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A Laboratory Method For Teaching Analog To Digital And Digital To Analog Conversion

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2010 Annual Conference & Exposition


Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010



Conference Session

Laboratory Development in ECE

Tagged Division

Electrical and Computer

Page Count


Page Numbers

15.43.1 - 15.43.14



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Paper Authors


Joseph Hoffbeck University of Portland

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Joseph P. Hoffbeck is an Associate Professor of Electrical Engineering at the University of Portland in Portland, Oregon. He has a Ph.D. from Purdue University, West Lafayette, Indiana. He previously worked with digital cell phone systems at Lucent Technologies (formerly AT&T Bell Labs) in Whippany, New Jersey. His technical interests include communication systems, digital signal processing, and remote sensing.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

A Laboratory Method for Teaching Analog-to-Digital

and Digital-to-Analog Conversion


Since analog-to-digital converters (ADC’s) and digital-to-analog converters (DAC’s) are used in such a wide variety of electronic systems, it is important for engineers to have a deep understanding of the distortions caused by ADC’s and DAC’s such as aliasing and quantization, and to realize that the digital signal is not a perfect representation of the original analog signal. In fact, if the system is set up poorly, the digital signal can be corrupted enough that it is completely unusable. Furthermore, students are often curious how ADC’s and DAC’s work and benefit from building, testing, and using these important circuits.

This paper proposes a laboratory method for teaching the process of converting between analog and digital signals using circuits that students can construct in a laboratory. The ADC is a 3-bit flash converter made from comparators, a priority encoder, flip-flops, and buffers. The DAC is a simple R-2R resistor network. These circuits work well to demonstrate the effects of aliasing and quantization on various laboratory signals, such as D.C. signals and sinusoids. Furthermore, with the addition of an op-amp adder and an audio amplifier, the students can pass music from a portable music player through the system so they can hear the result, which is definitely recognizable, although it does have noticeable quantization noise.

The advantage of this method of teaching the conversion process is that the students can actively experiment with the system to see and hear the effects of aliasing and quantization in real time. They can measure quantization errors and see the distortion on an oscilloscope that occurs when the analog signal is too big or too small for the input range of the ADC. They can see and hear the distortion caused by aliasing while adjusting the input frequency and the sampling rate. Thus the experiment is more interesting and engaging than a purely theoretical presentation.


In many electronic systems, analog signals are processed using digital hardware, which makes it necessary to convert between analog and digital signals. Examples of such systems include audio and image processing systems, communication systems, control systems, and instrumentation systems, and many others. However, in practice an analog signal cannot be represented exactly in digital form, and so it is important that engineers that design and use such systems be aware of the distortions that are caused by ADC’s and DAC’s such as quantization error and aliasing.

Hoffbeck, J. (2010, June), A Laboratory Method For Teaching Analog To Digital And Digital To Analog Conversion Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--16160

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