Analog to Digital Converter (Estimation of Input Voltage)

[GreenLRan]

Homework Statement

A 0-10 V, 10-bit A/D converter displays an output in straight binary code of 1010110111. Estimate the input voltage to within 1 LSB (Least Significant Bit).

Homework Equations

Resolution = Efsr/2^M. (where M= 10 in this case)

Eout = X/2^M (where Eout is the output Voltage, X is the actual input binary number [I'm also not sure if this equation is valid... I found it under the digital to analog converter section rather than analog to digital])

The Attempt at a Solution

I calculated the resolution and got it to be 10 V/2^10 = 9.77 mV. I am unsure of what to do next (my book is terrible). I was thinking of converting the output binary (which i believe to be the output voltage) to base 10, then I didn't know if there was an equation for the input Voltage as a function of Output voltage.


I also thought about taking the quantization error to be 1/2 the resolution. the somehow getting the input voltage from that.

Honestly, I am lost. Any help would be great. Thanks!

 

[chroot]

You're making this too hard.

You found the resolution, which is 9.77 mV per code. An input of 0 V to 9.77 mV would produce an output of 00 0000 0000. An input of 9.77 mV to 19.54 mV would produce an output of 00 0000 0001. Each additional step represents 9.77 mV.

Convert the 10-bit output code to decimal -- that's the number of codes above zero -- and multiply it by 9.77 mV. That's the boundary between the given 10-bit code and the next one up.

You might want to draw a picture of the transfer function (not all 2^10 codes of course) to help you visualize the behavior.

- Warren

 

[piercas]

I would first make sure that my equations are correct and applicable to the problem at hand. In this case, the resolution equation seems correct, but the output voltage equation may not be applicable to an analog to digital converter. I would suggest double checking with reliable sources or consulting with a colleague or mentor for clarification.

After confirming the equations, I would proceed with the solution by using the resolution value to estimate the input voltage. Since the output code is in straight binary, we can assume that the output voltage is equal to the input voltage. Thus, we can use the resolution value to estimate the input voltage to within 1 LSB.

In this case, the LSB is 9.77 mV, so the input voltage can be estimated to be within the range of 1010110111 ± 4.88 mV. This means that the input voltage could be anywhere between 3.86 V and 3.87 V. However, since the output code is an odd number, we can assume that the input voltage is closer to the upper bound, so the estimated input voltage would be approximately 3.87 V.

It is important to note that this is just an estimation and may not be the exact input voltage. To get a more accurate value, it would be necessary to use a more precise A/D converter or perform multiple measurements and take an average.