RMS value of the square wave signal

The formula you wrote is valid only for rectangular waveform that goes from 0 to a given voltage. If you apply the AC coupling you will have a zero mean waveform going from -Vm/2 to Vm/2. From the definition of RMS (root mean square) you have to consider that the negative part folds on the positive y axis (that is -Vm/2 will go to a level Vm/2) then the result will be a constant voltage of amplitude Vm/2.

Thanks for the answer, what if there is such a chart for a different duty cycle?
DC DC converters regulate the duty cycle, so the RMS value of the voltage that goes to the transformer winding must change.
How to determine the RMS of such a waveform for different duty cycle?

Hi,

this is not a square wave (2 levels) but now you show a three level signal. Here one needs to now the timing.

For a square wave -4V / +4V levels (no 0V level)
--> the RMS always is 4V (independent of duty cycle)

But I don´t know how this refers to a transformer. Please explain.

Klaus

For waveforms with discrete voltage levels, integral calculus reduces to a simple square root of sum of squares.

E.g.

|V| = V1 for delta t = T1
|V| = V2 for delta t = T2

Vrms = sqrt((T1*V1² + T2*V2²)/(T1+T2))

Pixelx said:

I would like to understand it in a simple and mathematical way

Click to expand...

At some time the definition of RMS for an arbitrary waveform was a way of answering the question "If DC can produce an identical heating effect on a resistor, what DC voltage do you apply?" Amid math and meter readings some consensus emerged as to the proper coefficients relating RMS to Average to AC to DC.

The more recent version of Falstad's animated interactive simulator can be commanded to tell these figures onscreen in edit windows or scope traces. Example, you can choose a sine wave readout in peak amplitude or RMS value, or both.

FvM said:

Vrms = sqrt((T1*V1² + T2*V2²)/(T1+T2))

Click to expand...

referring to the picture of post#3:
I´d repalce (T1 + T2) with (Tperiod)

--> Vrms = sqrt((T1*V1² + T2*V2²)/(Tperiod))
Because it also includes the times where V = 0

Klaus

Thank you for your answers.

I think I calculated something wrong and I don't get the exact Vrms results from the oscilloscope.
Could you substitute the values based on these screenshots to get what the oscilloscope shows?

How to calculate the voltage generated on the oscilloscope?
I will add that the RMS depends on the given half of the filling. If the upper rectangles are at 10% and the lower ones at 40%, the RMS is also different.
What is the formula to calculate this?
If you know how to derive this formula from integral form, it would be great.

Pixelx said:

How to calculate the voltage generated on the oscilloscope?

Click to expand...

--> see post#5 / post#7.

It´s on you to give the timing vlaues.

Pixelx said:

What is the formula to calculate this?

Click to expand...

--> see post#5 / post#7.

You coulld use a calculator or something like eXcel.

Klaus