## Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection

June 18, 20173 comments

Other articles in this series:

This article is mainly an excuse to scribble down some cryptic-looking mathematics — Don’t panic! Close your eyes and scroll down if you feel nauseous — and...

## Donald Knuth Is the Root of All Premature Optimization

April 17, 20172 comments

This article is about something profound that a brilliant young professor at Stanford wrote nearly 45 years ago, and now we’re all stuck with it.

TL;DR

The idea, basically, is that even though optimization of computer software to execute faster is a noble goal, with tangible benefits, this costs time and effort up front, and therefore the decision to do so should not be made on whims and intuition, but instead should be made after some kind of analysis to show that it has net...

## Zebras Hate You For No Reason: Why Amdahl's Law is Misleading in a World of Cats (And Maybe in Ours Too)

February 27, 20171 comment

I’ve been wasting far too much of my free time lately on this stupid addicting game called the Kittens Game. It starts so innocently. You are a kitten in a catnip forest. Gather catnip.

And you click on Gather catnip and off you go. Soon you’re hunting unicorns and building Huts and studying Mathematics and Theology and so on. AND IT’S JUST A TEXT GAME! HTML and Javascript, that’s it, no pictures. It’s an example of an

## The Other Kind of Bypass Capacitor

January 3, 20173 comments

There’s a type of bypass capacitor I’d like to talk about today.

It’s not the usual power supply bypass capacitor, aka decoupling capacitor, which is used to provide local charge storage to an integrated circuit, so that the high-frequency supply currents to the IC can bypass (hence the name) all the series resistance and inductance from the power supply. This reduces the noise on a DC voltage supply. I’ve...

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

December 11, 2016

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

November 22, 20163 comments

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

April 12, 20166 comments

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

March 1, 20166 comments

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

December 6, 20152 comments

“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

November 11, 20159 comments

Other articles in this series:

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...

## Another 10 Circuit Components You Should Know

October 30, 20131 comment

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...

## The Least Interesting Circuit in the World

October 7, 20185 comments

It does nothing, most of the time.

It cannot compute pi. It won’t oscillate. It doesn’t light up.

Often it makes other circuits stop working.

It is… the least interesting circuit in the world.

What is it?

About 25 years ago, I took a digital computer architecture course, and we were each given use of an ugly briefcase containing a bunch of solderless breadboards and a power supply and switches and LEDs — and a bunch of

## Lost Secrets of the H-Bridge, Part I: Ripple Current in Inductive Loads

July 8, 2013

So you think you know about H-bridges? They're something I mentioned in my last post about signal processing with Python.

Here we have a typical H-bridge with an inductive load. (Mmmmm ahhh! It's good to draw by hand every once in a while!) There are four power switches: QAH and QAL connecting node A to the DC link, and QBH and QBL connecting node B to the DC link. The load is connected between nodes A and B, and here is represented by an inductive load in series with something else. We...

## Lazy Properties in Python Using Descriptors

November 7, 2017

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...

## Oscilloscope Dreams

January 14, 20125 comments

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:...

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

July 3, 20175 comments

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,...

## The CRC Wild Goose Chase: PPP Does What?!?!?!

October 23, 20142 comments

I got a bad feeling yesterday when I had to include reference information about a 16-bit CRC in a serial protocol document I was writing. And I knew it wasn’t going to end well.

The last time I looked into CRC algorithms was about five years ago. And the time before that… sometime back in 2004 or 2005? It seems like it comes up periodically, like the seventeen-year locust or sunspots or El Niño,...

## Slew Rate Limiters: Nonlinear and Proud of It!

October 6, 2014

I first learned about slew rate limits when I was in college. Usually the subject comes up when talking about the nonideal behavior of op-amps. In order for the op-amp output to swing up and down quickly, it has to charge up an internal capacitor with a transistor circuit that’s limited in its current capability. So the slew rate limit $\frac{dV}{dt} = \frac{I_{\rm max}}{C}$. And as long as the amplitude and frequency aren’t too high, you won’t notice it. But try to...

## Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World

September 7, 20136 comments

When I posted an article on estimating velocity from a position encoder, I got a number of responses. A few of them were of the form "Well, it's an interesting article, but at slow speeds why can't you just take the time between the encoder edges, and then...." My point was that there are lots of people out there which take this approach, and don't take into account that the time between encoder edges varies due to manufacturing errors in the encoder. For some reason this is a hard concept...

## 10 More (Obscure) Circuit Components You Should Know

February 5, 20121 comment

The interest in my previous article on obscure but useful electronics parts, "10 Circuit Components You Should Know" was encouraging enough that I thought I would write a followup. So here are another 10:

1. "Ideal Diode" controllers

Load-sharing circuits use diodes tied together at their cathode terminal to take the most positive voltage among the sources and connect it to a load. Works great: you have a DC/DC power supply, a battery, and a solar cell, and it will use whichever output is...