. The exception you mentioned in your post:

"The term “effective current” refers to a low-frequency-sine-current that causes the same thermal “effect” in a resistor as a DC-Current. You just measure the temperature in this resistor and if the temperatures are equal, you can say that the “effective” values of these currents are equal. "

We are strictly dealing with low frequency current. There may or may not be significant harmonics in our 50-60Hz sinusoids and their effects will be negligable to a resistive heating element.

*Military uses 400Hz power systems to save on weight, but that is an exception to this "civilian" discussion about a simplistic concept under general terms.

 

[ScottyUK]

Hi Allmend,

Are you a physicist?

This world must really irritate you! Our instrument manufacturers can't make instruments with infinite bandwidth, our mechanical colleagues can't make anything flat (always some pesky atom sticking up), the electronics guys among us have not yet managed to get rid of thermal noise...

The mathematical definition of RMS, and any calculations based upon it, certainly appear inviolable. I spent a long time on Google looking for any evidence to the contrary, and couldn't find anything. The problem you perceive is that we, in our imperfect world, cannot measure what can be modelled by equations so well.

You are indeed correct that none of the sampling meters can measure from DC to infinite frequency, which is theoretically what is needed for a true rms instrument. But for most real-world measurements the minute error introduced by a bandwidth of a few hundred kHz on a high-end bench meter, or the 50MHz bandwidth of the excellent Tektronix current probe connected to a 'scope with a math function, is of no practical significance. The typical engineer has to work with primary transducers which are at best 0.1% accurate. The inaccuracy caused by the bandwidth limitation is likely to be at least one order of magnitude below this except in specific applications, for example where measurements may have to be made on the broad-spectrum pollution caused by an arc furnace. In these specific applications, instrument (and transducer)bandwidth is undoubtably important. Knowing when it is important, and when it isn't, is part of an engineer's job.

For applications such as the microwave engineering example you chose, the plumbers have probably found methods which meet their requirements, although I don't pretend to have anything but the most basic understanding of microwave engineering. I have noticed that most of their phenomenally expensive instruments often don't start measuring until a couple of GHz. That's a hell of a lot of spectrum to ignore, especially on an instrument with a six-digit pricetag. If it made a difference in their application, wouldn't they include it?

 

[buzzp]

Hehe.
This is good. In the context, the rms value is equal to the effective value.
Yes you can find the RMS value of any waveform by squaring the sample summing it with the other squared samples, take the average and then square root this. The whole idea of doing it this way (rather than the averaging method) is to get the real rms value, which includes other "frequencies" of the fundamental. Ultimately, there is only one waveform to measure. It does not break itself down. So if you sample a waveform over some specific time period and do the math above, you will get the rms value (harmonics and all).
No true rms meters? Yes there is and there are also averaging rms meters (as the salesman like to call them). See

http://www.fluke.com/products/specifications.asp?SID=5&AGID=3&PID=30405

 

[allmend]

Hi ScottyUK,

Hi Laplacian,

I’m German and I work in a Public Utility and my job is power quality maintenance.

In Germany they do not use the term RMS, they still say “effective value” (Effektivwert).

You cannot neglect the harmonics in a public utility net. If the THD of your voltage is less than 8% and U5 less than 6%, you do not have to take any measures.

There are no limitations to the harmonics level in the current (according to DIN EN 50160). The current you measure in a public net has nothing to do with a sine wave, it is always very “ugly”.

A public utility sells to their customers 50-Hz-Power, but the induction meter (Ferraris) measures the RMS of the total active power. Customers can sue the utility, because they didn’t agree to pay for harmonics.

An electronic power meter can measure the fundamental frequency of 50 Hz, but the customer may profit from harmonics if he uses the power for heating.

The utilities have big problems with the correct measurements of the electric power.

Besides, you have to derate the power of your transformers, because they can get overheated through the harmonics. You have to increase the diameter of your PEN. You have very high 150-Hz-Currents in the PEN, even if you have a balanced burden. The 150-Hz-Current in the PEN is a sum of the 150-H-Curents in your three phases.

Laplacian, how can you say that “their effects will be negligable to a resistive heating element“.

 

[ScottyUK]

Hi Allmend,

I'm going to let someone else post some comments, but I just wanted to compliment you on your technical English. I'm very impressed. I can barely ask for a large beer politely in German!

 

[allmend]

„I can barely ask for a large beer politely in German!“

Thanks, Schotty. My English is far from perfect, but I try my best.

PS:

You do not have to speak German when you ask for a bear in Germany. Every German speaks basic English.

;-)

 

[jghrist]

Allmend,

You were doing great until you mispelled beer!

I have found that even if you don't find someone who speaks English in Europe, a variation of the words "beer" or "bier" will get you a very good brew just about anywhere.

 

[allmend]

Hi jghrist,

I noticed right away that I misspelled “Scotty” and “beer”, but you cannot edit your postings in this forum, can you?

Ich wollte keinen Baeren aufbinden!

P.S.

In Spain you have to say: Una cerveza, por favor

 

[Skogsgurra]

I think that this discussion eventually has found a matter worth discussing. Namely the beverage that you get when you mix water, malt, yeast and hops and let Nature do its thing. I also think that allmend was right in his first posting in saying "a large beer". He did not say "ein grosses Bier". So "beer" was right.

There is a possibility, however, that he was trying to say "a lager beer" and in that case, he misspelled "lager" when he wrote "large". Is not that an important aspect in this discussion?

I mean, if we are discussing the difference between RMS and effective value, we could as well discuss the spelling of "beer" and "large".

Those who think that secondary effects are proof that RMS and effective value and DC are different should rethink. All these terms are definitions and, as such, equivalent. Any difference that you might think that you notice is the result of inadequate instrumentation and/or badly designed experiments. Or pure lack of understanding.

But we can agree - I hope - that there is nothing like a large beer.

 

[RalphChristie]

Prost!!

RCC

 

[allmend]

skogsgurra,

English spelling and beer are really very interesting matters to discuss, but I guess that you are referring to the posting of Scotty, when you talk about a “large beer”. I just typed “bear” instead of “beer”. I couldn’t correct my spelling, because I cannot find in this forum the “edit” button.

P.S. English spelling is really very tricky. You can even misspell the word “mis(s)pell”.

;-)

 

[jbartos]

Suggestion: Major misconception appears to be in what is plotted and indicated on the ordinate axis. It makes a big difference, if there is Irms or Iav or Idc. This however needs a background from mathematics.
The areas for RMS are different from areas for Average values.
Therefore, there is the relationships between Iav=0.634 Imax
and Irms=0.707 Imax. This has not been properly addressed by most postings above.

 

[allmend]

„Therefore, there is the relationships between Iav=0.634 Imax
and Irms=0.707 Imax. This has not been properly addressed by most postings above.“

jbartos,

We are not talking about sine waves, we are talking about „ugly current“.

 

[ScottyUK]

jB,

You have filled one thread with ill-founded nonsense based on your misunderstanding of RMS and average. Please desist from filling this one too.

 

[electricpete]

I agree with Scotty.

jbartos - Iav which you have described as average absolute value has no relevance to heating.