Switched CapacitorsIts difficult to construct a resistor with required accuracy and its relatively easy to implement capacitors and switches as well as opamps. Simulated resistors made by capacitors and MOSFET switch. Resistors are to be simulated because MOSFET connected as a resistor cannot make a linear resistor. Using switched capacitors networks analog circuits can be integrated along with digital circuits on the same chip using fabrication technology (CMOS technology). Switching Actiona) VGS > Vcr(Threshold Voltage)MOS is ON (R10k)Short Circuit ( )b) VGS < VcrMOS is OFF (R100M)OPEN Circuit ( )

The simplest switched capacitor (SC) circuit is the switched capacitor resistor, made of one capacitor C and two switches S1and S2which connect the capacitor with a given frequency alternately to the input and output of the SC. Each switching cycle transfers a chargefrom the input to the output at the switching frequency. The chargeqon a capacitorCwith a voltageVbetween the plates is given by:

whereVis the voltage across the capacitor. Therefore, when S1is closed while S2is open, the charge stored in the capacitor CSis:

When S2is closed, some of that charge is transferred out of the capacitor, after which the charge that remains in capacitor CSis:

Thus, the charge moved out of the capacitor to the output is:

Because this chargeqis transferred at a ratef, the rate of transfer of charge per unit time is:

LetVbe the voltage across the SC from input to output. So:

So the equivalent resistanceR(i.e., the voltagecurrent relationship) is:

Thus, the SC behaves like aresistorwhose value depends on capacitanceCSand switching frequencyf.Example