Why is driving a proportional solenoid with PWM more efficient than resistive current control?

In PWM the switching element is either fully on or fully off, so the power lost across it is very low. In resistive control the unwanted voltage is turned into heat; supplying 6V to a coil from a 12V supply means burning almost as much power in the resistor as goes to the coil. The coil's inductance smooths the pulses into an average current.

In resistive (linear) drive, the excess voltage is dropped across a semiconductor or resistor and converted entirely into heat. That is both an efficiency loss and a matter of heat sinks, enclosure volume and thermal failure risk.

In PWM, the switch turns fully on and fully off thousands of times per second. Since the voltage across it is low while conducting and the current is zero while off, losses are minimal. The coil's own inductance behaves like a low-pass filter; the current flows not as discrete pulses but as a smooth average corresponding to the duty cycle.

Practical gains:

The card we call a proportional amplifier does exactly this job: it converts the voltage signal coming from the joystick into the regulated current signal the valve needs.

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