An amplifier with a switched-capacitor circuit has an input resistor value of 20K ohms. If you want the switched-capacitor to emulate a 10K ohm resistor, at what frequency must the switch be operated? The value of the capacitor is 1000pF.

Question

Quizplus · Accepted Answer

The equivalent resistance $R_{eq}$ of a switched-capacitor is given by the formula $R_{eq} = \frac{1}{fC}$, where $f$ is the switching frequency and $C$ is the capacitance. Rearranging the formula to solve for $f$, we get $f = \frac{1}{R_{eq}C}$. Plugging in the values $R_{eq} = 10K\Omega = 10,000\Omega$ and $C = 1000pF = 1000 \times 10^{-12}F$, we find $f = \frac{1}{10,000 \times 1000 \times 10^{-12}} = 100,000,000Hz = 100KHz$.

An Amplifier with a Switched-Capacitor Circuit Has an Input Resistor