Circuit Theory II Lesson 4

1. Circuit Theory IILesson 4 Nilsson pp. 839 – 845 Irwin pp. 567 – 572 Even and Odd Symmetries Half- and Quarter-Wave Symmetries Computational Example Special Fourier Series

2. Types of Symmetry Even-Function Symmetry No sine components present in Fourier Series Odd-Function Symmetry No cosine components present in Fourier Series

3. Types of Symmetry Half-Wave Symmetry When the function is multiplied by –1 and shifted one-half period, the same function is obtained. No d.c. term and no even-harmonics present in Fourier Series

4. Types of Symmetry Quarter-Wave Symmetry • The function has half-wave Symmetry • There is symmetry about the midpoint of the positive and negative half-cycles Need only integrate only over a quarter period

5. Fourier Series of Square Wave

6. Triangle Wave yes no Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry

7. Right Triangular Wave yes no Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry

8. Saw Tooth Wave yes no Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry