The Analog-to-Digital
Conversion Process
By Chris Dohrmann
ADVANCE ORGANIZER
ABOUT THIS DOCUMENT
The purpose of this document is to provide readers with a technical description of
the analog-to-digital conversion process performed by analog-to-digital
converters (ADC’s). The scope of this document will include an overview of the
process along with fundamental concepts and theory of operation. It will not
include specifics about a particular method of analog-to-digital conversion,
information about device physics or hardware design.
ABOUT THE AUDIENCE
Due to the technical nature of this document, readers should have a basic
understanding of the following subjects:
˗
˗
˗
˗
Analog and digital signals
Sinusoids
Complex exponentials
Binary numbers
After reading this document, the audience will have a general understanding of
the fundamentals of the ADC process. This knowledge will be useful to readers
who are interested in digital signal processing, embedded development, audio
engineering, communications, or similar disciplines. With some basic knowledge
of embedded development and digital design, in addition to the information in this
document, it is possible to implement simple analog-to-digital conversion
systems.
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INTRODUCTION
An analog-to-digital converter (ADC) is an electronic device that converts analog
signals into digital representations. ADC’s can be found within almost all
personal computers and smartphones. ADC’s are also used in commercial
applications such as scientific measurement, digital signal processing, and audio
recording. The process of analog-to-digital conversion can be broken down into
three components; analog input, sampling, and digital output.
INPUT
OUTPUT
ADC
Figure 1 - Electrical symbol for an ADC
Figure 2 – 8-channel 10-bit ADC
(~$3.00)
Figure 3 – 2GSPS 10-bit ADC
(~$37,500)
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THE PROCESS
INPUT
Voltage
The most common analog input is voltage and because this is the only form of
analog input that an ADC is capable of processing directly, it will be the focus of
this document. To input a signal representing something such as sound, light, or
force, a transducer (a device that converts energy into another form of energy)
will be used. This transducer will take the original signal and transform it into an
analog voltage signal with varying frequency and amplitude. Nearly all
waveforms can be represented through a summation of various sinusoidal
signals. An example of a time varying analog voltage input is shown below.
Time
Figure 4 – Time-varying analog voltage
Common expressions of sinusoidal signals:
𝑓(𝑡) = 𝐴𝑐𝑜𝑠(𝜔𝑡 + 𝜃) (Sinusoidal)
𝐹 = 𝐴𝑒 𝑗𝜃 (Phasor)
where 𝜔 = frequency and 𝑗 is the imaginary unit
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SAMPLING
Voltage
While the analog signal is being fed through the input terminal the ADC will take
voltage measurements at a predefined frequency. This process is known as
sampling. The frequency of sampling (𝑓𝑠 ) is the rate at which samples are taken.
𝑓𝑠 is measured in hertz, so if you take 1000 samples per second 𝑓𝑠 = 1000Hz.
This is the process responsible for transforming continuous time signals (analog)
into discrete time signals (digital). By sampling an analog signal at the correct
frequency it is possible to retain all or nearly all of the information contained in
that signal in a digital form. Shown below is the result of sampling the original
signal from the previous example. The arrows represent the measurements
taken by the ADC.
Time
Figure 5 – Sampled time-varying analog voltage
In order to be able to reproduce a sampled signal, it must be sampled at more
than twice the highest frequency contained within that signal.
𝑓𝑠 ≥ 2𝐵 where 𝑓𝑠 is the frequency of sampling and 𝐵 is the highest
frequency. (For a given band-limited signal) from Shannon-Nyquist
sampling theorem
A signal that is band-limited means that it contains a finite amount of
frequencies
Although taking these samples has transformed the original continuous time
signal into a discrete time signal it still cannot be used by modern electronics. In
order for this to be possible, these samples must be represented in binary code.
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DIGITAL OUTPUT
The process through which these samples are converted into binary code is
called encoding. By equating voltage levels to binary numbers it is possible to
write signals as a stream of binary numbers. Shown below is the result of
applying this process to these samples. The horizontal dotted lines represent the
levels that are associated with the binary values to the left. In this example the
ADC has a resolution of 3. This means that there are 23 or 8 intervals that are
recognized by the ADC. Higher resolution ADCs are available.
𝑇𝑜𝑡𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙𝑠 = 2𝑛 , 𝑤ℎ𝑒𝑟𝑒 𝑛 = 𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 (𝑖𝑛 𝑏𝑖𝑡𝑠)
111
110
101
100
011
010
001
000
Time
Figure 6 – Assigning binary values to reference intervals
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As shown by the picture on the previous page, some of these values fall between
the specified levels. If this is the case, the value will be quantized, or rounded to
the nearest level. Shown below is the result.
Figure 7 – Quantizing sample values to reference levels
So, instead of having a stream of values such as (0, 3, 6, 7 …)
You will have a stream of bits (000011110111…)
SOURCES OF ERROR
There are a few sources of error that can be introduced through the analog-todigital conversion process. Quantization can introduce noise caused by rounding
analog values to the nearest voltage levels. This is known as quantization error.
Physical imperfections in the device may also cause error. Non-ideal clock
properties are another common source of error
DESIRABLE ADC SPECIFICATIONS & PRICING
Today, simple ADC’s are available for less than $1.00, while those intended for
commercial use can cost around $1000 (with more advanced ADC’s reaching
prices as high as $35,000 or more). The difference in price is related to technical
specifications such as sampling rate, resolution, and power usage. Some
applications can require a sampling rate as high as 3+ Gigahertz or a resolution
as high as 24+ bits. Lower power consumption is also a highly desirable trait.
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Time
CONCLUSION
Analog-to-digital conversion is a powerful yet fundamentally simple process. By
assigning binary values to voltage reference levels it is possible to convert
analog signals into digital signals. Once this data has been converted into a
digital form it can be passed through additional circuitry to perform additional
functions or undergo further processing. This is what makes analog-to-digital
conversion so important in modern technology.
WORKS CITED
Lathi, B.P. (1998). Modern Digital and Analog Communication Systems (3rd
edition). Oxford University Press.
"Digitization of Analog Quantities". Iamechatronics.com. Retrieved 2014-24-3.
Figures 1 and 4-7 were created by Chris Dohrmann using Microsoft Word.
Figures 2 & 3 were taken from www.adafruit.com and www.mouser.com
respectively.
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