Chris's Waveform Experiment, RMS vs Average

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  • Last Post 24 July 2022
Chris posted this 16 July 2022

My Friends,

I want to share an experiment I have done, with Math Functions. I am taking 360 Degrees and converting each Degree to a point on a Sinusoidal Waveform:

So, the Math:

double Point = Math.Sin((Math.PI * i) / 180);

i = 0 then Point = 0.0;
i = 1 then Point = 0.017452406437283512;
i = 2 then Point = 0.034899496702500969;
and so on...

 

Example 1

The Below Data Points Represent the Data Points a Scope might capture from a Sine wave:

Sine Data Point: 0
Sine Data Point: 0.0174524064372835
Sine Data Point: 0.034899496702501
Sine Data Point: 0.0523359562429438
Sine Data Point: 0.0697564737441253
Sine Data Point: 0.0871557427476582
Sine Data Point: 0.104528463267653
Sine Data Point: 0.121869343405147
Sine Data Point: 0.139173100960065
Sine Data Point: 0.156434465040231
Sine Data Point: 0.17364817766693
Sine Data Point: 0.190808995376545
Sine Data Point: 0.207911690817759
Sine Data Point: 0.224951054343865
Sine Data Point: 0.241921895599668
Sine Data Point: 0.258819045102521
Sine Data Point: 0.275637355816999
Sine Data Point: 0.292371704722737
Sine Data Point: 0.309016994374947
Sine Data Point: 0.325568154457157
Sine Data Point: 0.342020143325669
Sine Data Point: 0.3583679495453
Sine Data Point: 0.374606593415912
Sine Data Point: 0.390731128489274
Sine Data Point: 0.4067366430758
Sine Data Point: 0.422618261740699
Sine Data Point: 0.438371146789077
Sine Data Point: 0.453990499739547
Sine Data Point: 0.469471562785891
Sine Data Point: 0.484809620246337
Sine Data Point: 0.5
Sine Data Point: 0.515038074910054
Sine Data Point: 0.529919264233205
Sine Data Point: 0.544639035015027
Sine Data Point: 0.559192903470747
Sine Data Point: 0.573576436351046
Sine Data Point: 0.587785252292473
Sine Data Point: 0.601815023152048
Sine Data Point: 0.615661475325658
Sine Data Point: 0.629320391049837
Sine Data Point: 0.642787609686539
Sine Data Point: 0.656059028990507
Sine Data Point: 0.669130606358858
Sine Data Point: 0.681998360062498
Sine Data Point: 0.694658370458997
Sine Data Point: 0.707106781186547
Sine Data Point: 0.719339800338651
Sine Data Point: 0.73135370161917
Sine Data Point: 0.743144825477394
Sine Data Point: 0.754709580222772
Sine Data Point: 0.766044443118978
Sine Data Point: 0.777145961456971
Sine Data Point: 0.788010753606722
Sine Data Point: 0.798635510047293
Sine Data Point: 0.809016994374947
Sine Data Point: 0.819152044288992
Sine Data Point: 0.829037572555042
Sine Data Point: 0.838670567945424
Sine Data Point: 0.848048096156426
Sine Data Point: 0.857167300702112
Sine Data Point: 0.866025403784439
Sine Data Point: 0.874619707139396
Sine Data Point: 0.882947592858927
Sine Data Point: 0.891006524188368
Sine Data Point: 0.898794046299167
Sine Data Point: 0.90630778703665
Sine Data Point: 0.913545457642601
Sine Data Point: 0.92050485345244
Sine Data Point: 0.927183854566787
Sine Data Point: 0.933580426497202
Sine Data Point: 0.939692620785908
Sine Data Point: 0.945518575599317
Sine Data Point: 0.951056516295154
Sine Data Point: 0.956304755963035
Sine Data Point: 0.961261695938319
Sine Data Point: 0.965925826289068
Sine Data Point: 0.970295726275996
Sine Data Point: 0.974370064785235
Sine Data Point: 0.978147600733806
Sine Data Point: 0.981627183447664
Sine Data Point: 0.984807753012208
Sine Data Point: 0.987688340595138
Sine Data Point: 0.99026806874157
Sine Data Point: 0.992546151641322
Sine Data Point: 0.994521895368273
Sine Data Point: 0.996194698091746
Sine Data Point: 0.997564050259824
Sine Data Point: 0.998629534754574
Sine Data Point: 0.999390827019096
Sine Data Point: 0.999847695156391
Sine Data Point: 1
Sine Data Point: 0.999847695156391
Sine Data Point: 0.999390827019096
Sine Data Point: 0.998629534754574
Sine Data Point: 0.997564050259824
Sine Data Point: 0.996194698091746
Sine Data Point: 0.994521895368273
Sine Data Point: 0.992546151641322
Sine Data Point: 0.99026806874157
Sine Data Point: 0.987688340595138
Sine Data Point: 0.984807753012208
Sine Data Point: 0.981627183447664
Sine Data Point: 0.978147600733806
Sine Data Point: 0.974370064785235
Sine Data Point: 0.970295726275996
Sine Data Point: 0.965925826289068
Sine Data Point: 0.961261695938319
Sine Data Point: 0.956304755963036
Sine Data Point: 0.951056516295154
Sine Data Point: 0.945518575599317
Sine Data Point: 0.939692620785908
Sine Data Point: 0.933580426497202
Sine Data Point: 0.927183854566787
Sine Data Point: 0.92050485345244
Sine Data Point: 0.913545457642601
Sine Data Point: 0.90630778703665
Sine Data Point: 0.898794046299167
Sine Data Point: 0.891006524188368
Sine Data Point: 0.882947592858927
Sine Data Point: 0.874619707139396
Sine Data Point: 0.866025403784439
Sine Data Point: 0.857167300702112
Sine Data Point: 0.848048096156426
Sine Data Point: 0.838670567945424
Sine Data Point: 0.829037572555042
Sine Data Point: 0.819152044288992
Sine Data Point: 0.809016994374947
Sine Data Point: 0.798635510047293
Sine Data Point: 0.788010753606722
Sine Data Point: 0.777145961456971
Sine Data Point: 0.766044443118978
Sine Data Point: 0.754709580222772
Sine Data Point: 0.743144825477394
Sine Data Point: 0.731353701619171
Sine Data Point: 0.719339800338651
Sine Data Point: 0.707106781186548
Sine Data Point: 0.694658370458997
Sine Data Point: 0.681998360062499
Sine Data Point: 0.669130606358858
Sine Data Point: 0.656059028990507
Sine Data Point: 0.642787609686539
Sine Data Point: 0.629320391049838
Sine Data Point: 0.615661475325658
Sine Data Point: 0.601815023152048
Sine Data Point: 0.587785252292473
Sine Data Point: 0.573576436351046
Sine Data Point: 0.559192903470747
Sine Data Point: 0.544639035015027
Sine Data Point: 0.529919264233205
Sine Data Point: 0.515038074910054
Sine Data Point: 0.5
Sine Data Point: 0.484809620246337
Sine Data Point: 0.469471562785891
Sine Data Point: 0.453990499739547
Sine Data Point: 0.438371146789077
Sine Data Point: 0.4226182617407
Sine Data Point: 0.4067366430758
Sine Data Point: 0.390731128489274
Sine Data Point: 0.374606593415912
Sine Data Point: 0.3583679495453
Sine Data Point: 0.342020143325669
Sine Data Point: 0.325568154457157
Sine Data Point: 0.309016994374948
Sine Data Point: 0.292371704722737
Sine Data Point: 0.275637355817
Sine Data Point: 0.258819045102521
Sine Data Point: 0.241921895599668
Sine Data Point: 0.224951054343865
Sine Data Point: 0.207911690817759
Sine Data Point: 0.190808995376545
Sine Data Point: 0.17364817766693
Sine Data Point: 0.156434465040231
Sine Data Point: 0.139173100960066
Sine Data Point: 0.121869343405148
Sine Data Point: 0.104528463267654
Sine Data Point: 0.0871557427476586
Sine Data Point: 0.0697564737441255
Sine Data Point: 0.0523359562429438
Sine Data Point: 0.0348994967025007
Sine Data Point: 0.0174524064372834
Sine Data Point: 1.22460635382238E-16
Sine Data Point: -0.0174524064372832
Sine Data Point: -0.0348994967025009
Sine Data Point: -0.0523359562429436
Sine Data Point: -0.0697564737441248
Sine Data Point: -0.0871557427476579
Sine Data Point: -0.104528463267653
Sine Data Point: -0.121869343405148
Sine Data Point: -0.139173100960066
Sine Data Point: -0.156434465040231
Sine Data Point: -0.17364817766693
Sine Data Point: -0.190808995376545
Sine Data Point: -0.207911690817759
Sine Data Point: -0.224951054343865
Sine Data Point: -0.241921895599668
Sine Data Point: -0.25881904510252
Sine Data Point: -0.275637355816999
Sine Data Point: -0.292371704722736
Sine Data Point: -0.309016994374948
Sine Data Point: -0.325568154457157
Sine Data Point: -0.342020143325669
Sine Data Point: -0.3583679495453
Sine Data Point: -0.374606593415912
Sine Data Point: -0.390731128489274
Sine Data Point: -0.4067366430758
Sine Data Point: -0.422618261740699
Sine Data Point: -0.438371146789077
Sine Data Point: -0.453990499739546
Sine Data Point: -0.469471562785891
Sine Data Point: -0.484809620246337
Sine Data Point: -0.5
Sine Data Point: -0.515038074910054
Sine Data Point: -0.529919264233205
Sine Data Point: -0.544639035015027
Sine Data Point: -0.559192903470747
Sine Data Point: -0.573576436351046
Sine Data Point: -0.587785252292473
Sine Data Point: -0.601815023152048
Sine Data Point: -0.615661475325658
Sine Data Point: -0.629320391049838
Sine Data Point: -0.642787609686539
Sine Data Point: -0.656059028990507
Sine Data Point: -0.669130606358858
Sine Data Point: -0.681998360062498
Sine Data Point: -0.694658370458997
Sine Data Point: -0.707106781186547
Sine Data Point: -0.719339800338651
Sine Data Point: -0.73135370161917
Sine Data Point: -0.743144825477394
Sine Data Point: -0.754709580222772
Sine Data Point: -0.766044443118978
Sine Data Point: -0.777145961456971
Sine Data Point: -0.788010753606722
Sine Data Point: -0.798635510047293
Sine Data Point: -0.809016994374947
Sine Data Point: -0.819152044288992
Sine Data Point: -0.829037572555041
Sine Data Point: -0.838670567945424
Sine Data Point: -0.848048096156426
Sine Data Point: -0.857167300702112
Sine Data Point: -0.866025403784438
Sine Data Point: -0.874619707139396
Sine Data Point: -0.882947592858927
Sine Data Point: -0.891006524188368
Sine Data Point: -0.898794046299167
Sine Data Point: -0.90630778703665
Sine Data Point: -0.913545457642601
Sine Data Point: -0.92050485345244
Sine Data Point: -0.927183854566787
Sine Data Point: -0.933580426497202
Sine Data Point: -0.939692620785908
Sine Data Point: -0.945518575599317
Sine Data Point: -0.951056516295154
Sine Data Point: -0.956304755963035
Sine Data Point: -0.961261695938319
Sine Data Point: -0.965925826289068
Sine Data Point: -0.970295726275996
Sine Data Point: -0.974370064785235
Sine Data Point: -0.978147600733806
Sine Data Point: -0.981627183447664
Sine Data Point: -0.984807753012208
Sine Data Point: -0.987688340595138
Sine Data Point: -0.99026806874157
Sine Data Point: -0.992546151641322
Sine Data Point: -0.994521895368273
Sine Data Point: -0.996194698091746
Sine Data Point: -0.997564050259824
Sine Data Point: -0.998629534754574
Sine Data Point: -0.999390827019096
Sine Data Point: -0.999847695156391
Sine Data Point: -1
Sine Data Point: -0.999847695156391
Sine Data Point: -0.999390827019096
Sine Data Point: -0.998629534754574
Sine Data Point: -0.997564050259824
Sine Data Point: -0.996194698091746
Sine Data Point: -0.994521895368273
Sine Data Point: -0.992546151641322
Sine Data Point: -0.99026806874157
Sine Data Point: -0.987688340595138
Sine Data Point: -0.984807753012208
Sine Data Point: -0.981627183447664
Sine Data Point: -0.978147600733806
Sine Data Point: -0.974370064785235
Sine Data Point: -0.970295726275997
Sine Data Point: -0.965925826289068
Sine Data Point: -0.961261695938319
Sine Data Point: -0.956304755963035
Sine Data Point: -0.951056516295154
Sine Data Point: -0.945518575599317
Sine Data Point: -0.939692620785909
Sine Data Point: -0.933580426497202
Sine Data Point: -0.927183854566787
Sine Data Point: -0.92050485345244
Sine Data Point: -0.913545457642601
Sine Data Point: -0.90630778703665
Sine Data Point: -0.898794046299167
Sine Data Point: -0.891006524188368
Sine Data Point: -0.882947592858927
Sine Data Point: -0.874619707139396
Sine Data Point: -0.866025403784439
Sine Data Point: -0.857167300702112
Sine Data Point: -0.848048096156426
Sine Data Point: -0.838670567945424
Sine Data Point: -0.829037572555042
Sine Data Point: -0.819152044288992
Sine Data Point: -0.809016994374948
Sine Data Point: -0.798635510047293
Sine Data Point: -0.788010753606722
Sine Data Point: -0.777145961456971
Sine Data Point: -0.766044443118978
Sine Data Point: -0.754709580222772
Sine Data Point: -0.743144825477395
Sine Data Point: -0.731353701619171
Sine Data Point: -0.719339800338652
Sine Data Point: -0.707106781186548
Sine Data Point: -0.694658370458998
Sine Data Point: -0.681998360062498
Sine Data Point: -0.669130606358858
Sine Data Point: -0.656059028990507
Sine Data Point: -0.64278760968654
Sine Data Point: -0.629320391049838
Sine Data Point: -0.615661475325659
Sine Data Point: -0.601815023152048
Sine Data Point: -0.587785252292473
Sine Data Point: -0.573576436351046
Sine Data Point: -0.559192903470747
Sine Data Point: -0.544639035015027
Sine Data Point: -0.529919264233206
Sine Data Point: -0.515038074910054
Sine Data Point: -0.5
Sine Data Point: -0.484809620246337
Sine Data Point: -0.469471562785891
Sine Data Point: -0.453990499739547
Sine Data Point: -0.438371146789077
Sine Data Point: -0.4226182617407
Sine Data Point: -0.4067366430758
Sine Data Point: -0.390731128489275
Sine Data Point: -0.374606593415912
Sine Data Point: -0.358367949545301
Sine Data Point: -0.342020143325669
Sine Data Point: -0.325568154457158
Sine Data Point: -0.309016994374948
Sine Data Point: -0.292371704722736
Sine Data Point: -0.275637355817
Sine Data Point: -0.258819045102521
Sine Data Point: -0.241921895599668
Sine Data Point: -0.224951054343865
Sine Data Point: -0.20791169081776
Sine Data Point: -0.190808995376545
Sine Data Point: -0.173648177666931
Sine Data Point: -0.156434465040231
Sine Data Point: -0.139173100960066
Sine Data Point: -0.121869343405148
Sine Data Point: -0.104528463267653
Sine Data Point: -0.0871557427476583
Sine Data Point: -0.0697564737441248
Sine Data Point: -0.0523359562429444
Sine Data Point: -0.0348994967025008
Sine Data Point: -0.0174524064372844

 

These Data Points Draw the following Sinusoidal Waveform:

 

 

The Peak Voltage here is 1.0 Volts, so the peak voltage value is controlled and can not fluctuate. This is true for both Negative and Positive Values.

The Calculated Mean or Average and RMS is:

  • Mean: 0.636603611829498
  • RMS: 0.707106781186548

 

These are expected Values for a Sinusoidal Waveform.

The factor 0.707 for rms value is derived as the square root of the average (mean) of all the squares of the sine values. If we take the sine for each angle in the cycle, square each value, add all the squares, divide by the number of values added to obtain the average square, and then take the square root of this mean value, the answer is 0.707. These Calculations are shown in Table 16-2 for one alternation from 0 to 180°.

 

Ref: Alternating Voltage and Current.

 

RMS was conceived specifically for Sinusoidal Waveforms:

For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load.

 

RMS means ‘Root Mean Square’ in mathematics. It is also referred to as quadratic mean. The RMS is very useful in many fields, particularly in electrical engineering and in the domain of signal amplifiers. RMS is very useful when the random variables in the data are negative and positive such as sinusoids.

Read more: Difference Between RMS and Average

 

 

Example 2

Now for a Alternating Square Waveform, this may be the H-Bridge DC, we get quite a different story!

Lets look at the Data Points:

Square Data Point: 0
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
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Square Data Point: 1
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Square Data Point: 1
Square Data Point: 1
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Square Data Point: 1
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Square Data Point: 1
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Square Data Point: 1
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Square Data Point: 1
Square Data Point: 1
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Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
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Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: 1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
Square Data Point: -1
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These Data Points Draw the following Alternating DC Pulsed Waveform:

 

The Peak Voltage here is 1.0 Volts, so the peak voltage value is controlled and can not fluctuate. This is true for both Negative and Positive Values.

The Calculated Mean or Average and RMS is:

  • Square Mean: 0.997222222222222
  • Square RMS: 0.998610145263016

 

Now, I have to say, Both Waves have been calculated using the same Math:

double Mean = 0.0;
double Integration = 0.0;
foreach (double Point in DataPoints)
{
     Mean += Math.Abs(Point);
     Integration += Math.Pow(Point, 2);
}

richTextBox1.AppendText($"{Type} Mean: " + (Mean / 360).ToString() + Environment.NewLine);
richTextBox1.AppendText($"{Type} RMS: " + Math.Sqrt((Integration / 360)).ToString() + Environment.NewLine);

 

 

Example 3

Now for a Pure DC Pulsed Waveform, lets calculate the Data. First, we get the following Data Points:

Square Data Point: 0
Square Data Point: 1
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These Data Points Draw the following DC Pulsed Waveform:

 

The Peak Voltage here is 1.0 Volts, so the peak voltage value is controlled and can not fluctuate. This is true for Positive Values Only, as we have no Negative Values.

The Calculated Mean or Average and RMS is:

  • Square Mean: 0.5
  • Square RMS: 0.707106781186548

 

Again, all Waves have been calculated using the same Math:

double Mean = 0.0;
double Integration = 0.0;
foreach (double Point in DataPoints)
{
    Mean += Math.Abs(Point);
    Integration += Math.Pow(Point, 2);
}

richTextBox1.AppendText($"{Type} Mean: " + (Mean / 360).ToString() + Environment.NewLine);
richTextBox1.AppendText($"{Type} RMS: " + Math.Sqrt((Integration / 360)).ToString() + Environment.NewLine);

 

It should be very clear to everyone here, that the total Area in this example, is Wrong for RMS!

 

Analogy:

Lets say that you're filling your Ice cream cup, and the flow of ice cream is regulated by the pump. We have calculated the cup size to be 100% full after 360 degrees of rotation of the pump. A technical fault occurs with the pump, and the ice cream only flows for 180 degrees = 0.5 x 360, or half the revolution! How much Ice Cream fills the Cup? 

  • 0.5 or 50%
  • 0.707106781186548 or 70.7106781186548%

 

The Answer should be obvious!

This RMS Value: 0.707106781186548, is Wrong and it should be clear as to why RMS should Not be used on DC Pulsed Systems, especially if one has a Non-Linear Load!

Really simple, if we have 360 Data Points, and half are Zero, the other half are 1.0, then we do some very simple Math to verify this:

double AverageDataPoints = ((360.0 / 2.0 * 1.0) + (360.0 / 2.0 * 0.0)) / 360.0;

 

NOTE: The Oscilloscope has not recorded any Positive Data for 180 points! There is Zero Potential here, nothing! No Voltage Potential, so Zero is Recorded.

This should be enough proof, to show that it is important to correctly ascertain the right Value: ( Average or Mean vs RMS ) to use when Measuring specific Waveforms.

 

Non-Linear Loads

A perfect example of the importance of knowing what values to use for measurement, is seen very clearly in Non-Linear Loads, where Power can be sent back to the DC Source:

 

EG:

  • 1.28 Watts RMS
  • 0.0957 Watt's Average

 

I have provided all the data you need to prove this for yourself, please go ahead and do so! Its all there, accurate and straightforward. This very clearly shows some engineers don't get it right all the time! Adrian S. Nastase, PHD in Electronic Engineering, does not show these discrepancies, and derives RMS for DC Values, that maybe sometimes he shouldn't, just recently discussed. No disrespect to anyone, I am only making a point.

Best Wishes,

   Chris

Order By: Standard | Newest | Votes
Jagau posted this 17 July 2022

 

Hi Chris and all.

The calculation of the area either positive or negative should not be done with small perfect squares.


A square wave is not formed by small squares, it is formed by a multitude of harmonics and their summation gives an oscilloscope an image of a square wave and I assure you that it is not perfect. If you magnify it several times you will observe that the rise time and fall time are very different from being perfect.


To do a square wave calculation you have to do an integration versus time.

This is why we used integral in our formula.


Here i includes a square wave analyzed with fourier, in order to better understand you can do the same with your scope.

And you can see that summation form a square wave.

For more information about Fourrier analysis of a square wave see link here"

https://en.wikipedia.org/wiki/Square_wave

 

The real question of this debate would rather be:
In the input power calculation for an example square wave; from 0 to 12 volts, is it better to use the average voltage Vavg or the rms voltage Vrms, that's the real question, don't you think.

This can be verified by real practical experiments and this is what we are going to do all in order to have the real solution. The important thing is to know which is the right formula to use.

Jagau

Chris posted this 18 July 2022

Hey Jagau,

My Friend, these are excellent points and all valid, however, this is not what the Scope Measures. As we know, the Data is captured as Real Potential Values in the Scope Buffer, and used for its calculation from there.

I have thought on this for a few hours, and I agree with what you're saying, but still believe the average is the most accurate for a DC Pulsed Waveform, and RMS is best for AC Waveforms.

I am or the opinion, that perhaps providing both Average and Mean may be a good idea, at least for a while, so we can give others as much information as possible to ponder?

You are right you know, the most important thing is to know that Input Measurements may vary considerably. Observing Output that is well Above the Input, shows the Mean / RMS issue to be some what insignificant anyway 😉

It is important others be aware of this though.

Best Wishes,

   Chris

Jagau posted this 18 July 2022

 Totally agree my friend, I also invite those who want to comment to do so and experimented. This is the purpose of the forum, exchanged.

So with real practical experience with taking measurements on an oscilloscope, we try to find a consensus for everyone.
As we all get along in AC, the experiment will focus on pulsed DC only.

I propose to use a load like 1157 incadescent lamp and pulse it with a DC voltage of 12 volts. So as not to be complicated I will take a frequency of 1000  hertz so with a standard DDM and a true rms DDM we will have values that the instruments can give us and compare these measurements.

The final goal is to find the power in Watt:
as P= E x I

with Eavg x Erms

compare to Irms x Irms

what is the real power in Watt and why ???


Jagau

scalarpotential posted this 18 July 2022

Hi all,

I'm sure I posted something, was it deleted?

https://www.desmos.com/calculator/zx1wk3vxro

This shows what R and S of RMS is doing, it makes DC from AC or it rectifies AC, because the average of a sine is zero. (not entirely correct, but that is the reason to square it)

That's why they say avg and rms are equal for DC.

Chris posted this 18 July 2022

Hello Scalarpotential,

I have provided the data, its pretty clear that for a DC Waveform that RMS is wrong, but I do urge others to have their own opinion. Also to put the work in to run through the proof! 

I believe the Average and RMS should be clear to most readers now.

Only two people can Delete your posts, you and me, I have not deleted anything.

The reason aboveunity.com is Light Years ahead of other forums, is we do the work, put the effort in and prove what needs to be proven instead of just ignoring all the hard stuff like other forums do! I bet they get frustrated by the lack of any real competition, they are just forced to accept we are World Leaders! Because we are!

Best Wishes,

   Chris

scalarpotential posted this 19 July 2022

Hi Chris, there's no delete button anymore. You're probably right, I'm going to think this through, I only knew the surface. So RMS takes the mean of the area below the curve squared, and then the squareroot. Average is the mean of the area of the original signal. Why is the order of operators square-mean-root and not square-root-mean that rectifies AC and then takes the mean? Guess this answers it, hence "effective": For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. https://electronics.stackexchange.com/questions/101234/is-rms-value-of-a-positive-varying-dc-voltage-same-with-its-mean-value https://electronics.stackexchange.com/questions/113578/rms-vs-dcmean-value-when-calculating-power-of-pulsed-or-rectified-signals

Cheers

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scalarpotential posted this 19 July 2022

This image shows why rms of pulsed DC is actually correct for power calculations:

Vrms=5.sqrt(t/T)=5.sqrt(50/100)=5.sqrt(1/2)=5/sqrt(2)=3,536V
Vrms=5.sqrt(t/T)=5.sqrt(25/100)=2,5V

Makes sense to me.

edit
root and square in rms now makes sense too. A bit of math - please correct me if it's wrong.
de=sin(t)^2 / R . dt (the energy in the area of an infinitesimal period dt of a sine. VV/Rdt) e=1/R . int(sin(t)^2 . dt) (total energy in a period) p=e/deltaT (joule/sec, average power) [...] Vrms=sqrt(P*R)
Vrms=sqrt(1/deltaT.int(sin(t)^2 . dt)) = RMS formula

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scalarpotential posted this 19 July 2022

messed up layout, I disabled js because then the site load much faster.
https://www.desmos.com/calculator/toyzkug0uq

My earlier statement - my 1st post in this topic - isn't correct.

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SonOfLuck posted this 19 July 2022

Hi,

I made some playground for this in desmos too.

Sinus playground
https://www.desmos.com/calculator/crrvunadlk

Pulse playground
https://www.desmos.com/calculator/op0svsmndy

Approx. pulse playground(this is a bit slow)
https://www.desmos.com/calculator/1pjhiotx1p

 

You can set the parameters of the V and A waveforms if you open the first block. You can rotate trough the parameters given interval, like this:
https://www.desmos.com/calculator/nirmpwepaz

From this I think any time when the Volt and Amp are in phase, the RMS is correct to use for watt calculation. But if it's not in phase it can screw you, and without an oscilloscope you cant even know how much it screwing you. But if you have an oscilloscope the best to use  the math multiplication on the Volt and Amp channels then take the mean of it.

Best regards,
SonOfLuck

Chris posted this 19 July 2022

Hi SonOfLuck,

When you say:

From this I think any time when the Volt and Amp are in phase, the RMS is correct to use for watt calculation.

 

Can you give us a detailed explanation as to why you say this, and why you think RMS is what should be used? Some hard data backing up your opinion would be great to see, because so far, there is nothing but an opinion.

Of course, this is the whole goal, to provide the proof, with backing data to show the best approach! 

Best Wishes,

   Chris

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Jagau posted this 19 July 2022

Hi ALL
Proof by experiment is something to do. We must not forget the main goal,

to reproduce an experimental experiment with a pulsed DC from 0 to 12 volts,

not with a sinusoidal signal but with a DC pulse.
Not easy to achieve I admit but wr will that to take a big step.
I have an experiment in progress and I will present it soon.
Jagau

SonOfLuck posted this 20 July 2022

Hi

Can you give us a detailed explanation as to why you say this, and why you think RMS is what should be used? 

Sure, I can include some image from the links I given.(a correction in the first one here)

Sinus...

pulse...

approx pulse...

 

Best regards,
SonOfLuck

scalarpotential posted this 20 July 2022

Awesome, SonOfLuck. This was my first time using desmos, I'm going to use your sheets t learn how it works.

https://agcsystems.tv/rms-power-fallacy/

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Jagau posted this 20 July 2022

Hey sonofluck
It looks like a useful tool
The real formula for integrated time for a DC pulse is this one

all other components as you programmed them are correct except the w

Could you replace your w here from this formula you programmed here

 

and replaced it only by Vpeak only, will have a real value with this program? 

Take for exemple Vpeak of 10volts

Jagau

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Chris posted this 20 July 2022

Hi SonOfLuck,

I am sorry, but there is no conclusive proof or demonstration that shows RMS to be the correct equation for a DC Pulse? Am I missing something?

I mean, some may say: I think RMS is the correct measurement method on a DC Pulsed Systems because its easier to spell, but this does not make this statement even remotely conclusive! Evidence is what we are looking for, not a bunch of stuff that I have already shown using my Calculator on my PC.

The world is going Crazy:

 

I think its time we set the bar higher than the other forums, which we have always done anyway:

 

Dont you think we should expect more? Dont you think we should be more sensible and Question the reasoning of others especially when its very easy to prove it wrong!

Of course, a DC Power Source is Incapable of Supplying Negative Conventional Current when it is designed to Supply a Positive Conventional Current!

 

EG:

  • 1.28 Watts RMS
  • 0.0957 Watt's Average

 

They insist that all that Negative Current is used Current, when it is not, and its very easily shown its not!

Do you see why our Measurement protocol is the best in the world? We simply are the best! We are Light Years Ahead of the others!

Best Wishes,

   Chris

SonOfLuck posted this 21 July 2022

Hey Jagau 

The formula was taken from here:
https://en.wikipedia.org/wiki/Mean_of_a_function


Which I think is correct to use here. V is a function, and A also a function, W a function of that two.

I assume in your formula t1 is the ON time and T is the Full Time/Time of 1 cycle. If this is the case...
Your formula is the same as mine, but mine is more general. Maybe yours a bit more accurate for a perfect pulse waveform.

You take the ON area of the function and divide it by the Full Time. That's basically Vp x duty cycle written in a complex way.
While I take the area on an interval and divide it by the Full Time.
This 2 are the same because if V(x) = 0 there is no area, so in the end I just take the ON area in the given interval and divide it by the Full Time.

 


Hi Chris

My maaan.
Wow I don't even know how to write this...

It feels like you just taken some words that don't fit your world view, and after that you didn't read anything else.
I didn't say anywhere to use RMS on the W signal(which you are showing us in your scope shot), 
I even said if you have an osciloscope use the math function(with multiplication) and take the mean of it.


If W is the end product( end stuff that we want to calculate ) AND
RMS is a rectification/absolute value
=
You will miss a whole lot if you RMS the W signal.
Any time the W signal will go under 0, you will miss that.


There is a difference in the whys in calculating V RMS and W RMS.  ( Which you are mixing in the origin post in this thread, first talking about V rms, after that in the scopeshot you talking about W rms)
V RMS is NOT the end, V RMS will be used in other places.
Like for example in the W calculation.
You can say W = Vrms * Irms
AND this will be EQUAL to mean( V * I ) when... (and you missed This KEY POINT )

when the Volt and Amp are in phase

Now for me the "in phase" means: the sign of I and V at any given instance of time the same.
from that you can see, this means the sign of W will be positive at all time.

And what I saying you can see and verify (and play around with) in the links i given and in the videos(I stepping through some hundreds of phase shifts and each has its calculations).
So I don't think what I saying is this:

I think RMS is the correct measurement method on a DC Pulsed Systems because its easier to spell


Best Regards,
SonOfLuck

Chris posted this 21 July 2022

Hi SonOfLuck,

When I make posts, I mostly post more broadly, and not so much directly at people. I hope you can see this and understand what I am trying to say.

Although one or two comments were directed at you, because I felt there was nothing conclusive there, nothing that was substantial for basing your opinion, nothing that we could see anyway.

From this I think any time when the Volt and Amp are in phase, the RMS is correct to use for watt calculation.

 

RMS is only applicable for Alternating Current with Linear Loads.

Also, I believe you do not know how a Scope Works, V and I Phase is not Applicable here! Instantaneous Data Taken voids this! RMS has absolutely nothing to do with V and I Phase!

 

It feels like you just taken some words that don't fit your world view, and after that you didn't read anything else.

 

No, I believe to many do not know the origins of RMS and why RMS was conceived, specifically for AC. So I think you're attempting to cloud a simple subject here. I have provided all the necessary evidence to show what RMS works for, and does not work for.

I think, I see you have taken offence to my asking for what based your opinion, this seems to have caused some what of a rift.

Your opinion, to use RMS, even in the light of Evidence to show otherwise, is not based in Logic! You have provided Zero evidence to the contrary!

You should be providing Proof, if you think RMS should be used, don't you think?

Please don't take offence to my posts, they are not meant to be offensive, although I know many do take offense they are really not meant that way. Like I said, they are meant to challenge people, challenge beliefs challenge those misconceptions we have had from days of old and to make progress well beyond the VERY Low Bar that has been set by other forums and by Physics and Engineering institutions.

We all can be better, if we do better, sometimes all it takes is a push in the right direction!

Worth Noting: It amazes me how sparse the Goon Squad have become in the light of this topic! Where are they all? Hiding? These are the people that tried to throw me under the buss when I shared a Scope Screenshot with AC Coupling, now gone in the wind when it comes to the worlds most accurate Scope Measurements? WTF...

 

 

The Ball always falls, its always falling, Gravity assists this machine! Do we RMS or Mean this System?

Best Wishes,

    Chris

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Jagau posted this 22 July 2022

Thank you for the explanation Sonofluck, I understand your formula better now.


As you say your w represents function and in my formula it's just a peak voltage, Vpeak coming from theses expressions:

to arrive at the final formula.

 


thanks for the precision, 


Jagau

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scalarpotential posted this 22 July 2022

RMS applies to powercalculations ONLY. It is based on the average power of a signal v or i through any r, and then the equivalent DC value is taken which gives the exact same power through r which is mathematically cancelled Accurate shortcuts for the complex calculations are sqrt(2) and sqrt(t/T) and those are not approximations.

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Chris posted this 22 July 2022

Hi Jagau, SonOfLock,

Mathematically deriving the RMS Value from Peak Voltage and Duty Cycle is not an argument for using RMS, its how to Derive RMS Mathematically and nothing more.

Its like saying I am going to mathematically derive a donut so from now on it is correct to use donuts for calculating power. I guess some people just love RMS and Donuts?

Best Wishes,

   Chris

 

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Chris posted this 24 July 2022

My Friends,

From this post Here, we can further our simple little experiment. Using the Example in question:

 

Example 3

Now for a Pure DC Pulsed Waveform, lets calculate the Data. First, we get the following Data Points:

Square Data Point: 0
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These Data Points Draw the following DC Pulsed Waveform:

 

The Peak Voltage here is 1.0 Volts, so the peak voltage value is controlled and can not fluctuate. This is true for Positive Values Only, as we have no Negative Values.

The Calculated Mean or Average and RMS is:

  • Square Mean: 0.5
  • Square RMS: 0.707106781186548

 

Again, the Definition for DC Power is Voltage V x Current I = Power P and we can use Ohms Law to verify the answer:

 

Integrating the Data Points and using Ohms Law, one can find the Power used in the DC Pulsed Waveform: Power P = Voltage V x Current I.

float P = 0;
for (int i = 0; i < 360; i++)
{

    P += (float)(Voltage * Current);
}

Power = P / 360;

 

This also proves RMS is Wrong for a DC Pulse and Mean is correct. Basically, there is no individual Value Squaring

  1. Math.Pow(Value, 2)

 

and no Square Root

  1. Math.Sqrt((Integration / 360))

 

of any Average!

The Guru's are very welcome to try to tell us that Ohms Law is not Correct and does not hold if they now wish to?

Best Wishes,

   Chris

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