About control 10V PWM using 5V sensor

Hello there,
I am studying on a ebike motor controller. I control it with a PWM controller using the POT that working on 10V. I have a e-bike throttle by which i want to control speed using this through PWM controller. Main problem is the e bike throttle working on hall sensor and can work only on <5V. I am looking for the methods by which I control 0-10V PWM using 0-5V signal. I found op-amp can do that but I don't have much idea about that.
If you have any solution or suggestion please mentioned.

To make 10 volt PWM use a transistor.
To make things more clear please draw a wiring and post it. Pen and paper is fine.


As I shown in image. the hall effect sensor that is available only is in range of 0-5V signal whereas PWM require 0-10V signal. How should I proceed.

You can't replace a pot by a hall sensor. What is the idea?

POT and hall sensor, both are analog device in this case. POT meter I have to vary it by hand in all value. But in hall sensor, Its cased in a throttle body same like bike or car throttle - we have to push it manually but will become in it's initial position as we off are hand from it.
That's why I want to replace POT with hall sensor. But main problem is POT signal range is 0-10V that controller required. And hall sensor working range is 0-5V only.

This will do it

Proceed by searching for linear hall effect sensor for automotive use. That will ensure your device will operate in the voltage range you need.

Thanks for guide me.
I have attempted to simulate the circuit I designed using the LM358 as an op-amp. I will test it, and as I proceed, I'll provide updates.

With a 358 the supply needs to be 12V or more and the output may not go all the way to 0V

Are you sure that the control is not just an analog voltage, 0-10V DC?

The very simplest approach for that is to use a 0-10V DAC module.

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