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I am trying to understand this. When a induction motor is driven PWM Drives, the current is not chopped-up but filtered into nice sinosoidal wave because of inductive nature of motor.

I understand in a simple circuit shown below--when the voltage is first applied, the current slowly ramp up slowly.

schematic

simulate this circuit – Schematic created using CircuitLab

Now if I make voltage source to 0, the current will ramp down to 0.

Now instead of making voltage source 0, I open a switch the switch: the current would not ramp down , but drop suddenly.

so I think in motor drives(PWM), second case is happening. So why does motor current not dropped to zero?

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If you use actual switch, before dropping down the current will create huge voltage, you will see an arc, and all energy stored in the inductor will be wasted.

In a switching motor driver the switch is actually two switches- one to VCC, one to GND. So it does connect to zero.

Now, the sine you see on current is made not by filtering the PWM, but by current control loop.

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