So i have calculated the settling time for the capacitor C in an RC circuit. The RC circuit is the result of connecting an ADC with a mutiplexer. The ADC is a 12-bit type.
In the assignment information was given in order to fulfill the equation Vc=Vin(1-e^-t/RC) in order to find the time t (t=1164.487 ns).
Now the time is still the parameter that is to be calculated but only 6 of the most significant bits of the result should be taking into account. So i was wondering, what is the effect of just looking at the 6 most significant bits of the result? What factors changes going in to calculating the settling time of the capacitor once more?
Thanks!
Best Answer
The settling time is infinity so you don't really need to do any calculations - you just need to understand that a capacitor will never perfectly charge to the full value on a simple RC circuit: -
(source: gsu.edu)
However, for each time constant (R*C) it will get closer by 63%\$^1\$ so, in the first RC time period the cap will attain 63% of the value of the input voltage. At the end of the 2nd RC time period, the gap will close by another 63% and the cap will attain a voltage of 86% of the input voltage.
Hint - You have to work how much of an ONLY error 6 bits gives you and how much that represents in RC time periods.
\$^1\$ the 63% comes from \$1-e^{-1}\$