University of California at Berkeley Physics 111 Laboratory Basic Semiconductor Circuits (BSC) Lab 10 Analog to Digital and Digital to Analog Conversion ©2013 by the Regents of the University of California. All rights reserved. References: Wells & Wells Entire Book on LabView. Horowitz & Hill Chapters 8.01-8.04, 9.15-9.23 and Chapter 15. Web resource Wikipedia.org In this lab you will learn how to convert data between analog and digital, and the many pitfalls in doing so. Several LabVIEW programs are mentioned in this lab writeup. Many of these programs can be downloaded from http://socrates.berkeley.edu/~phylabs/bsc/LV_Programs and can also be found on your lab computers in 111 Lab Network Drive on your computer in My Computer folder. Two versions of the programs are typically available for download: an executable version that should run without LabVIEW (but requires a large download from National Instruments, which should occur automatically, and only needs to be done once) and should run on PC’s, Mac’s and Linux boxes; and the original LabVIEW source code which requires LabVIEW. Before coming to class complete this list of tasks: • Completely read this Lab Write-up • Answer the pre-lab questions utilizing the references and this write-up • Perform any circuit calculations or anything that can be done outside of lab. • Begin and if possible complete programming tasks in this lab write-up • Plan out how to perform Lab exercises in this write-up. Pre-lab questions: 1. Given the DAC in Exercise 10.2 has a resolution of 5 bits, how close to their ideal values must each resistor be? 2. Assuming that the DAQ digital output high level is exactly 5V, what is the full scale value (larg-est output) of the DAC in this exercise? Background: Digital representation of numbers Our world is largely analog and continuous; quantities vary smoothly. There are, of course, intrinsi-cally discrete exceptions to this rule, like the quantization of charge or the quantum hall effect. But even measurements of discrete phenomena tend to be confounded by noise and produce continuous Last Revision: April 2013 Page 1 of 20 ©2013 by the Regents of the University of California. All rights reserved.Physics 111 BSC Laboratory Lab 10 LabVIEW Programming data. Internally, however, modern computers1 deal only with discrete quantities; specifically, they deal only with quantities take on only two values: on or off. This so-called digital representation of information has many advantages over analog representations, most importantly that digital infor-mation is relatively immune to noise. If a 0, or off state, is represented by a voltage near 0, and a 1, or on state is represented by a voltage near 4 (a scheme used by a common family of digital devices called TTL logic), then noise is unlikely to cause a fluctuation great enough to confuse the two. Because computers can only represent two states, numbers are stored in binary, or base 2. The dig-its in a base 2 number are called bits, thus, a typical number in base 2 number is a collection of bits like 01011010. Numbers are decoded using a power series in 2: 01 2 3012 302 2222nnna a aa a∞== ++ + +∑ where the naare the series of bits used to represent the number. Thus, Base 10 0 1 2 3 4 5 6 7 Base 2 000 001 010 011 100 101 110 111 The more bits used, the larger the integer number that can be represented. Non-integer numbers are represented by multiplying in an appended exponent; thus, the more bits, the greater the precision of the number. Eight bits taken together constitute a byte, and computers are typically organized around byte pro-cessing, not bit processing. Conversion Since the real world is analog, but the computer world is binary, we need to be able to convert signals between the two. Devices that change an analog signal to a digital signal are called analog to digital converters (ADC). Devices that change a signal the other way, from digital to analog, are called digi-tal to analog converters (DAC). Both are important; DACs are used to control experiments, while ADCs are used to read data from experiments. 1 Originally, computers were analog, and did computations in ways similar to the way that you did computations in your RMS converters. Programming was done by wiring patch panels, as can be seen in the photos of the analog computers below. Last Revision: April 2013 Page 2 of 20 ©2013 by the Regents of the University of California. All rights reserved.Physics 111 BSC Laboratory Lab 10 LabVIEW Programming Sampling Real-world signals are continuous in time as well as level. Thus, to represent a time-varying signal, we build up a table of the value of the signal as a function of time, for example: Time Signal 0 1.000 0.125 0.649 0.250 -0.156 0.375 -0.853 0.500 -0.951 0.625 -0.383 0.750 0.454 0.875 0.972 1.000 0.809 1.125 0.078 1.250 -0.707 1.375 -0.997 1.500 -0.588 1.625 0.233 1.750 0.891 1.875 0.924 2.000 0.309 These values are called samples. Last Revision: April 2013 Page 3 of 20 ©2013 by the Regents of the University of California. All rights reserved.Physics 111 BSC Laboratory Lab 10 LabVIEW Programming We can better visualize sample tables with a graph. The curve in upper plot of the graph below rep-resents a signal to be sampled. The dots are the samples. If we then use the samples to represent the signal, we get the signal in the lower plot, where the points are joined by the dashed line. Sampling always approximates the signal. How accurate is the representation? There are two basic limits on the accuracy, resolution and sampling rate. Resolution The number of bits available to represent each sample is called the resolution. In base 2, the number of levels that can be represented by an n bit sample is 2n. Thus, for 8 bits (the number of bits in a typical low end converter) there are 256 levels, while for 24 bits (the maximum common2 converter resolution) there are 16,777,216 levels. It is rare that we would need precisions better than 1 part in 1000, or 10 bits. What then is the point of going to higher resolution? Higher resolution provides greater range. It is uncommon for the sig-nal amplitude to exactly match the full-scale value of the converter. Typically, we might have a margin of over a factor of ten; perhaps 4 bits. Thus, to get 10 bit accuracy we would need a 14 bit converter. Even if the maximum amplitude of our signal