Component Tolerance

Accuracy Unmasked

We take for granted sometimes that the tolerances of our electronic components fit the needs of our designs. In this article, Robert takes a deep look into the subject of tolerances, using the simple resistor as an example. He goes through the math to help you better understand accuracy and drift along with other factors.

By Robert Lacoste

One of the last projects I worked on with my colleagues was a kind of high-precision current meter. It turned out to be far more difficult than anticipated, even with our combined experience totaling almost 100 years. Maybe this has happened with your projects too: You discover that, even when you’re not looking for top performance out of your electronic components, the accuracy and stability of those components can be pernicious. My topic this month is examining component tolerances. And, for simplicity, I will focus on the simplest possible electronic device: a resistor.

FIGURE 1 A very simple voltage divider. With these values, Uout will be 1 V with Uin=100 V

Let’s start with a basic application. Imagine that you have to design a voltage divider with a ratio of 1/100 (Figure 1). I will assume that the source impedance is very low and that the load connected on the output draws no current at all. With those parameters the calculations are very easy. You just need to know Ohm’s Law. Because the resistors are in series, the current circulating through the two resistors is:

Similarly, the output voltage is:

Given that the current I is the same in both equations, we get:

This circuit is indeed a voltage divider, with a ratio of R2/(R1+R2). We want a ratio of 1/100, so one resistor could be fixed arbitrarily and the second easily calculated. For example: R1=9,900 Ω and R2=100 Ω will do the job as:

Of course, you can easily simulate such a circuit with any SPICE-based circuit simulator if you wish. I personally used Proteus from Labcenter to draw and simulate the small schematic provided on Figure 1, and the output voltage is 1 V with 100 V applied on the input, as expected. As usual, I encourage you to reproduce these small examples with your preferred simulator: for example the free LT-Spice.

Now let’s talk about accuracy. You want your divider to be as precise as possible and therefore you want to buy reasonably accurate resistors. But what if your budget is constrained? Will you use a high accuracy resistor for R1 (9,900 Ω)? Or for R2 (100 Ω)? Or for both? The good answer is both. In that case, a 1% error on either R1 or R2 gives close to a 1% error of the output voltage, as shown in Figure 2. Even if R1 has a stranger value than R2—9,900 Ω vs. 100 Ω—their accuracy is just as critical.

Figure 2
A 1% error either on the top or bottom resistors will induce a roughly 1% error on the output. That would not be the case for other division ratios.

Maybe you think this is too obvious? In that case I will give you another exercise: What happens with a divide-by-2 circuit using two resistors of the same value? Do the calculation or simulate it and you will find that both resistors have still the same impact on accuracy. But now a 1% error on one of the resistors has only a 0.5% impact on the output voltage. That means you could buy slightly less expensive resistors for the same overall precision! In fact, the higher the division ratio, the higher is the impact of each resistor on the overall accuracy.

E Series Resistors

Let’s go back to the 1/100 divider example. If you want to build it and look for a
9,900-Ω resistor, you will have some difficulties because nobody sells them.. …

Read the full article in the April 333 issue of Circuit Cellar

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March Circuit Cellar: Sneak Preview

The March issue of Circuit Cellar magazine is coming soon. And we’ve got a healthy serving of embedded electronics articles for you. Here’s a sneak peak.

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TECHNOLOGY FOR THE INTERNET-OF-THINGS

IoT: From Device to Gateway
The Internet of Things (IoT) is one of the most dynamic areas of embedded systems design today. This feature focuses on the technologies and products from edge IoT devices up to IoT gateways. Circuit Cellar Chief Editor Jeff Child examines the wireless technologies, sensors, edge devices and IoT gateway technologies at the center of this phenomenon.

Texting and IoT Embedded Devices
Texting has become a huge part of our daily lives. But can texting be leveraged for use in IoT Wi-Fi devices? Jeff Bachiochi lays the groundwork for describing a project that will involve texting. In this part, he gets into out the details for getting started with a look at Espressif System’s ESP8266EX SoC.

Exploring the ESP32’s Peripheral Blocks
What makes an embedded processor suitable as an IoT or home control device? Wi-Fi support is just part of the picture. Brian Millier has done some Wi-Fi projects using the ESP32, so here he shares his insights about the peripherals on the ESP32 and why they’re so powerful.

MICROCONTROLLERS HERE, THERE & EVERYWHERE

Designing a Home Cleaning Robot (Part 4)
In this final part of his four-part article series about building a home cleaning robot, Nishant Mittal discusses the firmware part of the system and gets into the system’s actual operation. The robot is based on Cypress Semiconductor’s PSoC microcontroller.

Apartment Entry System Uses PIC32
Learn how a Cornell undergraduate built a system that enables an apartment resident to enter when keys are lost or to grant access to a guest when there’s no one home. The system consists of a microphone connected to a Microchip PIC32 MCU that controls a push solenoid to actuate the unlock button.

Posture Corrector Leverages Bluetooth
Learn how these Cornell students built a posture corrector that helps remind you to sit up straight. Using vibration and visual cues, this wearable device is paired with a phone app and makes use of Bluetooth and Microchip PIC32 technology.

INTERACTING WITH THE ANALOG WORLD

Product Focus: ADCs and DACs
Makers of analog ICs are constantly evolving their DAC and ADC chips pushing the barriers of resolution and speeds. This new Product Focus section updates readers on this technology and provides a product album of representative ADC and DAC products.

Stepper Motor Waveforms
Using inexpensive microcontrollers, motor drivers, stepper motors and other hardware, columnist Ed Nisley built himself a Computer Numeric Control (CNC) machines. In this article Ed examines how the CNC’s stepper motors perform, then pushes one well beyond its normal limits.

Measuring Acceleration
Sensors are a fundamental part of what make smart machines smart. And accelerometers are one of the most important of these. In this article, George Novacek examines the principles behind accelerometers and how the technology works.

SOFTWARE TOOLS AND PROTOTYPING

Trace and Code Coverage Tools
Today it’s not uncommon for embedded devices to have millions of lines of software code. Trace and code coverage tools have kept pace with these demands making it easier for embedded developers to analyze, debug and verify complex embedded software. Circuit Cellar Chief Editor Jeff Child explores the latest technology trends and product developments in trace and code coverage tools.

Manual Pick-n-Place Assembly Helper
Prototyping embedded systems is an important part of the development cycle. In this article, Colin O’Flynn presents an open-source tool that helps you assemble prototype devices by making the placement process even easier.

January Circuit Cellar: Sneak Preview

The January issue of Circuit Cellar magazine is coming soon. And it’s got a robust selection of embedded electronics articles for you. Here’s a sneak peak.

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                                     IMPROVING EMBEDDED SYSTEM DESIGNS

Special Feature: Powering Commercial Drones
The amount of power a commercial drone can draw on has a direct effect on how long it can stay flying as well as on what tasks it can perform. Circuit Cellar Chief Editor Jeff Child examines solar cells, fuel cells and other technology options for powering commercial drones.

CC 330 CoverFPGA Design: A Fresh Take
Although FPGAs are well established technology, many embedded systems developers—particularly those used the microcontroller realm—have never used them before. In this article, Faiz Rahman takes a fresh look a FPGAs for those new to designing them into their embedded systems.

Product Focus: COM Express boards
COM Express boards provide a complete computing core that can be upgraded when needed, leaving the application-specific I/O on the baseboard. This brand new Product Focus section updates readers on this technology and provides a product album of representative COM Express products.

TESTING, TESTING, 1, 2, 3

LF Resonator Filter
In Ed Nisley’s November column he described how an Arduino-based tester automatically measures a resonator’s frequency response to produce data defining its electrical parameters. This time he examines the resultsand explains a tester modification to measure the resonator’s response with a variable series capacitance.

Technology Spotlight: 5G Technology and Testing
The technologies that are enabling 5G communications are creating new challenges for embedded system developers. Circuit Cellar Chief Editor Jeff Child explores the latest digital and analog ICs aimed at 5G and at the test equipment designed to work with 5G technology.

                                     MICROCONTROLLERS IN EVERYTHING

MCU-based Platform Stabilizer
Using an Inertial Measurement Unit (IMU), two 180-degree rotation servos and a Microchip PCI MCU, three Cornell students implemented a microcontroller-based platform stabilizer. Learn how they used a pre-programmed sensor fusion algorithm and I2C to get the most out of their design.

Designing a Home Cleaning Robot (Part 2)
Continuing on with this four-part article series about building a home cleaning robot, Nishant Mittal this time discusses the mechanical aspect of the design. The robot is based on Cypress Semiconductor’s PSoC microcontroller.

Massage Vest Uses PIC32 MCU
Microcontrollers are being used for all kinds of things these days. Learn how three Cornell graduates designed a low-cost massage vest that pairs seamlessly with a custom iOS app. Using the Microchip PIC32 for its brains, the massage vest has sixteen vibration motors that the user can control to create the best massage possible.

AND MORE FROM OUR EXPERT COLUMNISTS:

Five Fault Injection Attacks
Colin O’Flynn returns to the topic of fault injection security attacks. To kick off 2018, he summarizes information about five different fault injection attack stories from 2017—attacks you should be thinking about as an embedded designer.

Money Sorting Machines (Part 2)
In part 1, Jeff Bachiochi delved into the interesting world of money sort machines and their evolution. In part 2, he discusses more details about his coin sorting project. He then looks at a typical bill validator implementation used in vending systems.

Overstress Protection
Last month George Novacek reviewed the causes and results of electrical overstress (EOS). Picking up where that left off, in this article he looks at how to prevent EOS/ESD induced damage—starting with choosing properly rated components.

December Circuit Cellar: A Sneak Preview

The December issue of Circuit Cellar magazine is coming soon. Want a sneak peak? We’ve got a great selection of excellent embedded electronics articles for you.

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MICROCONTROLLERS IN MOTION

Special Feature: Electronics for Wearable Devices
Circuit Cellar Chief Editor Jeff Child examines how today’s microcontrollers, sensors and power electronics enable today’s wearable products.

329 Cover Screen CapSimulating a Hammond Tonewheel Organ
(Part 2)

Brian Millier continues this two-part series about simulating the Hammond tonewheel organ using a microcontrollers and DACs. This time he examines a Leslie speaker emulation.

Money Sorting Machines (Part 1)
In this new article series, Jeff Bachiochi looks the science, mechanics and electronics that are key to sorting everything from coins to paper money. This month he discusses a project that uses microcontroller technology to sort coins.

Designing a Home Cleaning Robot (Part 1)
This four-part article series about building a home cleaning robot starts with Nishant Mittal discussing his motivations behind to his design concept, some market analysis and the materials needed.

SPECIAL SECTION: GRAPHICS AND VISION

Designing High Performance GUI
It’s critical to understand the types of performance problems a typical end-user might encounter and the performance metrics relevant to user interface (UI) design. Phil Brumby of Mentor’s Embedded Systems Division examines these and other important UI design challenges.

Building a Robotic Candy Sorter
Learn how a pair of Cornell graduates designed and constructed a robotic candy sort. It includes a three degree of freedom robot arm and a vision system using a Microchip PIC32 and Raspberry Pi module.

Raster Laser Projector Uses FPGA
Two Cornell graduates describe a raster laser projector they designed that’s able to project images in 320 x 240 in monochrome red. The laser’s brightness and mirrors positions are controlled by an FPGA and analog circuitry.

ELECTRICITY UNDER CONTROL

Technology Spotlight: Power-over-Ethernet Solutions
Power-over-Ethernet (PoE) enables the delivery of electric power alongside data on twisted pair Ethernet cabling. Chief Editor Jeff Child explores the latest chips, modules and other gear for building PoE systems.

Component Overstress
When an electronic component starts to work improperly, Two likely culprits are electrical overstress (EOS) and electrostatic discharge (ESD). In his article, George Novacek breaks down the important differences between the two and how to avoid their effects.

AND MORE FROM OUR EXPERT COLUMNISTS:

Writing the Proposal
In this conclusion to his “Building an Embedded Systems Consulting Company” article series, Bob Japenga takes a detailed look at how to craft a Statement of Work (SOW) that will lead to success and provide clarity for all stakeholders.

Information Theory in a Nutshell
Claude Shannon is credited as one of the pioneers of computer science thanks to his work on Information Theory, informing how data flows in electronic systems. In this article, Robert Lacoste provides a useful exploration of Information Theory in an easily digestible way.

2.5 A Step-Down Regulator Keeps EMC/EMI Emissions Low

Analog Devices, which recently acquired Linear Technology, has announced the LTM8065, a µModule (power module) step-down regulator with up to 40 V input voltage (42 V abs max), which can safely operate from unregulated or fluctuating 12 V to 36 V input supplies in noisy environments such as industrial robotics, test and measurement, medical, factory automation and avionics systems. The Silent Switcher architecture minimizes EMC/EMI emissions enabling the LTM8065 to pass CISPR 22 class B for use in noise-sensitive signal processing applications, including imaging and RF systems. The LTM8065’s small 6.25 mm x 6.25 mm x 2.32 mm BGA package includes a switching regulator controller, power switches, inductor and other supporting components. With only two 0805 sized capacitors and two 0603 sized resistors, the LTM8065’s solution occupies approximately 100mm², about half the size of equivalent power level module solutions.

LTM8065The LTM8065 can deliver 2.5 A of continuous (3.5 A peak) output current to a 5 V load from a 12 V input at up to 85°C ambient without a heat sink or airflow. The output voltage is adjustable with one resistor from 0.97 V to 18 V. This wide output voltage range provides versatility, using one product to generate common system bus voltage of 3.3 V, 5 V, 12 V and 15 V. The switching frequency is adjustable by an external single resistor or can be synchronized to an external clock from 200 kHz to 3 MHz. It enables customer operation of the device in or out of the specific frequency. The LTM8065 has four modes: Burst Mode® operation, pulse-skipping mode, pulse-skip mode with spread spectrum modulation and external synchronization mode. The quiescent current at burst mode is 8 µA, making it ideal for battery operating systems.

The LTM8065 operating temperature range is –40°C to 125°C. 1,000-piece pricing starts at $7.75 each.

Analog Devices – Linear Technology | www.linear.com

November Circuit Cellar: A Sneak Preview

The November issue of Circuit Cellar magazine is coming soon. Want a sneak peak? We’ve got a great section of excellent embedded electronics articles for you.

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TECHNOLOGY IN A CONNECTED WORLD

IoT Gateway Advances Take Diverse Paths: Flexible Networked Solutions
The Internet-of-Things (IoT) phenomenon offers huge opportunities. Circuit Cellar Chief Editor Jeff Child explores how IoT gateways play a vital role in those systems by providing Nov 328 coverbidirectional communication between the devices in the field and the cloud.

Power Analysis Attack on RSA: Asymmetric Adventures
Colin O’Flynn has done a number of great columns about cryptography—in particular symmetric cryptography. This time he’s tackling an asymmetric algorithm: a RSA implementation. Colin describes what’s unique about an RSA cryptosystem and takes us through a power analysis attack.

FOCUS ON ANALOG

Analog Solutions Fuel Industrial System Needs: Connectivity, Control and IIoT
Whether it’s connecting with analog sensors or driving actuators, analog ICs play many critical roles in industrial applications. Here, Circuit Cellar Chief Editor Jeff Child examines the latest analog technologies and products serving the needs of today’s industrial systems.

Using Power Audio Amplifiers in Untypical Ways (Part 2): More Alternative Uses
In Part 1 Petre Petrov described many interesting ways to use power audio amplifiers (PAAs) as universal building blocks similar to the op amps and comparators. Here, he discusses several more things that can be built from PAAs including wave generators and transformer drivers.

SPOTLIGHT ON MONITORING AND TESTING

Gas Monitoring and Sensing (Part 2): Putting the Sensor to Work
Columnist Jeff Bachiochi continues his exploration of gas monitoring and sensing. This time he discusses some of the inexpensive sensors available that can be applied to this application. Jeff then tackles the factors to consider when calibrating these sensors and how to use them effectively.

Logger Device Tracks Amp Hours (Part 2): Alternative Energy Sources
n this follow on to Part 1 of his story, William Wachsmann describes putting to use the amp-hour logger he built using a microcontroller and a clamp-on ammeter. This time he discusses modifying the amp-hour software so it can be used as an analog input logger to measure solar and wind power.

Negative Feedback in Electronics: A Look at the Opposite Side
Complementing his discussion last month on positive feedback, columnist George Novacek now takes a look at negative feedback. Just like positive feedback, negative feedback can significantly change or modify a circuit’s performance.

LF Quartz Resonator Tester: A Stimulating Discussion
Ed Nisley returns to the rich topic of low-frequency quartz resonators. This time he describes a tester built with an ordinary Arduino Nano and an assortment of inexpensive RF modules.

INTERESTING EMBEDDED PROJECTS

Simulating a Hammond Tonewheel Organ (Part 1) Mimicking a Mechanical Marvel
Hammond tonewheel organs were based upon additive sine-wave synthesis. Because of that, it’s possible to simulate the organ using a microcontroller program that feeds its output waveform to a DAC. Brian Millier takes on this project, making use of an ARM-based Teensy module to do the heavy lifting.

Machine Auto-Sorts Resistors: MCUs, Measurement and Motor Control
Typical electronics lab benches become littered with resistors from past projects. These three Cornell University graduates tackled this problem by building a resistor sorting system. It enables users to input multiple resistors, measure their resistance and sort them. The project integrates motor controllers, resistance measurement and a graphical user interface.