ex 6

The 10 kOhms resistor (Rctl) from the control pin of the 555 to ground modifies the reference voltages of the two comparators inside the timer. The reference voltage of the threshold comparator (control voltage) now becomes Vcc/2, the reference voltage of the trigger comparator now becomes Vcc/4. It can be verified from the graph; the output voltage goes low when the timing capacitor voltage crosses 2.5 V, the output goes high when the timing capacitor voltage crosses 1.25 V. In this circuit and in the traditional 555 astable multivibrator circuit the period of the low state is Tlow = [ln(2)](Rtb)(Ct). In the traditional 555 astable multivibrator circuit the period of the high state is Thigh = {ln [(Vcc - Vcc/3) / (Vcc - 2Vcc/3)]} (Rta + Rtb)(Ct) Thigh = {ln [( 2Vcc/3) / (Vcc/3)]} (Rta + Rtb)(Ct) Thigh = [ln (2)](Rta + Rtb)(Ct) The two periods have the same factor [ln (2)] but for the high state the timing resistor is always higher than the timing resistor in the low state, (Rta + Rtb) > Rtb. Thus the period of the high state is always greater than the period of the low state and the duty cycle is always greater than 50%. In this circuit the period of the high state is Thigh = {ln [(Vcc - Vcc/4) / (Vcc - Vcc/2)]} (Rta + Rtb)(Ct) Thigh = {ln [( 3Vcc/4) / (Vcc/2)]} (Rta + Rtb)(Ct) Thigh = [ln (3/2)](Rta + Rtb)(Ct) The factor [ln(2)] has now been lowered to [ln(3/2)] so the two periods can now be made equal to get a 50% duty cycle.