As you know the figure of transformer magnetizing current goes to square wave related to degree of its core saturation.
In ORTHOGONAL FUNCTIONS, Φi
, defined in a≤x ≤b is called orthogonal (or unitary, if complex) if it satisfies the following condition:
The Fourier series of an even function contain only cosine terms and may also include a DC component. Thus, the coefficients bi are zero.
The Fourier series of an odd function contain only sine terms. The coefficients ai are all zero.
The Fourier series of a function with half–wave symmetry contain only odd harmonic terms with ai
= 0 for i = 0 and all other even terms and bi
= 0 for all even values of i.
For example consider the periodic function of square function in Figure below
Applying the orthogonality relations , we find that all ai coefficients are zero. We also can determine the coefficients associated with the sine function in this series. For example, the first term, b1
, is calculated as follows:
As you see in square wave the peak amount of bigger harmonic will be smaller (bi
=4/iπ) in comparison of smaller harmonic.