R-2R ladder D/A converter problem

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Discussion Overview

The discussion revolves around the calculation of voltage output for an R-2R ladder digital-to-analog (D/A) converter. Participants are exploring how to determine the reference voltage (Vref) and its implications for the output voltage (Vout) based on given input voltages.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the correctness of the initial equation for Vout and seeks clarification on the role of the two voltages (2.5V and 5V) in determining Vref.
  • Another participant suggests that Vref should be 0V and proposes forming a Thevenin equivalent circuit to calculate Vout.
  • A different participant expresses confusion about why Vref is considered 0V, given the presence of two input voltages, and questions the implications for Vout.
  • Another contributor speculates that the 2.5V might be an internal voltage rather than an input and emphasizes that Vout will be negative due to the inverting nature of the amplifier.
  • One participant advises setting certain voltages (B, C, and D) to zero to find Vref that fits the equation, suggesting a method to isolate the contribution of voltage A.
  • Another participant reiterates the need to set C and D to 0V while noting that A and B are both at 5V, indicating a lack of familiarity with multiple input scenarios in binary systems.

Areas of Agreement / Disagreement

Participants express differing views on the value of Vref, with some asserting it is 0V while others question this assumption based on the input voltages. The discussion remains unresolved regarding the correct approach to determining Vref and its effect on Vout.

Contextual Notes

There are uncertainties regarding the definitions of inputs and the treatment of internal voltages. The discussion reflects varying levels of familiarity with the concepts involved in analyzing the R-2R ladder circuit.

Name15
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Homework Statement


R-2R ladder question.png

Simplify in order to find voltage output.

Homework Equations


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

The Attempt at a Solution


R-2R ladder Q attempt.png

Firstly is this even correct?
Secondly, I have 2 voltages (2.5V and 5V), what should I do now? what is my Vref?
 
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Name15 said:
what is my Vref?
Vref = 0V

I think that what is meant is that you must form a Thevenin equivalent from R1, R2:
Vth12 = 0V , Rth12 = R1 || R2 = 1Ω.
Now, this equivalent is connected in series with R3, giving Rth123 = 2Ω , Vth123 = 0V.

In this way you successive form new equivalents from left to right, until you have an equivalent for R1 . . R8 and VD . . VA.
Then you can calculate Vout.
 
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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?
 
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 :smile:.
 
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.
 
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.
 
Name15 said:
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.
 

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