Design equations

Circuit diagram

Initial specifications

performance specification

Table performance specification
symboldescriptionvalueunits
$n_{s}$Number of bits for $\tau_{n_s}$$8$
$\tau_{n s}$Maximum n-bit settling time$1.0 \cdot 10^{-6}$$\mathrm{s}$
$v_{n max}$Maximum RMS output voltage noise$1.0 \cdot 10^{-5}$$\mathrm{V}$

Output voltage noise

Spectral density of the output voltage noise

\begin{equation} S_{vno}=\frac{1.035 \cdot 10^{8} R}{2.5 \cdot 10^{28} \pi^{2} C^{2} R^{2} f^{2} + 6.25 \cdot 10^{27}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

RMS output noise voltage

\begin{equation} V_{no}=\frac{6.436 \cdot 10^{-11}}{C^{0.5}}\,\left[ \mathrm{V}\right] \end{equation}

Minimum capacitance

\begin{equation} C_{min}=4.142 \cdot 10^{-11} \end{equation}

Selected capacitance

\begin{equation} C_{sel}=4.7 \cdot 10^{-11} \end{equation}

Unit step response

\begin{equation} a{\left(t \right)}=1 - e^{- \frac{t}{C R}} \end{equation}

Error versus time

\begin{equation} \epsilon{\left(t \right)}=e^{- \frac{t}{C R}} \end{equation}

Settling error to $n_s$ bits

\begin{equation} \tau_{s}=7.819 \cdot 10^{-7} \end{equation}

Maximum resistance

\begin{equation} R_{max}=3837.0 \end{equation}

Selected resistance

\begin{equation} R_{sel}=3000.0 \end{equation}

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SLiCAP: Symbolic Linear Circuit Analysis Program, Version 2.0.1 © 2009-2024 SLiCAP development team

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Last project update: 2024-10-21 14:35:10