When the circuit is connected as showed (pin2 "trig" and pin6 "thr" connected) it triggers itself and free runs as a multivibrator. The external capacitor charges through R1 and R2 and discharges through R2 only.
Thus the duty cycle may be precisely set by the ratio of these two resistors.
In the astable mode of operation, C1 charges and discharges between 1/3 Vcc and 2/3 Vcc. As in the triggered mode, the charge and discharge times and therefore frequency are independent of the supply
voltage.
NOTE: In this example we have,
R1 = 10 khoms
R2 = 5 khoms
C1 = 100 nF
C2 = 10 nF (Recommended value)
The charge time (output HIGH) is given by :
t1 = 0.693 (R1+ R2) C1
and the discharge time (output LOW) by :
t2 = 0.693 (R2) C1
Thus the total period T is given by :
T = t1 + t2 = 0.693 (R1 + 2R2) C1
The frequency of oscillation is them:
f = 1/T = 1.44 / ( (R1+ 2R2) C1)
and may be easily found by figure 15 of datasheet available below.
The duty cycle is given by :
D = R2 / (R1+ 2R2)
Datasheet:
http://www.st.com/resource/en/datasheet/ne555.pdf
