Loading....
Coupon Accepted Successfully!

 

Solved Problems-4

Problems-4
Find the trigonometric Fourier series for the waveform shown in figure and sketch the spectra.
 
Description: Description: 4525.png
Solution
Here, Description: Description: 4536.png; for 0 < ωt < π and
 
= 0; for π < ω t < 2π
 
 Description: Description: 4542.png
 
⇒ Description: Description: 4549.png
 
Description: Description: 4555.png; for n odd.
 
= 0 ; for n even.
 
⇒ Description: Description: 4562.png
 
Description: Description: 4571.png; for n even.
 
 
Description: Description: 4577.png; for n odd.
 
∴ Description: Description: 4583.png


Line Spectra
The even harmonic amplitudes are given directly by bn coefficients, since there are no even cosine terms.
Description: Description: 777.png
 
But, the odd harmonic amplitudes are given by computation
 
Description: Description: 4591.png
 
∴ Description: Description: 4609.png = Description: Description: 4615.png = 0.1885 V
 
Description: Description: 4621.png
 
and C2 = Description: Description: 4633.pngC4 = Description: Description: 4639.png = –0.0397 V
 
= – 0.08 V
 





Test Your Skills Now!
Take a Quiz now
Reviewer Name