555 timer equation
Hi,
if you know the equations of carging, and discharging a capacitor you will get the equations you mentioned.
the upper and lower limits of the capacitor voltages are 2/3 Vcc, and 1/3 Vcc (from NE555 datasheet).
the equation of discharging a capacitor is Vc(t) =2/3 Vcc * exp-t/Rc substitute Tlow for t and 1/3 Vcc for Vc(t) this will determine Tlow.
As for T high the following equation applies
Vc(t) = (Vc final _ Vc initial) (1- exp-t/rc) + Vc initial
substitute Vc final =Vcc ( the capacitor will try to charge to a final valur of Vcc but the comparator will allow it to charge t to 2/3 Vcc only and will change the output state ), Vc initial = 1/3 Vcc, and t=Thigh
If you do so you will get the equqtions you mentioned.
If I can help you more let me know
regards,
M.Mokhtar