It does not work this way. You need to calculate it with the square root of the sum of squares and also the signals have to be uncorrelated. The waveform has to be split in time, not amplitude. Read this article MasteringElectronicsDesign.com: How to Calculate the RMS Value of an Arbitrary waveform.

Thanks for the awesome material, I have a question, I tried to split the shape into a small triangle on the top with a square wave on the bottom, so my equation is like this

(V2-V1)*sqrt(t1/3T) + V1*sqrt(t1/T)

but I can’t seem to get the same results as in equation(5), can you tell me what I did wrong?

Thanks

Thank you for letting me know, Phil. I corrected it.

Minor edit – the “squared” symbol is missing in the second equation between equations 2 and 3.

Nice website!
Phil

You have a few question marks that most likely stand for characters that HTML did not understand. Write another post and replace characters like omega or pi with the word “omega” or “pi”, so that I could understand your equations.

Here is a quick method to calculate the RMS when a pulse goes through a capacitor C with a load R. The signal will spike up and then decay exponentially to zero with a time constant of tau = RC. Then repeats for the next pulse. Such a decaying function is

u(t) = Vp*exp(-t/tau), where tau is RC

Calculate this signal RMS by calculating the integral of u(t)^2. The result is

Vp*(-(1/2T)*tau*exp(-2*t/tau))^2, where Vp is the signal peak and T is the period.

I thought it was:

VRMS = Vp * ?RC/(1+(?^2*R^2*C^2))

where:
? = 2?f (angular frequency)
C = ac coupled CAP value in Farads
R = Load in ohms

but the numbers don’t match my results under different “R” loads