"Design equations for $R$ and $C$"

Design equations for $R$ and $C$

The unit step response

\begin{equation} \mu_{t}=1 - e^{- \frac{t}{C R}} \end{equation}

The settling error versus time

\begin{equation} \epsilon_{t}=e^{- \frac{t}{C R}} \end{equation}

The n-bit settling time

\begin{equation} \tau_{s}=C R n \log{\left(2 \right)} \end{equation}

The design equation for $R$

\begin{equation} R=\frac{\tau_{s}}{C n \log{\left(2 \right)}} \end{equation}

The design equation for $C$

\begin{equation} C=\frac{\tau_{s}}{R n \log{\left(2 \right)}} \end{equation}

Numeric example.

We will determine R for the case in which we need 10 bit settling within 100ns with a capacitance C=10pF. We obtain:

\begin{equation} R=1443.0 \end{equation}

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Last project update: 2021-04-04 13:40:27