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