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Racing to Sleep

Jason Sachs December 30, 2019

Today we’re going to talk about low-power design.

Suppose I’m an electrical engineer working with wildlife biologists who are gathering field data on the Saskatchewan ringed-neck mountain goat. My team has designed a device called the BigBrotherBear 2000 (BBB2000) with a trip cable and a motor and a camera and a temperature sensor and a hot-wire anemometer and a real-time clock and an SD card and a battery and a LoRa transceiver. The idea is something like...


Jaywalking Around the Compiler

Jason Sachs December 9, 20193 comments

Our team had another code review recently. I looked at one of the files, and bolted upright in horror when I saw a function that looked sort of like this:

void some_function(SOMEDATA_T *psomedata) { asm volatile("push CORCON"); CORCON = 0x00E2; do_some_other_stuff(psomedata); asm volatile("pop CORCON"); }

There is a serious bug here — do you see what it is?


Shibboleths: The Perils of Voiceless Sibilant Fricatives, Idiot Lights, and Other Binary-Outcome Tests

Jason Sachs September 29, 2019

AS-SALT, JORDAN — Dr. Reza Al-Faisal once had a job offer from Google to work on cutting-edge voice recognition projects. He turned it down. The 37-year-old Stanford-trained professor of engineering at Al-Balqa’ Applied University now leads a small cadre of graduate students in a government-sponsored program to keep Jordanian society secure from what has now become an overwhelming influx of refugees from the Palestinian-controlled West Bank. “Sometimes they visit relatives...


Wye Delta Tee Pi: Observations on Three-Terminal Networks

Jason Sachs December 23, 2018

Today I’m going to talk a little bit about three-terminal linear passive networks. These generally come in two flavors, wye and delta.

Why Wye?

The town of Why, Arizona has a strange name that comes from the shape of the original road junction of Arizona State Highways 85 and 86, which was shaped like the letter Y. This is no longer the case, because the state highway department reconfigured the intersection


The Least Interesting Circuit in the World

Jason Sachs 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


Linear Feedback Shift Registers for the Uninitiated, Part XVIII: Primitive Polynomial Generation

Jason Sachs August 6, 20182 comments

Last time we figured out how to reverse-engineer 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 16-bit 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 16-bit LFSR with taps in bits 0, 5,...


R1C1R2C2: The Two-Pole Passive RC Filter

Jason Sachs July 28, 20181 comment

I keep running into this circuit every year or two, and need to do the same old calculations, which are kind of tiring. So I figured I’d just write up an article and then I can look it up the next time.

This is a two-pole passive RC filter. Doesn’t work as well as an LC filter or an active filter, but it is cheap. We’re going to find out a couple of things about its transfer function.

First let’s find out the transfer function of this circuit:

Not very...


Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC

Jason Sachs July 7, 20181 comment

Last time, we continued a discussion about error detection and correction by covering Reed-Solomon encoding. I was going to move on to another topic, but then there was this post on Reddit asking how to determine unknown CRC parameters:

I am seeking to reverse engineer an 8-bit CRC. I don’t know the generator code that’s used, but can lay my hands on any number of output sequences given an input sequence.

This is something I call the “unknown oracle”...


Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction

Jason Sachs June 19, 2018

Last time, we talked about error correction and detection, covering some basics like Hamming distance, CRCs, and Hamming codes. If you are new to this topic, I would strongly suggest going back to read that article before this one.

This time we are going to cover Reed-Solomon codes. (I had meant to cover this topic in Part XV, but the article was getting to be too long, so I’ve split it roughly in half.) These are one of the workhorses of error-correction, and they are used in...


Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction

Jason Sachs June 12, 2018

Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.

This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.

Ernie, You Have a Banana in Your Ear

I have had a really really tough time writing this article. I like the...


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

Jason Sachs November 17, 201312 comments

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...


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

Jason Sachs April 29, 20147 comments

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


Development of the MOS Technology 6502: A Historical Perspective

Jason Sachs June 18, 20222 comments

One ubiquitous microprocessor of the late 1970s and 1980s was the MOS Technology MCS 6502. I included a section on the development of the 6502 in Part 2 of Supply Chain Games, and have posted it as an excerpt here, as I believe it is deserving in its own right.

(Note: MOS Technology is pronounced with the individual letters M-O-S “em oh ess”,[1] not “moss”, and should not be confused with another semiconductor company,


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

Jason Sachs March 24, 20122 comments

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...


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

Jason Sachs 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...


Which MOSFET topology?

Jason Sachs September 1, 20119 comments

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...

Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons

Jason Sachs November 11, 20142 comments

Other articles in this series:

Today’s topic is the singleton. This article is unique (pun intended) in that unlike the others in this series, I tried to figure out a word to use that would be a positive concept to encourage, as an alternative to singletons, but


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

Jason Sachs July 3, 20176 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...


R1C1R2C2: The Two-Pole Passive RC Filter

Jason Sachs July 28, 20181 comment

I keep running into this circuit every year or two, and need to do the same old calculations, which are kind of tiring. So I figured I’d just write up an article and then I can look it up the next time.

This is a two-pole passive RC filter. Doesn’t work as well as an LC filter or an active filter, but it is cheap. We’re going to find out a couple of things about its transfer function.

First let’s find out the transfer function of this circuit:

Not very...


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

Jason Sachs 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...