Digital Analog Converter design project

About running apps:

  • If you have Mathematica(R), download the .nb APP files.
  • If you don't have Mathematica(R), you will need to download the free  Wolfram CDF player . Then download .cdf  APP files and run.

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Additional thing to learn: We know that the resistors have quite a bit of variation, especially if you have only silver-band (10% variation) or gold-band (5% variation) resistors. If so, how well does your DAC work?




You can use the APP for this project to simulate the resistor variation and how it may affect your DAC performance. The key figure of merit is the magnitude of the resistor-based output error relative to the voltage of the least significant bit (LSB).

If you use 1 Volt, for example, then the LSB voltage is 1/256= 0.00390625 V which is =3.90625 mV or < 0.4% of your bit-ON voltage. Intuitively, you would guess that your 5%-error resistors would be not good enough. However, it is not as bad as you think. The reason is "random variation". The resistors can cancel each other error out a little and the chance for the error to be the largest possible is extremely small. Nevertheless, you will likely need 1% or 0.5% resistors for high performance, or even better resistors, such as 0.1% surface-mount stuffs for a typical 16-bit DAC that is commonly used for music players. 

We will ask the class to measure the node voltages (see the chart on the right) and collect the data of the whole class, and plot a histogram so that we can collectively study the error via the method of large ensemble population.




Items in your report: You will input a text (see the example below) that includes your name, student ID, and up to 160-character summary if you wish, of what you accomplish in this project. You will obtain the output signal and submit the chart as shown. (Very easy if you use the Apps developed for this course. For example, you can use this App on the Course App page to enter the output voltage as you flip the bits on-off). It would be even easier when you can program an Arduino or Raspberry Pi to output 7-bit ASCII binary code as input into your circuit and use Labview GPIB control of your DMM to read into your computer. You might not be able to do this yet in this course, but you will be by the time you are in Senior Capstone Design. This course is a beginning.



If you want to hear what your signal sounds like, you can make an array of repeated signals, select a sampling rate (e. g. 8 kHz, 11.025 kHz, 22.050 kHz etc.) and ListPlay it with Mathematica. (you can remove space character, which is "32" in decimal and %20 in hexadecimal that gives a high-frequency shrill component). For example, this is the sound of the above signal without space characters:

Did you listen to the sound? If you did, you just witnessed a digital-analog-conversion: your digital device (computer, tablet, or phone) has a built-in DAC that converts the digital signal we have into an electrical signal that drives the speakers so that we can hear.



Appendix

See below how to analyze your data. If you want an example of data file: download this: DAC_data_example. Put the file in any folder that is easy to access. For WIN OS, it is suggested that you put in My Documents. Any folder is OK as long as you know where it is. You can use the APP to open this example data file to see how it works.










 







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