Electrical – Binary Weighted DAC

dac

I tried to do this question but do not understand what this graph is. I know it is a binary value for the D0,D1,D2,D3 inputs but what is the value ?

And is this the correct formula for final Vout?

$$ V_{out}= -(\frac{D3}{1}+\frac{D2}{2}+\frac{D1}{4}+\frac{D0}{8})*V_{in}*\frac{Rf}{R}$$

QUESTION

Best Answer

While this is a summing amplifier, the output voltage will change depending on when \$D_0,D_1,\$ etc. is on or off, which is provided to you in the graph on right.

First of all, let me explain how a voltage representation can determine a binary number. This graph below is not related to your problem but it is an example of how a binary number can change depending on the output. Everyone has seen the "stair step" DAC graph before.

enter image description here

Do you see how different output voltage can alter the binary number? This is an example of DAC. Now let's get back at your problem. You given the duty cycle of D1,D2, etc. Now look at this figure below.

enter image description here This is from the Sedra/Smith (7th edition) textbook. Assuming that \$D_0,D_1,\$ etc. have the same input voltage, the binary number that will be represented when each input is high or low. The output voltage will tell you what binary number it's representing. Create truth table of each value to see the output voltage for every single possibility starting from 0000 to 1111. Now use your graph that was given to you and see at time \$t\$. Depending on that output voltage, you will see what binary value you will receive. Think of your graph that is given as switches for each network you have on the amplifier, like the picture above.

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