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2021-04-12, 08:01:18
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Author Topic: Power Measurement - Misconceptions  (Read 10550 times)

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It's not as complicated as it may seem...
Let's look at this post by Lawrence Tseung:

When to use rms value for comparison?

There appears to be some misunderstanding of rms value and exactly when to use it.

The answer is as follows:
1.   The term rms stands for root mean square.  For a true sine wave, there will be values on the positive side and the same values will appear on the negative side.  If we take the mean or average value, the result is zero.
2.   Since we cannot compare two zero sine waves with the mean value, the industry devised the concept of root mean square.  Essentially, the value is taken (either positive or negative) and then the value is multiplied by itself or squared.
3.   For a positive number (e.g. 5), the squared value is 25 positive.  For a negative number (e.g. -5), the squared value is also 25 positive.  Thus, only the actual numeric value is effectively used.
4.   In sampling a waveform, there may be many (e.g. 100) sampling points.  There will be 100 squared numbers.  The mean of these 100 squared numbers is taken.  Then the square root function is applied.
5.   Thus different sine waves can be compared with the rms value.

Once we understand the basic method, we know that we should apply this technique in the case when the voltage or current has positive and negative components.  In fact, even if we are not sure, we can use the rms value for comparison purposes.  We cannot go wrong in all cases!

Thus when the PhysicsProf and his experienced University colleague displayed their screen shots, they chose to display the rms Power value.  That is the CORRECT and scientifically acceptable display.

Hope this explanation helps all.  Science is reason and understanding.  Science is not dogma or the belief or experience of an individual or a group of individuals no matter their position or background.


The concept of RMS is a somewhat confusing topic among both amateurs and professionals. In short, RMS is an equivalent DC value. The following will hopefully clearly illustrate why the last 3 paragraphs in the above quote should be reconsidered.

Using a very basic example of a 60Hz sine wave, let's look at two different methods of measuring the REAL power in the simple circuit shown in the pictures. Utilized are separate voltage and current sources so that the phase relationship between them can be readily changed. The two wave forms are initially in perfect phase, and are multiplied together to produce an instantaneous power trace, just as would happen with our scope measurement. This exercise could readily be done to equal validity on the bench with real circuitry and test equipment, but it is much easier and more precise to accomplish with a circuit simulation.



The following first example uses two DMMs (not shown) with a simple circuit such as the top one shown in the schematic rms_ave_01.gif. The current would be measured with a DMM in series with the circuit. With R1 as a pure resistance, and no reactive components present, the phase relationship between the voltage and current is "zero", therefore the DMM method is valid in this case.

Given: (60Hz sine wave, continuous, non-reactive circuit) ("p" is "peak") (RMS values as measured with a standard or RMS-capable DMM)
1) Voltage: 10Vp = 7.07VRMS
2) Current: 200mAp = 141.4mARMS
3) Power: VRMS x IRMS = 1W = REAL power in R1.

So, we have taken the RMS of the voltage and current, and their product gives us the REAL power dissipated in R1. Note that we have not performed any computation on the resulting power value, it was derived only from the voltage and current. With a purely resistive circuit where no phase shift occurs, two DMM's can be used to accurately measure the V and I values.



Let's now compare this measurement with one made using the oscilloscope method, where we sample the voltage and current wave forms of each generator (V1 and I1) at a sufficiently high rate.

1) Voltage: The scope is set to indicate the RMS value of the displayed wave form voltage measurement, and it displays 7.07VRMS
2) Current: The scope is set to indicate the RMS value of the displayed wave form current measurement, and it displays 141.4mARMS
3) Power: The scope is set to multiply in real time, the voltage and current wave forms to produce a third wave form trace showing us the instantaneous power. The scope is set to indicate the RMS value of the displayed wave form power computation, and it displays 1.22W
4) The scope is set to indicate the MEAN value of the displayed wave form power computation, and it displays 1.00W

Note that the MEAN setting produced the correct result of 1W, whereas the RMS setting did not. The following pictures illustrate this example, as well as the results with a progressive increase in the phase differential between the voltage and current. Rather than MEAN, the abbreviation AVG is used to denote "average" which is the terminology used in PSpice, and which is the equivalent to "MEAN".

In Summary:

rms_ave_01.gif illustrates the two generators used throughout these last tests, and indicates that the phase relationship between the voltage and current is zero in this first case. The amplitudes are set to the same values as the example with the DMM's.

rms_ave_02.gif illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. This again illustrates the example given above where the phase is zero and the AVG computation gives the correct result.

rms_ave_03.gif illustrates the voltage and current with a 45º phase differential.

rms_ave_04.gif illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace now deviates slightly below the 0 mark, but still exhibits a 2Wp-p swing. The bottom plot clearly indicates the discrepancy between the RMS and AVG computations, the RMS being 1W and the AVG being 0.707W. The reader may recall that the power factor for phase-shifted wave forms is: PF=COS (q), where "q" is the phase angle. In this case we have PF=COS (45) and PF=0.707, so the AVG computation is correct in this case also.

rms_ave_05.gif illustrates the voltage and current with a 90º phase differential.

rms_ave_06.gif illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace now deviates evenly below and above the 0 mark, but still exhibits a 2Wp-p swing. The bottom plot clearly indicates the discrepancy between the RMS and AVG computations, the RMS being 0.707W and the AVG being 0.00W. In this case we have PF=COS (90) and PF=0.00, so the AVG computation is again correct. The RMS computation has provided a gross error in terms of indicating the REAL power in the circuit.

Whether or not the RMS computation on an instantaneous power wave form can and should be used for comparisons, or even at all, is left to the reader.

.99
   
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Once again, I must congratulate you, Poynt, on not only purveying accurate information in the perfect context, but for your immaculate and clear presentation skills.  I wouldn't have the patience.  Kudos to you and let us pray that some of the previously confused will take heed and actually learn.  With your ultra-clear lesson, they really have no excuse now for confusion.

Humbugger

P.S.  I vote for putting a link to this post every time the issue arises in any thread.  My only grouse is that the scope waveforms could be a lot brighter.  Why don't you turn up the brightness control on your sim-scope?   ;D
   

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It's not as complicated as it may seem...
Thanks Bryan.

I really do hope it will make a difference.

.99

PS. You can expand the picture to 100% size by clicking on the box with the arrow at the top right of the window.
   
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Now if you wanted to carry it a bit further and you have the time and inclination, it would be neat to apply the same lesson to some Zero-centered and DC offset square waves and triangle waves that are asymmetrical about zero volts.  Then you will have covered all the bases.  I'm far too burned out from just trying to convince Rosemary that E^2/R is not the meaning of RMS!

 :-X
   
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Thanks Bryan.

I really do hope it will make a difference.

.99

PS. You can expand the picture to 100% size by clicking on the box with the arrow at the top right of the window.

Ahhh...much better!  I did not know that part!   :)
   
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Topic for a good scientific fight

It sounds like the Power Measurement Method is a good topic for a good scientific fight so that the World can learn together.

The fighters are likely to be Poynt99 and Lawrence Tseung.  They hold very different opinions and are unlikely to back down.  The discussions will be heated but with much scientific backing.  Who would like to be the Moderator?

The Moderator must have moderator privilege in at least two threads.  One for the fighters and himself.  One for the general public (other forum members).  The Moderator must remove all accidental comments from the general public that might appear in the reserved “fighting ring thread”.  If a particular comment from a general public were excellent, the Moderator may ask the fighters to examine (or fight along those lines).

The Moderator must be neutral and refrain from giving his own opinion.  In other words, he must be the fair referee.  If the fighters get too excited and deviate from scientific reasoning, he should redirect them.

The question again – who would like to be the Moderator?  Poynt99 and Lawrence Tseung have no choice but to become fighters.  Both of them hold strong views and would like to get the true scientific answer. 

Please indicate your willingness to become a Moderator of this fight by posting in this thread.

The topic of the fight is – In Instantaneous Power Measurement where the Power Waveform is NOT DC and NOT sinusoidal, what should be the most accurate measurement method using the oscilloscope?  If an approximation is desirable, which one should be used – the mean or the rms value?   

*** As the moderator, you may rephrase the topic.

Lawrence

Let the World enjoy and learn from the fight. Amen.
   

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It's not as complicated as it may seem...
Topic for a good scientific fight


The topic of the fight is – In Instantaneous Power Measurement where the Power Waveform is NOT DC and NOT sinusoidal, what should be the most accurate measurement method using the oscilloscope?  If an approximation is desirable, which one should be used – the mean or the rms value?    

*** As the moderator, you may rephrase the topic.

Lawrence

The only "wave form" where RMS and MEAN will provide the same result, is DC. So DC is not a consideration.

Aside from that, the question must pertain to any wave form, because in fact it does; sinusoidal, square, etc., it applies to all wave forms. So I propose your question should be re-phrased more precisely and to the point, to something like the following:

In Instantaneous Power Measurements, which computation must be used in order to obtain the actual value of REAL power being dissipated in a circuit with any wave form; MEAN or RMS?

A related sub-question may also be asked: Which type of computed power should be used for making comparisons of circuit efficiency; APPARENT or REAL?

.99
   
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The only "wave form" where RMS and MEAN will provide the same result, is DC. So DC is not a consideration.

Aside from that, the question must pertain to any wave form, because in fact it does; sinusoidal, square, etc., it applies to all wave forms. So I propose your question should be re-phrased more precisely and to the point, to something like the following:

In Instantaneous Power Measurements, which computation must be used in order to obtain the actual value of REAL power being dissipated in a circuit with any wave form; MEAN or RMS?

A related sub-question may also be asked: Which type of computed power should be used for making comparisons of circuit efficiency; APPARENT or REAL?

.99

Poynt99,

It looks like you are prepared for the fight.  Now we need to find a referee (Moderator).
I do not mind having the Moderator rephrase the topic.  We do not need to start the fight until we agree to the wording of the topic and have a mutually acceptable Moderator.

Looking for a good fight to benefit the World.

Any one willing to volunteer as the Moderator?
   

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It's not as complicated as it may seem...
Omnibus at OU requested I perform some sim runs with something closer to 80º phase angle (I used 75º), and also a run with a DC offset in the circuit. See the following for the results:



rms_ave_07.gif illustrates the voltage and current with a 75º phase differential. Offset is 0V and 0A.

rms_ave_08.gif illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace now deviates almost symmetrically about the 0 mark, but still exhibits a 2Wp-p swing. The bottom plot clearly indicates the discrepancy between the RMS and AVG computations, the RMS being 0.753W and the AVG being 0.259W. The reader may recall that the power factor for phase-shifted wave forms is: PF=COS (q), where "q" is the phase angle. In this case we have PF=COS (75) and PF=0.259, so once again the AVG computation provides a correct result, while the RMS does not.

rms_ave_09.gif illustrates the voltage and current again with a 75º phase differential. This time the offset is 2VDC and 40mADC (with a DC offset voltage, there will be a DC current in the circuit).

rms_ave_10.gif illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace normally shows a symmetrical wave form that is double the voltage/current frequency, but it is now asymmetrical in form due to the offset in voltage and current.

In order to obtain the total dissipated power in the circuit, we simply add the previous power values obtained when there was no offset present (see above), to the power produced by the offset alone. This is easily accomplished because the offset is a pure DC value, and is computed to be:

2VDC * 40mADC = 80mW.

Therefore, the new plots should indicate 80mw + 753mW = 833mW for the RMS plot, and 80mW + 259mW = 339mW for the AVG plot.

The bottom plot not only indicates the discrepancy between the RMS and AVG computations, (the RMS being 0.904W and the AVG being 0.342W), but the RMS computation with the DC offset has produced an even worse error than before, whereas the AVG computation is nearly exact to what we would expect for the REAL power in the circuit. The RMS power computation produced an erroneous increase of about 151mW rather than the correct ~80mW increase produced by the AVG computation.

.99
   
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Further to the topic of rms or mean values perhaps I can make things a little clearer.  Clearly you cannot use the average or mean values of voltage or current in order to compute power (If you did this with pure sine waves where the average is zero your power would be zero which is nonsense).  So you have to use something else and that is why the rms value was invented.  As its name implies you square the waveform (or the train of values that sample the waveform) to get a handle on the power capability, and that now represents a power waveform.  Next you take the mean value of that power waveform, then take the square root of that mean value.  Note we take the mean of the power waveform to get the effective DC power, then its square root is the effective DC value of the voltage or current.  Now we can multiply the rms voltage by the rms current to get power, not forgetting to take account of phase angle by also multiplying by the cosine of that angle.

For simple continuous waveforms we don't need to take samples and do the math, there are standard values relating peak or peak-to-peak to rms and we use those.  But modern digital 'scopes can do math and they do not use those simple values, they calculate it properly from the train of samples so they can give correct rms values for arbitrary waveforms.  But there is a catch here, the averaging has to be done over an integral number of cycles else the result is wrong.  For a continuous waveform where the samples just keep coming the 'scope math averaging effectively takes place over many many cycles so the error for not using an integral number becomes insignificant.  But this is not so for single shot or a small number of cycles, so there you need care in using the scope.  Some scopes allow you to set cursors to select integral cycles.

Some scopes can multiply the voltage and current waveforms to display the power waveform.  Its "DC" value is the average.  But again the average must be taken over an integral number of cycles.  Just because scopes can give you rms or mean there appears to be confusion over the use of the rms function applied to the power waveform.  For us engineers this has no real meaning and is useless.  It should not be used.  In the electrical world the RMS function gives you an effective DC value for the power capability of a voltage or current waveform and the M stands for Mean.  That is the Mean of a power waveform, not the RMS of a power waveform.

Smudge
   
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Right. Let me crunch that down to a summary to see if my own understanding is proper:

When one does the sample-by-sample multiplication of current and voltage one gets an "instantaneous power curve" IPC. This curve takes into account the "cos (phase angle)" already and yields a correct instantaneous power value at any time along the curve without having to do any trig computation. "RMS power" really has no meaning, even though you see it as a spec on audio equipment quite often. The DC power equivalent of the instantaneous power curve over a sample interval is the Mean (or Average, same thing here) of that curve, not the "RMS" value. Even though the scope can compute an RMS value for this power curve, that doesn't mean it is useful or significant.
Many scopes that are just above the basic level can do two-stage math. That is, they can do the instantaneous multiplication V x I to produce the power curve, then they can actually integrate that curve over a given time period to produce the integral graph. Any point on the Power curve is a value in Watts, and when integrated over a time interval, the points on the integral curve are in Watt-seconds: that is, Joules. So the integral of the power curve gives an indication of the actual energy passing your measurement point over the specified time interval.

To be safe this should be computed between cursors, positioned to select an integral number of cycles of the IPC.

To get the equivalent average DC power, just ask the scope for the _average_ or _mean_ of the IPC, not the "RMS" value of it.

I hope I got that right!
   
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Yes TK you got that exactly right and put it better than I did.  The only change I would make to your summary is that I wouldn't use the words "to be safe", I would use the words "to get the correct answer".

Smudge
   
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There is another issue that I'm not sure about and would like some help with.

For example, if one has V and I traces that are similar to those shown below.... a 180 degree phase shift.... the IPC will be completely negative. You are always multiplying a positive value by a negative one, so every data point is negative. Should one insert an "absolute value" in the equation for the IPC?  Like  Power = |V x I|  ? Or is there information in the sign of the IPC that is important, such as whether the computation involves a Source, or a Sink, of the power?

(The below traces aren't actually V and I, they are just used for the example of 180 degree oop signals.)
   
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