Machine riddle no.2 - 100 HZ signal producing

He knew that in synchronous generator, if the magnetic flux of the field system is distributed perfectly sinusoidal around the air gap, then e.m.f generated in each full-pitched armature coil will be sinusoidal completely.
He had an old and small 50HZ generator. He decided to use it for 100HZ signal producing.
For this purpose, he changed standard distributed windings of armature that located in stator slots. Also he connected one electronically mid-pass filter which tuned with 100HZ frequency in generator output.
The output voltage of generator was not sinusoidal and it is distorted by new space flux distortion. He had a lot of harmonics in output stage of generator, but he never observed 100HZ signal in filter output.
He more and more tried and changed the stator winding distribution frequently, but he couldn't to produce purposed signal.

Why? Why couldn't he?

#1
Sun, October 28, 2007 - 03:42
Other than pure sine wave have harmonics; but keep in mind it depends that Even or Odd
harmonics are in the distorted wave-form Square & Triangular waveforms have only one of the even or odd harmonics, I do not remember. Fourier Analysis can reveal it.
So filter may pass such harmonics if those are there in the distorted waveform.

#2
Sun, October 28, 2007 - 11:16
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, 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:

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