Complex MOS ICs, such as microcontrollers, require on$-$chip data conversion

capabilities using only MOSFETs and capacitors. A weighted capacitor digital$-$

to$-$analog converter $($DAC$)$ is a good example of such a DAC.

$($i$)$ You are asked to design a $4-$bit weighted capacitor DAC and told that

the input capacitance of the available operational amplifier $($OPAMP$)$

buffer is $4$ pF$.$ Briefly explain the principle of operation of this DAC

and then determine the required capacitor values if the OPAMP input

capacitance forms part of the DAC circuit. $[8]$

$($ii$)$ What is the output voltage when the digital input is $1001,$ and the

reference voltage VREF $=5$ V$?$