# Accelerometers Revisited

MEMS and More

In his March article, George reviewed the major aspects of acceleration, along with its measurement and the design fundamentals of the sensors known as accelerometers. Here, he expands on the topic exploring the electronics portion of accelerometers along with a look at how MEMS technology plays a role in these sensors.

By George Novacek

The key aspects of accelerometers can be loosely categorized by their acceleration range, frequency response and typical applications as shown in Table 1. Many characteristics must be taken into account when selecting an accelerometer suitable for the given task. Besides having to satisfy the required range of acceleration to be measured, you must consider the measurement resolution, accuracy, bandwidth, stability and repeatability. Just as important are the weight, size, cost, electrical interfaces, power consumption, availability and operating environmental conditions. And don’t forget susceptibility to the effects of conducted and radiated emissions, that is electromagnetic interference (EMI).

Fundamentally, accelerometers are electromechanical devices—as I have shown in my March 2018 article (Circuit Cellar 332). Electronics play only a supporting role—needed to convert the displacement of the proof (also called seismic) mass into a useful electrical signal. Accelerometer interfaces can take many forms, both analog and digital.

Figure 1
The mechanical principle of an accelerometer

The behavior of the mechanical system illustrated in Figure 1 is described by just a few simple equations, where the variables are the force F = kx developed by the spring, the opposite force F = Dv developed by the damper and the seismic mass’ inertial force F = Ma. Consequently, the static displacement of the mass equals to:

The combination of the spring, the damper and the mass form a second-order system. Such a system, when exposed to varied acceleration of angular frequency ω which equals to 2πf, exhibits dynamic behavior described by equation:

The resonant frequency of this system will be:

and the quality factor:

The frequency response of such a system was shown in the March issue. The parameter ξ is the system damping factor.

MEMS and Acceleration

At present, the most popular manufacturing technology for accelerometers as well as many other inertia-based sensors—such as gyroscopes—is MEMS. MEMS is an acronym for “micro electro-mechanical system.” MEMS accelerometers measure the proof mass displacement by piezoresistive or capacitive sensors.  …

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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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Here’s a sneak preview of March 2018 Circuit Cellar:

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

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.