RC time formula

hi,

i have read articles about computing time,

one says T1 = 0.67 (Ra + Rb) C F = 1.49/(Ra + 2Rb) C

the other says T1 + 0.693 (Ra + Rb) C F=1.44/(Ra+2Rb)C

in computation the time difference is very small, but which one is the correct formula.

T = 1.0986RaC others they just round it to 1.1. where or how this constant figure was derived?

T = 0.693 (Ra + Rb) C, where or how this 0.693 was derived?

thanx

I asked a similar question over on Google awhile back, this is what i got.

For the monostable:

2/3 = 1-e ^(-t/RC)
-1/3 = -e ^(-t/RC)
1/3 = e ^( -t/RC)
ln(1/3) = -t/RC
(Use your scientific calculator to find the natural logrythm (ln or e^x) of 1/3)
-1.0986123 = -t/RC
t= 1.0986123 RC
Rounding off gives: 1.1RC

For the astable:

Charging: t1 = -ln(1/2)(Ra+Rb)C
(natural log of 1/2=-0.69314718)
= 0.693(Ra+Rb)C

Discharging: t2 = -ln(1/2)(Rb)C
= .693(Rb)C

Total period T = t1+t2

time constant

Looks like the Time for a 555 timer in the astable mode.

The forumlae are of 555 astable and monostable multivibrator.

For astable
Ton = 0.693*(Ra+Rb)*C
Toff = 0.693*Rb*C
Duty cycle = Ton / (Ton + Toff) = (Ra+Rb)/(Ra+2Rb)
Frequrnct = 1 / (Ton + Toff)

For monostable
Ton = 1.1*R*C

time formula

hi,

thanx to nettron1000, k7elp60, & kinjalp.

have been using these formulas but had never known where where the 1.0986 and 0.693 came from. again thanx