The circuit in Figure 1 satisfies all these criteria. The circuit delivers a unipolar (adjustable from 0 to 12V) pulse with adjustable frequency and pulse width. The first half of a dual, retriggerable monostable multivibrator, IC1A, generates the frequency of the pulse train. The 100-k potentiometer, R1, along with R2 and C1, sets the adjustable frequency. R3, R4, and C2 set the adjustable pulse width in the second section of the multivibrator, IC1B.
multivibrator circuit with variable frequency and duty cycle, 10 Hz-20 KHz (schematic)
Hackaday The 555 operation is almost identical to the astable , however the trigger input is not connected to the timing capacitor. This means the circuit does not “self trigger”, requiring an input (in this case from the astable