One thing to keep in mind The RMS voltage is the property of a waveform that would produce the same heating effect as an equal DC voltage. The RMS voltage, say 120VRMS would produce the same heating as 120VDC for a given resistive (only) load.
It't the equivalent heating effect we want to measure.
So, what about that symmetric sine wave? We already know the mean value is 0V, how does that work? Well, conceptually, the resistor doesn't care which direction the current is flowing so we simply flip the negative excursion of the waveform to positive (the classic double hump waveform) and do the math on that. The link below shows the AC derivation.
The case of the symmetric square wave is the easiest to see: The part below 0V is flipped up and then we notice that VRMS = VPK.
https://www.rfcafe.com/references/electrical/square-wave-voltage-conversion.htm
The math for the sine wave is a bit more ugly but VRMS = 1/sqrt(2) * VPK
https://www.rfcafe.com/references/electrical/sinewave-voltage-conversion.htm
For more arbitrary waveforms, the math gets completely out of hand so we tend to talk about just square and sine waveforms. At least in the early days. Piecewise integration can wait for a later date.
VRMS is all about the DC voltage that would have an equivalent heating effect as the test waveform.
thanks rstofer.
my study is only for the periodic square wave (sine wave already studied
)
The perfectly alternating square wave (zero value in the middle of the wave) is quite easy to understand.
The only thing that is not clear to me: we said that the average value Vm of an alternating periodic signal is always zero!
But if you look at your link:
https://www.rfcafe.com/references/electrical/square-wave-voltage-conversion.htmOk, I understand that in this wave the effective value is equal to the peak value.
But why do they say that the average value is also equal to the peak value? (and therefore not equal to zero?)
do they mean a different average value? (and not the sum of the areas of tension?)
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My doubts, however, concern a square wave signal, for example unipolar (such as the compensation of the siglent, see my message 556).
So not alternating (and for now also without offset)
In the presence of such a signal and measuring with a DMM I understood that:
-the signal has a DC component of 1.5vdc (equal to the Vm of the signal by calculating the white area)
-the signal has an AC component (visible for example by setting the oscilloscope in ac coupling), which the DMM measures me in 1.5Vrms; I understood that the Vrms value of a signal like this is always the same as Vpk-pk / 2 (I did several tests with the simulator, changing the amplitude of the signal)
So I would like to understand, if in the presence of a signal like this (periodic square wave, not alternating, Vpk 3v, Vmin 0v), I can say this: the signal is a square wave, composed of a DC component of 1.5vdc and an AC component of 1.5Vrms
Can this statement of mine be correct and is it all that this sign can indicate?
I do not ask for more for now, just to understand this (then I switch to the same signal but with offset to study it ..)
thanks