Hello, I was working on some problems that my prof had assigned but his solutions were pretty unclear and did not reason his answers very justly. I have finished most of the question but I'm wondering if someone can help me out.

Here is the question:

My solutions:

I finished the first part and received the correct solutions, but I have no idea how to to the second part, where they ask to find a value for resistor R that will cause the gain error to be zero, noting that all the switches have an on-resistance of 200 ohms in this case.

I am not sure what they are relating the gain error to, as the gain is not constant in the previous example. Am I to pick an R that meets specification with an ideal case?

The solution that Jaeger and Blalock (Q12.79 - 4th Edition) posted was R = 1.0742 kohms. No idea how they came to that though.

Can anyone lend a hand?

Thanks!

 

Wherever you have 1.288k in your calculations, substitute it with x, and use the actual values for the others.

Outputs should be linear so double check your solution with other outputs once you solve for x. That, or compare your answer with the one you got from the other book.

 

In the printed question 5 there is the statement ...

"Suppose each switch in the DAC has an on-resistance of 200Ω and."

Was there further information that comes after the "and" part?

Perhaps you are allowed to tweak the Rref value as well and that might give a successful solution.

I actually don't see how simply changing the feedback resistance will reduce the linearity errors to zero. Have you tried plugging the stated value of R = 1.0742 kohms into your analysis and proved that the result is a zero error case?

I'd be interested to see the final outcome.

EDIT:

After some thought I suggest that adjusting Rref or R independently or in combination is unlikely to lead to zero error output linearity with the stated conditions applied.

I think one can discount the feedback resistance R quite easily. R is simply a scaling value. The linearity is entirely subject to what happens on the input side of the op-amp in the binary-weighted switched resistor network.