R-2R ladder D/A converter problem

[Name15]

Homework Statement

Simplify in order to find voltage output.

Homework Equations

Vout= -Vref x (A + B/2 + C/4 + D/8)

The Attempt at a Solution

Firstly is this even correct?
Secondly, I have 2 voltages (2.5V and 5V), what should I do now? what is my Vref?

 

[Hesch]

what is my Vref?

Vref = 0V

I think that what is meant is that you must form a Thevenin equivalent from R1, R2:
V_th12 = 0V , R_th12 = R1 || R2 = 1Ω.
Now, this equivalent is connected in series with R3, giving R_th123 = 2Ω , V_th123 = 0V.

In this way you successive form new equivalents from left to right, until you have an equivalent for R1 . . R8 and V_D . . V_A.
Then you can calculate Vout.

 

[Name15]

Hi, I don't understand why Vref = 0. I have 2 inputs; 5V and 2.5V. I thought one or both of those would be Vref. Also if Vref is zero, wouldn't Vout also be zero?

 

[Hesch]

The 2.5V is not an input, but ( I assume ) an internal analog voltage you have calculated. I don't know how.

The ⊥ - symbol is Vref = 0V, and the terminals: A . . D are inputs ( something like TTL-level logic ( 0V = low level, 5V = high level ) ).

Vout will be a negative voltage, due to an inverting amplifier. Don't care about that, just calculate .

 

[gneill]

If you are looking for the $V_{ref}$ that fits your relevant equation, then set voltages B,C, and D to zero and then find the output due to voltage A alone. Then set $V_{ref}$ to a value that satisfies the reference equation for that scenario.

 

[Name15]

The problem is only C and D are 0V (A and B are both 5V), so I don't know how to do this problem. I've only been taught binary inputs where there is only one input.

 

[gneill]

The problem is only C and D are 0V (A and B are both 5V), so I don't know how to do this problem. I've only been taught binary inputs where there is only one input.

Just set B,C, and D to zero volts for purposes of finding your Vref. It should be clear that A,B,C,and D are inputs for this circuit, and apparently the logic levels are 0V and 5V.

After you determine Vref you can find the output given any combination of inputs by using your relevant equation.