Join

Sign
In with my.TI Login

Products

Applications

Tools
& Software

Support &
Community

Sample & Buy

About
TI

Sample
& Purchase Cart

Just this
area

Advanced

Support Forums

Blogs

Groups

Videos

简体中文

More
...

TI
Home » TI E2E
Community » Blogs
» Precision
Hub » How
to combine error terms

How to combine error terms

Precision
Hub

Subscribe to this Blog by Email

Subscribe

RSS for
posts

RSS
for comments

More from Precision Hub

Precision
Hub

Do
I always need an amplifier to drive my SAR ADC?

A successive approximation register
(SAR) analog-to-digital converter (ADC)...

Posted 3
days ago

by
Lokesh
Ghulyani

Part
1- A voltage reference duel of duals

Posted 5
days ago

by
Ying
Zhou1

Part
II – Get CerTIfied, not certi-FRIED! Electromagnetic compatibility testing
explained.

Posted 13
days ago

by
Ian
Williams

How
to combine error terms

Posted 19
days ago

by
Timothy
Claycomb

Industrial
DACs: Protecting 3-wire analog outputs

Posted 26
days ago

by
Kevin
Duke

Tweet

How to combine error terms

Timothy
Claycomb

Aug 19 2014 16:07 PM

Comments 0

Calculating
the total error of a system can be tricky, especially when the specifications
units vary widely. When calculating the total error, all specifications must be
converted into a common unit before combining. This blog will show you how to
convert between units of volt, percentage and parts per million (ppm) to ensure
proper calculation of total system error.

Most errors
in a linear device’s datasheet are referred to the input (RTI).  Referring
errors to the input has three main benefits: It separates each error’s
contribution to the total error at the output, eliminates the need to know the
gain of the device, and simplifies the calculations to refer the total error to
the output. To convert input referred specifications between units of volts,
percentage, parts per million, and refer the total error to the output use the
following equations.

To
convert from volts to percentage:

Where,

Error(V) = The error in units of volts.

Error(%) = The error as a percentage of the full-scale range.

FSRInput = The full-scale range of the input.

To
convert from percentage to ppm:

Where,

Error(ppm) = The error in parts per million of the full-scale
range.

To
refer all errors to the output in units of volts:

Where,

Total Output Error(V) = Total error referred to the output in units of
volts.

FSROuput = The full-scale range of the output.

To
show an example of how to use the above equations, we will use the circuit shown
in Figure 1 and calculate the combined error in ppm due to a couple
specifications of the INA826. The circuit has an input signal of 20mVpp, and RG is
set for the INA826 to have a gain of 100V/V.

The first
error we will look at is input offset voltage. Figure 2 shows the input offset
voltage specification for the INA826.

Since this
specification is in units of volts, use Equations 1 and 2 to convert this to
ppm. To solve Equation 1 we need to know the full-scale range of the input. The
FSR of Figure 1 is the total voltage range at the input of the INA826. In this case, it is 20mVpp. Now that we have all the
needed information, let’s plug in the numbers.

Now lets
look at gain error. Figure 3 shows the gain error specification for the INA826.

The gain
error specification is given as a percentage. Therefore, we only need to use
equation 2 to convert to ppm.

Now that
both sources of error are in units of ppm, we can combine them by calculating
the RSS, or root-sum-square, value as shown in Equation 7.

This is the
total error due to the gain error and offset voltage referred to the input.
However, most people want to see how much error they can expect to measure at
the output. To refer the error to the output, use Equation 3. Equation 3 uses
the variable FSROutput, which is the full-scale range of the
output. In the example shown in Figure 1, the FSR of the output is 2Vpp. This is
calculated by multiplying the input signal (20mVpp) and the gain (100V/V). The
total voltage error at the output is calculated in Equation 8.

Although
these are not all the errors of the INA826, a similar analysis can be done to include
them.

Now that
you know how to convert specifications between units of volts, percentage, and
parts per million, you can now calculate the total error of your system. If you
would like another example of how to calculate total system error, check out
Appendix B in TI Design TIPD156.

$core_v2_language.FormatString($ti.GetResource('Blog_PostQuestionAnswerView_CommentsCountFormatString'),
$post.CommentCount)

INA826,
TIPD156

Sign
in to Comment

TI E2E™ Community

Support
Forums

Blogs

Videos

Groups

Site Support
& Feedback

Settings

TI E2E™ Community Groups

TI
University Program

Make the
Switch

Microcontroller
Projects

Motor Drive
& Control

Other Communities

Deyisupport

Designsomething.org

beagleboard.org

TI
on Element 14

TI
on TechXchangeSM

Other Technical & Support Resources

WEBENCH® Design Center

Product Information
Centers

Technical
Documents

TI Design Network

TI
Technical Articles

TI
Training

All content and materials on this site are provided "as is". TI and its
respective suppliers and providers of content make no representations about the
suitability of these materials for any purpose and disclaim all warranties and
conditions with regard to these materials, including but not limited to all
implied warranties and conditions of merchantability, fitness for a particular
purpose, title and non-infringement of any third party intellectual property
right. TI and its respective suppliers and providers of content make no
representations about the suitability of these materials for any purpose and
disclaim all warranties and conditions with respect to these materials. No
license, either express or implied, by estoppel or otherwise, is granted by TI.
Use of the information on this site may require a license from a third party, or
a license from TI.

Content on this site may contain or be subject to specific guidelines or
limitations on use. All postings and use of the content on this site are subject
to the Terms of
Use of the site; third parties using this content agree to abide by any
limitations or guidelines and to comply with the Terms
of Use of this site. TI, its suppliers and providers of content reserve the
right to make corrections, deletions, modifications, enhancements, improvements
and other changes to the content and materials, its products, programs and
services at any time or to move or discontinue any content, products, programs,
or services without notice.

Follow Us

TI Worldwide | Contact Us |
my.TI
Login |
Site Map | Corporate
Citizenship |
m.ti.com (Mobile Version)

TI is a global semiconductor design and manufacturing company. Innovate with
100,000+ analog ICs and
embedded processors, along with software, tools and
the industry’s largest sales/support staff.

© Copyright
1995-2013 Texas Instruments Incorporated. All rights reserved.
Trademarks |
Privacy
Policy | Terms
of Use