Problem $18$: $(45$ points$)$

A voltage$-$controlled oscillator $($ VCO $)$ is an electronic oscillator whose frequency is controlled by an input voltage. The C$-$code in Figure $2$ implements a VCO using the dsPIC$33$EP$64$MC$502-$I$/$SP microcontroller.

$(7$ points$)$ Complete lines $23$ and $24$ to specify the peripheral pin to which the analog control voltage is applied. Justify your answer in one or two short sentences.

$(6$ points$)$ Add comments to lines $26,46,$ and $48.$

$(12$ points$)$ Specify an equation for PTPER in line $51,$ ensuring the output frequency linearly changed from $10$ kHz to $2$ kHz as the control voltage rises from $0$ V to $3\mathrm{.}3$ V $.$ Explain your logic in complete sentences and demonstrate relevant calculations.

$(3$ points$)$ Specify an equation for PDC$2$ in line $52$ so that the duty cycle of the square$-$wave output remains approximately $40\%$ regardless of the square$-$wave frequency. Justify your answer in one or two short sentences.

$(10$ points$)$ Modify the codes to accommodate the ADC module in $12-$bit operation mode. Provide the line numbers and corresponding modified codes. Explain your logic in complete sentences and show appropriate calculations.

$(7$ points$)$ Compare the advantages and disadvantages of $10-$bit and $12-$bit operation modes$\mathrm{.}232425$ AD$1$CHSObits. CHOSA$2=1$;$26$ AD$1$CON$1$bits.ADON $=1$;void Init$\_$PWM$\_$module$($void$)\{$PTCONbits$.$PTEN $=0$;PTPER $=737$;PDC$2=368$;IOCON$2$bits.PMOD $=1$;IOCON$2$bits.PENH $=1$;FCLCON$2$bits.FLTMOD $=3$;PTCONbits.PTEN $=1$;$\}$int main$($void$)\{$Init$\_$ADC$()$;Init$\_$PWM$\_$module$()$;while $(1)\{\_\_$delay$\_$ms$(50)$;AD$1$CON$1$bits.SAMP $=1$;$\_\_$delay$\_$us$(10)$;AD$1$CON$1$bits.SAMP $=0$;while $(!$AD$1$CON$1$bits.DONE$)$;PTPER;PDC$2$;$\}\}$

Figure $2$: C code for Problem $18.$