SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure C.19 – Amplitudes of harmonic components.
Figure C.18 and Figure C.19 should be compared to understand the harmonic content. The rotor-
stator flux linkages (or peak) are again reproduced below.
(C.14): ( ) NDY B cos( ) (CFP winding, sine rotor flux)
R r p r
(C.17): R( r) NDY Bpcos(
r)
(sine winding, sine rotor flux)
4
(C.18):
R NDY Bp
(CFP winding, squarewave rotor flux)
2
(C.19): ( ) NDY B cos( ) (sine winding, squarewave rotor flux)
R r p r
Looking at the amplitudes of rotor flux, the sinusoidal rotor flux profile has only the fundamental;
its amplitude is unity because the definition of the rotor flux is given by the peak value Bp. Since
the squarewave rotor flux was also defined by the peak value (of the squarewave) Bp, it’s
fundamental component is 4/ larger and the harmonics are given by the Fourier series of a
squarewave.
Now looking at the MMF (which is used here to “represent” the winding) we recall that the CFP
winding generated the maximum achievable amplitude for each MMF harmonic and that it did
not attenuate the fundamental. Therefore we use the Fourier series of a squarewave, but note well:
since “unity gain” is defined by normalizing the fundamental (as opposed to the squarewave
amplitude like usual) the expressions is scaled by /4 and the 4/ coefficient is eliminated.
Looking at the sinusoidal winding it is seen that its fundamental (and only) component is /4 of
unity; this directly follows from the previous statement and shows clearly the /4 attenuation of
301