According to electromagnetic laws, the curl of electrical field (E) must be zero, for the circulation is zero, and the curl of magnetic field (H) is not zero, however; its circulation per unit area is the current density by Ampere's circuital law.Therefor in all magnetic systems, if some magnetic flux lines export from a surface of one volume of space, then same flux lines import to that volume via its other surfaces.

It means, for mathematic function of magnetic flux we can write: f(-x) = - f(x) that named odd function. Also because of core symmetrical construction, the flux function can be written by f ( x ) = f ( L – x ) where 2L is the function period.

Also according to Fourier analysis, each periodical function with those properties can be written with the sum of odd harmonic elements.

In ORTHOGONAL FUNCTIONS, Φ

_{i}, 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 a

_{i }= 0 for i = 0 and all other even terms and b

_{i }= 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, b

_{1}, is calculated as follows:

So the serviceman can never produce even harmonic flux ( 100HZ,200HZ,…) in generator gap.

Author : Hamid - From: Iran