Hello..
I have an assignment with the 555 IC in the astable mode.
I'm trying to demonstrate the tHIGH and tLOW formulas.
tHIGH =ln (2)*(Ra+Rb)*C
tLOW = ln (2)*Rb*C
Now, for the tLOW I'm using the discharge capacitor equation:
τ = Rb*C
vC = V0*e^(-t/τ)
⇔(1/3)*Vcc = (2/3)*Vcc*e^(-t/τ)
⇔1/2 = e^(-t/τ)
⇔ln (1/2) = -t/τ
⇔t = ln (2)*Rb*C
Now for the tHIGH I'm using the charge equation formula: vC = V0*(1-e^(-t/τ)), with τ = Ra + Rb
vC = V0*(1-e^(-t/τ))
⇔(2/3)*Vcc = (1/3)*Vcc*(1-e^(-t/τ))
⇔2 = 1 - e^(-t/τ)
⇔ln (1) = -(-t/τ)
but this is not looking correct... ln (1) = 0...
Where am I going wrong?
I have an assignment with the 555 IC in the astable mode.
I'm trying to demonstrate the tHIGH and tLOW formulas.
tHIGH =ln (2)*(Ra+Rb)*C
tLOW = ln (2)*Rb*C
Now, for the tLOW I'm using the discharge capacitor equation:
τ = Rb*C
vC = V0*e^(-t/τ)
⇔(1/3)*Vcc = (2/3)*Vcc*e^(-t/τ)
⇔1/2 = e^(-t/τ)
⇔ln (1/2) = -t/τ
⇔t = ln (2)*Rb*C
Now for the tHIGH I'm using the charge equation formula: vC = V0*(1-e^(-t/τ)), with τ = Ra + Rb
vC = V0*(1-e^(-t/τ))
⇔(2/3)*Vcc = (1/3)*Vcc*(1-e^(-t/τ))
⇔2 = 1 - e^(-t/τ)
⇔ln (1) = -(-t/τ)
but this is not looking correct... ln (1) = 0...
Where am I going wrong?