Here's the LTspice simulation of AK's 555 circuit in post #9 with fixed resistors to give the desired duty-cycle of 0.1s ON with a 2s period:
I did not understand how you got these numbers when I saw this for the first time and numbers did not work in the book formula, but now I do. Book formulas don't work with parallel resistors. This is an interesting way to do this.
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Edit: Below's a modified circuit with only one diode.
The main advantage is that the timing circuit is not connected to the output, as in the above circuit, so any output loading has no effect on the timing.
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