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This is a switching circuit used for a switched reluctance motor. In this circuit there is a 47μF capacitor on the right side. What is the capacitors function in this circuit?

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    \$\begingroup\$ I suspect a 47u cap would do anything to any motor larger than a clock. More likely it's used to filter out the interference generated by the sparks of the brush so that it won't contaminate the 12V supply. \$\endgroup\$ – user3528438 Aug 2 '17 at 17:56
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The 47-uF capacitor is not used to supply the inrush current, which would be needed to start the motor: it's value is too low to do the job (the IGBT handles 7A, so the motor will be quite powerful).

It is likely used as a noise suppressor.

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This capacitor is used to keep the 12V supply 'stiff' -- i.e. reduces voltage dips when the motor draws current -- to prevent fluctuations in torque/speed under load. Put this cap as close to your motor as possible, or at least the connector for the motor on the PCB.

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This capacitor is used to keep the 12V supply stable as possible.

According to the equation P=VI, when the motor draws a high current, the voltage across the motor drops, when the voltage drops, your motor speed reduces. Therefore if you have a capacitor in parallel to the motor, in times of voltage drops, your capacitor provides that necessary current to the motor so that your motor voltage remains stable, thus keeping a constant speed.

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