Question

Consider a digital system where an input voltage Vin is converted to digital with an ADC, the output of which is converted back to an analog output voltage Vout with a DAC. Bit resolution n=12, VFS=15V,

Find Vout for Vin=6.83V

Answer 1

Vout=6.83 v

Step-by-step explanation:

The resolution steps are going to be from 0.00366 V from the DAC and from the ADC, with 12 bits resolution and VFS =15v

Because, 12 bits resolution means
`2^(12)` binary numbers, or 4096 positions. So to obtain the resolution in volts, is neccesary to divide the max input voltage in 4096.

`2^(12)=4096\\ \\VFS=15v\\\\Voltage_step=(VFS)/(4096) =(15)/(4096)=0.0036 v`

Then Vin=6.83, so the output from the ADC is Vin/Voltage_step

`ADC_(out) =(V_(in) )/(Voltagestep) =(6.83)/(0.00366) =1866`

in base 2: ADC out= 011101001010

Now, this is the same DAC input= 011101001010

And to calculate the output we multiply by the same resolution step

`011101001010_(2) =1866_(10) \\\\V_(out) =1866*0.00366=6.83 v`