Part $2-$ Digital to Analog Converter $($DAC$)$

In this part of the project, you will build a $4-$bit digital to analog converter $($DAC$).$

$-$ You must investigate DACs that are available in Literature. You should discuss at least $2$ different DAC. You will design an R$-2$R Ladder DAC.

$-$ Propose the schematic of a $4-$bit R$-2$R Ladder DAC.

$-$ Do a comprehensive theoretical analysis of the circuit. DETERMINE THE $\backslash ($ v$\_\{\backslash$text $\{$out $\}\}\backslash )$ as functions of the bit values.

$-$ Implement it in LTSpice.

$-$ Implement it in a physical circuit.

$-$ Do necessary measurements to completely validate the circuit and the desired behavior.

$-$ Feed the output of the ADC in the $\backslash (1^\{\backslash$text $\{$st $\}\}\backslash )$ part as the input of the DAC. Discuss the results.

An example of a $3$ bit version is provided in Figure $3.$ You can modify it as needed. You can use $\backslash (\backslash$pm $10\backslash$mathrm$\{$~V$\}\backslash )$ power supplies for the $741$ opamp. Pay careful attention to which resistors are $\backslash (1\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash )$ and which are $\backslash (2\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash ),$ this is critical for proper operation of the circuit.

ANALYZE THE MODIFIED CIRCUIT USING APPROPRIATE TECNIQUES AND DETERMINE THE v$\_$out as functions of the bit values.

Measure and record the output voltage of the circuit for each of the $164-$bit words.

NOTE THAT THE ORGANIZATION OF BITS IS REVERSED. THAT IS S$1$ REPRESENTS THE MSB WHEREAS S$3$ REPRESENTS THE LSB$.$ For instance, if you want to represent $1000,$ then the S$1$ should be in right position, but the rest should be in left position to be grounded.

Figure $3.$ A $3-$bit R$-2$R Ladder DAC Schematic

Double check that your recorded values increase as the binary value of the $4-$bit word increases, if they don't then you have likely made a mistake somewhere.