This is the end view of a low-cost Mabuchi RE-36 dc brush motor with endcap removed. The motor induced-voltage waveforms are derived from the motor geometry.
Induced-Voltage Waveform from Motor Geometry
As magnet edge sweeps across face of winding, flux through winding loop area changes, inducing a voltage into loop proportional to rate of flux change.
Constant w me and Br results in linearly changing l . Induced voltage is time derivative of l .
The waveform shown to the left is produced with full-pitch poles: magnet (pole) length = winding loop length.
For magnet arcs shorter than the winding arc lengths, no voltage induced while D l = 0 - while two edges are within loop area.
For given winding loop all turns go through same armature slots, resulting in square wave. If turns are distributed spatially in slots, other waveforms can be produced (such as sinusoids).
Example
Axial motor axis laid out linearly as developed diagram.
24° /div, 2-pole
Three phase-windings, U, V, and W. Two magnets WHT and BLU.
Shift magnets to right, over windings and draw flux waveforms. Flux value = amount of magnet-winding overlap.
Phase-windings connected to subtract in pairs: XY = X – Y
Induced voltages in series-pairs of phase-windings are time derivative of series-pair fluxes.
Voltage waveforms are squarewaves with deadtimes between half-cycles.
