Make equivarent sine waveform that has maximum value = 1 and RMS = 1/sqrt(2).

[ttokoro]

Show another waveform that is equivalent to a sine wave with a maximum value of 1 and an effective value of 1/sqrt(2), and find its Fourier series so that the effective value of the Fourier series is 1/sqrt(2).

Below is an exsample of the answers.

[Werner_E]

I'd be really curious to see how you get from e_m(t) with m->infinity to the expression for E using the usual RMS definition (integral) and the symbolic calculation possibilities of Prime 😈

[Werner_E · Accepted solution]

So here is the alternate signal:

[ttokoro]

Chopped DC can make 1/sqrt(n) RMS waveform by 1/n chopping.

Another waveforms with same 1/sqrt(2) RMS are there. Red dotted lines are fundamental component of Fourier series.

If anyone has another waveform with 1/sqrt(2) RMS, please share here your waveform and Fourier series.

[ttokoro]

My above answers have Average values

 ,.

So, they are not 2/pi of sine waveform.

Therefore, the next probrem is find RMS=1/sqrt(2) and Average=2/pi but not sine waveform.

[ttokoro]