# How to mathematically calculate of RMS of a Sine Wave filtered out PWM

I'm generating a Sine Wave without DC offset from a Square wave with 1Khz 1.5V offset by filtering it first with a High Pass firs (to remove the DC) and then with a 3rd Order Low Pass Active filter (fc=1kHz).

I simulated the circuit and the sine wave has a Vrms of 1.37V. What i would like to know is how can i calculate this value mathematically without simulating, just by knowing the Square Wave signal is filtered by a 1rd order High pass and 3rd Order Low Pass.

• Take the mathworld.wolfram.com/FourierSeriesSquareWave.html and take the rms of the fundamental (divide Amplitude by sqrt(2) ) – sstobbe May 30 '17 at 22:01
• I was looking for a less simple answer, because the filter is not ideal, thus neither the sine wave, so although the fundamental frequency ( 1kHz) has the higher magnitude, other harmonics have some contribution. However that takes in a good direction, determine the rms contribution of each harmonic, and i got the answer i think, i just need to sum each (odd) frequency magnitude and divide by sqrt(2) – Impe_dancer May 30 '17 at 22:30