Can this schematic be modified to set the freq of square wave?

Hello everyone!

I met a schematic that is a pulse generator with variable duty cycle, which looks something like this:

The potmeter RV4 is adjusting the duty cycle. I'm wondering if it was possible to modify this schematic that I get to modify the frequency as well, like in this schematic:

The frequency is controlled by RV4 and C, while the duty cycle is controlled by the porportion of resistance of RV4 on pins 1,3 in the first schematic. I'm breaking my brain trying to figure out how I could combine the 2 schematics and have the ability to control the duty cycle as well as the frequency.

Any tips are appreciated!

To the first schematic, add another variable resistor between the wiper of RV4 and the junction of R12 and R15.

That was my intuition as well. What I noticed though, is that the variable resistors resistor value gets added to the resistance of RV4, which does change frequency, but also limits how much I can change the duty cycle.

Assume the new variable resistor has a max value of 1MOhm. It's 10xRV4, which means I am now limiting the duty cycle between 40-60%. At least this is what practice showed.

I'm wondering if the frequncy and duty cycle can be changes independently from eachother.

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thank you!

Actually, I tried this circuit with a comperator (+ pullup resistor).

Doesn't work. I suppose that is because comperators sink current and not source them. There is a bit of a difference between the two, I'm not sure this can easily be done with a comparator.

You might need a current source to bias the comparator output in that case.