Calculating DAC Decimal Resolution with R-2R Ladder and 1 Volt Input

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Discussion Overview

The discussion revolves around calculating the decimal resolution of a digital to analog converter (DAC) using an R-2R ladder configuration with 7 bits and a 1 volt input. Participants explore the implications of this setup on the resolution and how to express it in volts.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions how to determine the decimal resolution of a 7-bit R-2R ladder DAC with a 1 volt input, suggesting that the smallest decimal equivalent resolution might be 1/128.
  • Another participant states that with 7 bits, the resolution is ±0.004 volts, based on the full scale of 1 volt.
  • A different participant expresses confusion regarding the ±0.004 volts figure, calculating a resolution of ±0.0078 volts instead.
  • One participant clarifies that the discussion involves the input to an A to D converter, explaining the output levels and their corresponding input voltage ranges, which align with the previous resolution claim.
  • A participant inquires if a resolution of 0.008 volts would be acceptable, to which another participant agrees.

Areas of Agreement / Disagreement

There is disagreement regarding the exact decimal resolution values, with some participants proposing different calculations. The discussion remains unresolved as participants have not reached a consensus on the correct resolution figure.

Contextual Notes

Participants' calculations depend on interpretations of resolution and the specifics of the DAC's output levels, which may involve assumptions about the input voltage and the nature of the conversion process.

foobag
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I have a question about digital to analog converters.

Lets say I am given a R-2R ladder type DAC with 7 "wrungs".

This implies that I have 2^7 = 128 bits.

Now if I want to represent an equivalent decimal resolution of that DAC, how do I go about doing that?

Let's say the input voltage is 1 volt.

Regardless does this mean my smallest decimal equivalent resolution will be:

1/128?
 
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You have 7 bits (binary) with 1 part in 128 (± ½ LSB (least significant bit)) resolution.
So with 1 volt full scale, the resolution is ±0.004 volts.

Bob S
 
i am a bit confused how you arrived at +/- 0.004 volts.

I understand 1 part in 128 resolution, but converting that scale back to 1 volt full scale I am getting: +/- 0.0078 volts.
 
You are now talking about the input to an A to D converter which has 128 possible output levels from an input of up to 1 volt.

Output level 0 will be produced from an input of between 0 and 0.00781 volts.
Output level 1 will be produced from an input of between 0.00781 volts and 0.0156 volts.
and so on, with all steps being 0.00781 volts wide.

You could say this was 0.0039 volts +/- 0.0039 volts for level 0 out
or 0.0117 volts +/- 0.0039 volts for level 1 out...
and so on.

This is the same as Bob said.
 
ok so a resolution of 0.008 volts would still be an acceptable answer?
 
Yes.
 

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