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

[foobag]

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?

 

[Bob S]

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

 

[foobag]

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.

 

[vk6kro]

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.

 

[foobag]

ok so a resolution of 0.008 volts would still be an acceptable answer?

 

[vk6kro]

Yes.