DiscreteTime PLLs, Part 1: Basics
Design Files: Part1.slx
Hi everyone,
In this series of tutorials on discretetime PLLs we will be focusing on PhaseLocked Loops that can be implemented in discretetime signal proessors such as FPGAs, DSPs and of course, MATLAB.
In the first part of the series, we will be reviewing the basics of continuoustime baseband PLLs and we will see some useful mathematics that will give us insight into the inners working of PLLs. In the second part, we will focus on...
Mounting plate for Arduino
While having a breadboard with your microcontroller is necessary, it is very cumbersome if the two aren't fastened together somehow. You can buy mounting plates, but I choose to make one.
I am using thin plexiglass type glazing material from the hardware store. You can use the thicker material, but may have to purchase longer screws for standoffs depending on what you use.
I like using the small Plano tackle boxes, because they can hold the plate, a few parts, batteries and a...
CortexM Exception Handling (Part 1)
This article describes how CortexM processors handle interrupts and, more generally, exceptions, a concept that plays a central role in the design and implementation of most embedded systems. The main reason of discussing this topic in detail is that, in the past few years, the degree of sophistication (and complexity) of microcontrollers in handling interrupts steadily increased, bringing them on a par with generalpurpose processors.
Coding Step 4  Design
Articles in this series:
 Coding Step 0  Development Environments
 Coding Step 1  Hello World and Makefiles
 Coding Step 2  Source Control
 Coding Step 3  HighLevel Requirements
 Coding Step 4  Design
The last article in this series discussed how to write functional highlevel requirements: specifications for what your software is supposed to do. Software design is the other side of the coin....
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials. When working in $GF(2^n)$ we don't have large enough powers to actually do a division, so we compute the inverse of the denominator and then multiply. This is usually done using Euclid's method, but if squaring and multiplying are fast we can take advantage of these operations and compute the multiplicative inverse in just a few steps.
The first time I ran across this...
Motion Sensor with Raspberry Pi and MPU6050  Part 1
This blog will help you build your own, low cost 3axis motion sensor using Raspberry Pi and Invensense MPU6050. For the benefit of the beginners, I will be beginning with the basics  setting up Raspberry Pi in part 1 of this blog series and then proceed to interfacing the MEMS based triaxial motion sensing unit  MPU6050 to Raspberry Pi board in part 2. The final part no. 3 will be about acquiring data on the client computer. I have tried multiple...
One Clock Cycle Polynomial Math
Error correction codes and cryptographic computations are most easily performed working with $GF(2^n)$ polynomials. By using very special values of $n$ we can build circuits which multiply and square in one clock cycle on an FPGA. These circuits come about by flipping back and forth between a standard polynomial basis and a normal basis representation of elements in $GF(2^n)$.
A normal basis is yet another form of polynomial but instead of adding powers of $\beta$ we add...
Basic hand tools for electronics assembly
Though the software tools vary with different microcontrollers, many hardware tools are the same.
If you are working on larger robotic or automotive systems, you will need a 3/8" and 1/2" drive socket set. There are occasions when even larger drive socket sets are needed. For small robots and taking things apart, the 1/4" drive socket set is useful. The sizes usually range from 5/32" to 9/16" and 4mm to 15mm. You will need both shallow and deep sockets, both standard and...
Elliptic Curve Cryptography
Secure online communications require encryption. One standard is AES (Advanced Encryption Standard) from NIST. But for this to work, both sides need the same key for encryption and decryption. This is called Private Key encryption. Public Key encryption is used to create a private key between two sides that have not previously communicated. Compared to the history of encryption, Public Key methods are very recent having been started in the 1970's. Elliptic...
The three laws of safe embedded systems
This short article is part of an ongoing series in which I aim to explore some techniques that may be useful for developers and organisations that are beginning their first safetyrelated embedded project.
In the last two weeks, I’ve had the opportunity to discuss the contents of my previous article on this site with a group of very smart and enthusiastic engineers in Cairo (Egypt). As part of this discussion, it has become clear that I should add a few more details to explain the work...
Lost Secrets of the HBridge, Part II: Ripple Current in the DC Link Capacitor
In my last post, I talked about ripple current in inductive loads.
One of the assumptions we made was that the DC link was, in fact, a DC voltage source. In reality that's an approximation; no DC voltage source is perfect, and current flow will alter the DC link voltage. To analyze this, we need to go back and look at how much current actually is being drawn from the DC link. Below is an example. This is the same kind of graph as last time, except we added two...
Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the BerlekampMassey Algorithm
The last two articles were on discrete logarithms in finite fields — in practical terms, how to take the state \( S \) of an LFSR and its characteristic polynomial \( p(x) \) and figure out how many shift steps are required to go from the state 000...001 to \( S \). If we consider \( S \) as a polynomial bit vector such that \( S = x^k \bmod p(x) \), then this is equivalent to the task of figuring out \( k \) from \( S \) and \( p(x) \).
This time we’re tackling something...
Thoughts on Starting a New Career
I recently completed a 16year stint at an engineering company. I started there fresh out of college in June 1996. This June I just started a new career as an applications engineer in the area of motor drives at Microchip Technology in Chandler, Arizona. The experience I had in switching jobs was a very enlightening one for me, and has given me an opportunity to reflect on my career. I want to share some of that reflection with you.
Disclaimer: the opinions expressed in this and other blogs...
How to Analyze a Differential Amplifier
There are a handful of things that you just have to know if you do any decent amount of electronic circuit design work. One of them is a voltage divider. Another is the behavior of an RC filter. I'm not going to explain these two things or even link to a good reference on them — either you already know how they work, or you're smart enough to look it up yourself.
The handful of things also includes some others that are a little more interesting to discuss. One of them is this...
Someday We’ll Find It, The Kelvin Connection
You’d think it wouldn’t be too hard to measure electrical resistance accurately. And it’s really not, at least according to wikiHow.com: you just follow these easy steps:
 Choose the item whose resistance you wish to measure.
 Plug the probes into the correct test sockets.
 Turn on the multimeter.
 Select the best testing range.
 Touch the multimeter probes to the item you wish to measure.
 Set the multimeter to a high voltage range after finishing the...
Basic hand tools for electronics assembly
Though the software tools vary with different microcontrollers, many hardware tools are the same.
If you are working on larger robotic or automotive systems, you will need a 3/8" and 1/2" drive socket set. There are occasions when even larger drive socket sets are needed. For small robots and taking things apart, the 1/4" drive socket set is useful. The sizes usually range from 5/32" to 9/16" and 4mm to 15mm. You will need both shallow and deep sockets, both standard and...
Dealing With Fixed Point Fractions
Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow. If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions. When integers overflow, they lose data off the most significant bits. When fractions overflow, they lose data off...
Linear Regression with EvenlySpaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curvefitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the bestfit linear curve, so \( \frac{x_i  \hat{x}_i}{\hat{\sigma}} = 0.3 \)) — Studentize me! would have been nice, but I couldn’t work it into the topic for today. Oh well.
I needed a little break from...
Your Career Archive
Clive Maxfield and Adam Taylor recently published a series of blog posts about how to get and keep an engineering job, discussing preparation in high school through early career stages. I've just started a new job, and wanted to add some information on a particular aspect of changing jobs, the employment background check.
Over the past 10 years, I've changed jobs several times. Three of those jobs, including the most recent two, have required background checks as part of...
C++ on microcontrollers 4 – input pins, and decoding a rotary switch
This blog series is about the use of C++ for modern microcontrollers. My plan is to show the gradual development of a basic I/O library. I will introduce the objectoriented C++ features that are used step by step, to provide a gentle yet practical introduction into C++ for C programmers. Reader input is very much appreciated, you might even steer me in the direction you find most interesting.
So far I...
Linear Feedback Shift Registers for the Uninitiated, Part XVIII: Primitive Polynomial Generation
Last time we figured out how to reverseengineer parameters of an unknown CRC computation by providing sample inputs and analyzing the corresponding outputs. One of the things we discovered was that the polynomial \( x^{16} + x^{12} + x^5 + 1 \) used in the 16bit X.25 CRC is not primitive — which just means that all the nonzero elements in the corresponding quotient ring can’t be generated by powers of \( x \), and therefore the corresponding 16bit LFSR with taps in bits 0, 5,...
Linear Feedback Shift Registers for the Uninitiated, Part VII: LFSR Implementations, Idiomatic C, and Compiler Explorer
The last four articles were on algorithms used to compute with finite fields and shift registers:
 multiplicative inverse
 discrete logarithm
 determining characteristic polynomial from the LFSR output
Today we’re going to come back down to earth and show how to implement LFSR updates on a microcontroller. We’ll also talk a little bit about something called “idiomatic C” and a neat online tool for experimenting with the C compiler.
Levitating Globe Teardown, Part 1
I've been kicking some ideas around for a long time for a simple and inexpensive platform I could use for control systems experimentation for the beginner. I want something that can be controlled easily in a basic fashion, yet that provides some depth: I want to be able to present evermore challenging goals to the student, that can be attained by fancier control algorithms all on the same device.
I'm currently looking at magnetic levitation. It's fun, it has the potential to be...
How to install Ubuntu 12.04 Precise, Xubuntudesktop and Open JDK7 on Beagleboard Rev. C2
My aim was to install Ubuntu 12.04, Xubuntudesktop graphical user interface and Java virtual machine (Open JDK7) on my beagleboard so that I could run my java application on the monitor connected to the BB. I encountered several problems and solved them one by one. Following is how I've done it..
I had all the accesorries for the beagleboard (usb hub, dvitohdmi cable, usbethernet converter, usb keyboard, usb mouse and a hdmi enabled monitor).
My host PC also has a Ubuntu 12.04...
You Will Make Mistakes
</scorpion>: FAILAnyone out there see the TV pilot of Scorpion? Genius hacker squad meets Homeland Security in a fastpaced thriller to save hundreds of airplanes from crashing after LAX air traffic control software upgrade fails and they didn’t save a backup of the old version (ZOMG!!!) so thousands of people are going to die because the planes… well, they just can’t land! They just can’t. Even if the weather is sunny and calm and there could quite possibly...
C++ on microcontrollers 4 – input pins, and decoding a rotary switch
This blog series is about the use of C++ for modern microcontrollers. My plan is to show the gradual development of a basic I/O library. I will introduce the objectoriented C++ features that are used step by step, to provide a gentle yet practical introduction into C++ for C programmers. Reader input is very much appreciated, you might even steer me in the direction you find most interesting.
So far I...
[ C Programming Techniques: integer type optimization ]
I am currently working on a voltage controller running on a ATMEGA328P, ATMEL AVR 8 bits microcontroller. The controller logic is implemented in the main() routine and relies on a periodical timer whose frequency is fixed at application setup. Among other things, the timer ISR handler increments some per tick counters which are then used by the main routine to implement the voltage controller timing logic.By looking at the code, one noticed that I use the uint8_t type for counters instead of...
StrangeCPU #4. Microcode
Summary:Sliding windows containing runs of microcode.
Table of Contents:
Part 1: A new CPU  technology review, reexamination of the premises; StrangeCPU concepts; x86 notes.

Part 2: SlidingWindow Token Machines, an indepth exploration of this curious technology; ARM notes.
Mutex vs. Semaphores – Part 2: The Mutex & Mutual Exclusion Problems
Part 1 of this series we looked at the history of the binary and counting semaphore, and then went on to discuss some of the associated problem areas. In this posting I aim to show how a different RTOS construct, the mutex, may overcome some, if not all, of these weaknesses.
To address the problems associated with semaphore, a new concept was developed during the late 1980’s. I have struggled to find it’s first clear definition, but the major use of the term mutex (another...
Fluxions for Fun and Profit: Euler, Trapezoidal, Verlet, or RungeKutta?
Today we're going to take another diversion from embedded systems, and into the world of differential equations, modeling, and computer simulation.
DON'T PANIC!First of all, just pretend I didn't bring up anything complicated. We're exposed to the effects of differential equations every day, whether we realize it or not. Your car speedometer and odometer are related by a differential equation, and whether you like math or not, you probably have some comprehension of what's going on: you...