## How to Succeed in Motor Control: Olaus Magnus, Donald Rumsfeld, and YouTube

Almost four years ago, I had this insight — we were doing it wrong! Most of the application notes on motor control were about the core algorithms: various six-step or field-oriented control methods, with Park and Clarke transforms, sensorless estimators, and whatnot. It was kind of like a driving school would be, if they taught you how the accelerator and brake pedal worked, and how the four-stroke Otto cycle works in internal combustion engines, and handed you a written...

## Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine

Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.

One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...

## Scorchers, Part 1: Tools and Burn Rate

This is a short article about one aspect of purchasing, for engineers.

I had an engineering manager once — I’ll leave his real name out of it, but let’s call him Barney — who had a catchy response to the question “Can I buy XYZ?”, where XYZ was some piece of test equipment, like an oscilloscope or multimeter. Barney said, “Get what you need, need what you get.” We used purchase orders, which when I started in 1996 were these quaint forms on...

## Padé Delay is Okay Today

This article is going to be somewhat different in that I’m not really writing it for the typical embedded systems engineer. Rather it’s kind of a specialized topic, so don’t be surprised if you get bored and move on to something else. That’s fine by me.

Anyway, let’s just jump ahead to the punchline. Here’s a numerical simulation of a step response to a \( p=126, q=130 \) Padé approximation of a time delay:

Impressed? Maybe you should be. This...

## Margin Call: Fermi Problems, Highway Horrors, Black Swans, and Why You Should Worry About When You Should Worry

“Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know that we know. There are known unknowns; that is to say, there are things that we now know we don’t know. But there are also unknown unknowns — there are things we do not know we don’t know.” — Donald Rumsfeld, February 2002

Today’s topic is engineering margin.

XKCD had a what-if column involving Fermi...

## Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 6: Green’s Theorem and Swept-Area Detection

Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of...

## The Dilemma of Unwritten Requirements

You will probably hear the word “requirements” at least 793 times in your engineering career, mostly in the context of how important it is, in any project, to agree upon clear requirements before committing to (and hastily proceeding towards) a deadline. Some of those times you may actually follow that advice. Other times it’s just talk, like how you should “wear sunscreen when spending time outdoors” and “eat a diet low in saturated fats and...

## Trust, but Verify: Examining the Output of an Embedded Compiler

I work with motor control firmware on the Microchip dsPIC33 series of microcontrollers. The vast majority of that firmware is written in C, with only a few percent in assembly. And I got to thinking recently: I programmed in C and C++ on an Intel PC from roughly 1991 to 2009. But I don’t remember ever working with x86 assembly code. Not once. Not even reading it. Which seems odd. I do that all the time with embedded firmware. And I think you should too. Before I say why, here are...

## How to Read a Power MOSFET Datasheet

One of my pet peeves is when my fellow engineers misinterpret component datasheets. This happened a few times recently in separate instances, all involving power MOSFETs. So it’s time for me to get on my soapbox. Listen up!

I was going to post an article on how to read component datasheets in general. But MOSFETs are a good place to start, and are a little more specific. I’m not the first person to write something about how to read datasheets; here are some other good...

## Lessons Learned from Embedded Code Reviews (Including Some Surprises)

My software team recently finished a round of code reviews for some of our motor controller code. I learned a lot from the experience, most notably why you would want to have code reviews in the first place.

My background is originally from the medical device industry. In the United States, software in medical devices gets a lot of scrutiny from the Food and Drug Administration, and for good reason; it’s a place for complexity to hide latent bugs. (Can you say “

## Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine

Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.

One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...

## Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough

Those of you who read my earlier articles about H-bridges, and followed them closely, have noticed there's some unfinished business. Well, here it is. Just so you know, I've been nervous about writing the fourth (and hopefully final) part of this series for a while. Fourth installments after a hiatus can bring bad vibes. I mean, look what it did to George Lucas: now we have Star Wars Episode I: The Phantom Menace and

## Ten Little Algorithms, Part 3: Welford's Method (and Friends)

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

Last time we talked about a low-pass filter, and we saw that a one-line...

## Which MOSFET topology?

A recent electronics.StackExchange question brings up a good topic for discussion. Let's say you have a power supply and a 2-wire load you want to be able to switch on and off from the power supply using a MOSFET. How do you choose which circuit topology to choose? You basically have four options, shown below:

From left to right, these are:

High-side switch, N-channel MOSFET High-side switch, P-channel MOSFET Low-side switch, N-channel...## 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.

## Lost Secrets of the H-Bridge, Part III: Practical Issues of Inductor and Capacitor Ripple Current

We've been analyzing the ripple current in an H-bridge, both in an inductive load and the DC link capacitor. Here's a really quick recap; if you want to get into more details, go back and read part I and part II until you've got equations coming out of your ears. I promise there will be a lot less grungy math in this post. So let's get most of it out of the way:

Switches QAH and QAL are being turned on and off with pulse-width modulation (PWM), to produce an average voltage DaVdc on...

## Byte and Switch (Part 2)

In part 1 we talked about the use of a MOSFET for a power switch. Here's a different circuit that also uses a MOSFET, this time as a switch for signals:

We have a thermistor Rth that is located somewhere in an assembly, that connects to a circuit board. This acts as a variable resistor that changes with temperature. If we use it in a voltage divider, the midpoint of the voltage divider has a voltage that depends on temperature. Resistors R3 and R4 form our reference resistance; when...

## Ten Little Algorithms, Part 1: Russian Peasant Multiplication

This blog needs some short posts to balance out the long ones, so I thought I’d cover some of the algorithms I’ve used over the years. Like the Euclidean algorithm and Extended Euclidean algorithm and Newton’s method — except those you should know already, and if not, you should be locked in a room until you do. Someday one of them may save your life. Well, you never know.

Other articles in this series:

- Part 1:

## Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields

Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.

— Évariste Galois, May 29, 1832

I was going to call this short series of articles “LFSRs for Dummies”, but thought better of it. What is a linear feedback shift register? If you want the short answer, the Wikipedia article is a decent introduction. But these articles are aimed at those of you who want a little bit deeper mathematical understanding,...

## Lazy Properties in Python Using Descriptors

This is a bit of a side tangent from my normal at-least-vaguely-embedded-related articles, but I wanted to share a moment of enlightenment I had recently about descriptors in Python. The easiest way to explain a descriptor is a way to outsource attribute lookup and modification.

Python has a bunch of “magic” methods that are hooks into various object-oriented mechanisms that let you do all sorts of ridiculously clever things. Whether or not they’re a good idea is another...

## How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part II (Tracking Loops and PLLs)

Yeeehah! Finally we're ready to tackle some more clever ways to figure out the velocity of a position encoder. In part I, we looked at the basics of velocity estimation. Then in my last article, I talked a little about what's necessary to evaluate different kinds of algorithms. Now it's time to start describing them. We'll cover tracking loops and phase-locked loops in this article, and Luenberger observers in part III.

But first we need a moderately simple, but interesting, example...

## Ten Little Algorithms, Part 3: Welford's Method (and Friends)

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

Last time we talked about a low-pass filter, and we saw that a one-line...

## How to Build a Fixed-Point PI Controller That Just Works: Part II

In Part I we talked about some of the issues around discrete-time proportional-integral (PI) controllers:

- various forms and whether to use the canonical form for z-transforms (don't do it!)
- order of operation in the integral term: whether to scale and then integrate (my recommendation), or integrate and then scale.
- saturation and anti-windup

In this part we'll talk about the issues surrounding fixed-point implementations of PI controllers. First let's recap the conceptual structure...

## Another 10 Circuit Components You Should Know

It's that time again to review all the oddball goodies available in electronic components. These are things you should have in your bag of tricks when you need to design a circuit board. If you read my previous posts and were looking forward to more, this article's for you!

1. Bus switches

I can't believe I haven't mentioned bus switches before. What is a bus switch?

There are lots of different options for switches:

- mechanical switch / relay: All purpose, two...

## Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough

Those of you who read my earlier articles about H-bridges, and followed them closely, have noticed there's some unfinished business. Well, here it is. Just so you know, I've been nervous about writing the fourth (and hopefully final) part of this series for a while. Fourth installments after a hiatus can bring bad vibes. I mean, look what it did to George Lucas: now we have Star Wars Episode I: The Phantom Menace and

## Ten Little Algorithms, Part 4: Topological Sort

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

Today we’re going to take a break from my usual focus on signal processing or numerical algorithms, and focus on...

## Important Programming Concepts (Even on Embedded Systems) Part II: Immutability

Other articles in this series:

- Part I: Idempotence
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines
- Part VI: Abstraction

This article will discuss immutability, and some of its variations in the topic of functional programming.

There are a whole series of benefits to using program variables that… well, that aren’t actually variable, but instead are immutable. The impact of...

## Byte and Switch (Part 2)

In part 1 we talked about the use of a MOSFET for a power switch. Here's a different circuit that also uses a MOSFET, this time as a switch for signals:

We have a thermistor Rth that is located somewhere in an assembly, that connects to a circuit board. This acts as a variable resistor that changes with temperature. If we use it in a voltage divider, the midpoint of the voltage divider has a voltage that depends on temperature. Resistors R3 and R4 form our reference resistance; when...

## Oscilloscope Dreams

My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.

When I was in college in the early 1990's, our oscilloscopes looked like this:

Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:

Oscilloscopes are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...

## Lost Secrets of the H-Bridge, Part III: Practical Issues of Inductor and Capacitor Ripple Current

We've been analyzing the ripple current in an H-bridge, both in an inductive load and the DC link capacitor. Here's a really quick recap; if you want to get into more details, go back and read part I and part II until you've got equations coming out of your ears. I promise there will be a lot less grungy math in this post. So let's get most of it out of the way:

Switches QAH and QAL are being turned on and off with pulse-width modulation (PWM), to produce an average voltage DaVdc on...