115A_1_FourSer

# 1 2 b m 0 m 1 2 where a a m and b m are the

This preview shows pages 1–5. Sign up to view the full content.

= 1 , 2 , ... b m = 0 , m = 1 , 2 , ... where a 0 , a m and b m are the coefficients corresponding to DC, the sines and the cosines respectively. The figures below show the signal being built up in steps starting with the fundamental and adding higher harmonics one by one. As the last figure in the series shows, the sawtooth ripple contains a large DC, a fundamental, and every harmonic but with a magnitude that diminishes with the index of the harmonic. In most (but not every) engineering application, it is good enough to think of the sawtooth as DC+fundamental frequency. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fig. 1: Frequency domain - Only 1st harmonic used Fig. 2: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC - Only 1st harmonic used. Fig. 3: Frequency domain - Only 1st and 2nd harmonics used 2
Fig. 4: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC - Only 1st and 2nd harmonics used Fig. 5: Frequency domain - Only 1st, 2nd and 3rd harmonics used 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fig. 6: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC + sin (6 πf in ) 6 π ( f in ) RC - Only 1st, 2nd and 3rd harmonics used Fig. 7: Frequency domain - Only 1st, 2nd, 3rd and 4th harmonics used 4
Fig. 8: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC + sin (6 πf in ) 6 π ( f in ) RC + sin (8 πf in ) 8 π ( f in ) RC - Only 1st, 2nd, 3rd and 4th harmonics used Fig. 9: Time domain signal - First 100 harmonics used 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern