Pulse generator with single op amp and diode
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The basic relaxation oscillator.

How it works:


OUT is initially low, C1 is discharging and the threshold voltage, Vt, is at 1/3 supply. (R1 and R2 form a half-supply voltage divider but R3 is in parallel with R2 pulling it down to V1/3.)
When Vc drops below V1/3 the op-amp output switches high, Vt changes to 2/3 V1 and C1 starts charging.
The half-cycle time could be roughly approximated by \$ \tau = R4 \cdot C1 = 10k \cdot 1µ = 10 \ \mathrm{ms} \$ if the capacitor was charging from 0 to 63%. As it is actually charging from 33% to 66% the time will be somewhat shorter - about 7 ms on the simulation below.




Figure 2. The waveforms obtained from Figure 1.

The simplest way to control the duty cycle is to control the charge and discharge times independently with diodes as shown in Figure 3.







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Figure 3. Duty-cycle control with diodes.



Figure 4. Resultant simulation.







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Figure 5. By adding a potentiometer the duty cycle can be adjusted while maintaining the frequency reasonably stable.









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Figure 6. You can also leave out one of the diodes. In this case discharging C1 is done through R5 only while charging is done through R5 and R4.



There's a useful calculator at Must Calculate that will work out the time constants for you. For the timing of my Figure 1 it worked out 6.93 ms.

You can play with the CircuitLab simulations by "editing" my question and editing the schematic. Just don't save them on your way out!

Note that I haven't included the voltage drop of the diodes in my calculations. It will affect the results a bit but the simulator should pick that up for you.