Make equivarent sine waveform that has Em = 1, Ea = pi/2 and E = 1/sqrt(2) .

[ttokoro]

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

Below waveform has RMS=1/sqrt(2) but Ea=2/3 not pi/2.

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Hard probrem. If you can make it, find the Fourier series of the waveform. Calculate the Ea and RMS values for 10, 100 and 1000 harmonics include. Symbolic evaluation by using below programming may causing a trouble.  

[ppal]

Is this sampled data  and you are creating phasors at the fundamental? What is being asked here?

[ttokoro]

My question is how to make equivqrent sine wave. 

The answer of same RMS waveform is solved by below.

Therefore, one of the same average and RMS values waveform is also solved as below.

These are good questions for electrical engineering students.

How to calculate the Fourier series by using Mathcad is also good question.

 

But this attempt is fail when increase the number of Fourier series Nt.

So this is good charenging practice for Mathcad users to calculate all 1 to 1999 harmonics and make the waveform below.

[ttokoro · Accepted solution]

Step 1. Solve a and b for the function f(x) that has same RMS and average values of sine wave. 

 

Step 2. Only use the function of 1/4 T to calculate the Fourier series for odd function with same f(t)=-f(t-T/2) and symmetory function. It only has odd B Fourier series. 

Step 3. Calculate the odd B Fourier series symbolically.

Step 4. Find the (2*n-1)th B Fourier series function symbolically.

Step 5. Make waveform by numerical engine with N=1000, that is 1999th harmonics included.

Step 6. Plot the waveform that has 1st to (2*N-1)th spectum signals what you want .