"Input Resistance Required to Minimize influance of Droop Error"

Input Resistance Required to Minimize influance of Droop Error

Figure: gainbudget.svg
Schematic diagram of proposed circuit

The Servo Function for the circuit is:

\begin{equation} \mathtt{\text{S}}=- \frac{A_{0} C_{f} R_{in} s}{R_{in} s \left(C_{f} \left(A_{0} + 1\right) + C_{s}\right) + 1} \end{equation}

The droop error is realted to the time constant from the Step Response , which is:

\begin{equation} \mu=- \frac{A_{0} C_{f} e^{- \frac{t}{R_{in} \left(C_{f} \left(A_{0} + 1\right) + C_{s}\right)}}}{C_{f} \left(A_{0} + 1\right) + C_{s}} \end{equation}

Therefore the Droop Error is determined by the equation:

\begin{equation} \tau=R_{in} \left(C_{f} \left(A_{0} + 1\right) + C_{s}\right) \end{equation}

Droop Error

If I take some budget from the Relative inaccuracy of the charge to voltage conversion to determine a maximum droop of 10.0% then I can determine a minimum Input Resistance for the op-amp.

\begin{equation} R_{in}=\frac{4.746 \cdot 10^{5}}{A_{0} + 151.0}\,\left[ \mathrm{\Omega}\right] \end{equation}

Go to Input-Resistance-Analysis_index

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Last project update: 2022-11-20 18:08:04