## Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials

Last time, we looked at the basics of LFSRs and finite fields formed by the quotient ring \( GF(2)[x]/p(x) \).

LFSRs can be described by a list of binary coefficients, sometimes referred as the polynomial, since they correspond directly to the characteristic polynomial of the quotient ring.

Today we’re going to look at how to perform certain practical calculations in these finite fields. I maintain a Python library on bitbucket called...

## Went 280km/h (174mph) in a Porsche Panamera in Germany!

Those of you who've?been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos. ?It all started with?Embedded World early this year, then continued at ESC Boston a couple of months ago and?the latest chapter just concluded as I returned from Germany after spending a?week at SEGGER's headquarters to produce a video to highlight their 25th anniversary. ?

## 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,...

## Going back to Germany!

A couple of blog posts ago, I wrote that the decision to go to ESC Boston ended up being a great one for many different reasons.??I came back from the conference energized and really happy that I went. ?

These?feelings were?amplified a few days after my return when I received an email from Rolf Segger, the founder of SEGGER Microcontroller (check out their very new website),?asking if I would be interested in visiting their headquarters...

## ESC Boston's Videos are Now Up

In my last blog, I told you about my experience at ESC Boston and the few videos that I was planning to produce and publish.? Here they are, please have a look and any feedback?(positive or negative) is appreciated.?

Short HighlightThis is a very short (one minute) montage of some of the footage that I shot at the show & conference. ?In future shows, I absolutely need to insert clips?here and there of engineers saying a few words about?the conference (why they...

## Back from ESC Boston

NOT going to ESC Boston would have allowed me to stay home, in my comfort zone.

NOT going to ESC Boston would have saved me from driving in the absolutely horrible & stressful Boston traffic1.

NOT going to ESC Boston would have saved me from having to go through a full search & questioning session at the Canada Customs on my return2.

2017/06/06?update:?Videos are now up!So two days...

## Launch of Youtube Channel: My First Videos - Embedded World 2017

I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience. ?I would try to make the vendors focus their pitch on the essential in order to produce a one to three minutes video per booth.

So far my experience with making videos was limited to family videos, so I knew I had lots of reading to do and lots of Youtube videos and tutorials to watch. ?Trade shows are...

## The Other Kind of Bypass Capacitor

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...

## New Comments System (please help me test it)

I thought it would take me a day or two to implement, it took almost two weeks...

But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year. ?

Which means that:

- You can easily add images, either by drag and drop or through the 'Insert Image' button
- You can add?MathML, TeX and ASCIImath equations and they will be rendered with Mathjax
- You can add code snippets and they will be highlighted with highlights.js
- You can edit...

## Use DPLL to Lock Digital Oscillator to 1PPS Signal

IntroductionThere are occasions where it is desirable to lock a digital oscillator to an external time reference such as the 1PPS (One Pulse Per Second) signal output from a GPS receiver. One approach would be to synchronize a fixed frequency oscillator on the leading edge of the 1PPS signal. In many cases, this will result in adequate performance. However, in situations where simple synchronization does not provide adequate performance, digital phase-lock techniques can be applied to a...

## Launch of EmbeddedRelated.tv

With the upcoming Embedded Word?just around the corner, I am very excited to launch the EmbeddedRelated.tv?platform.??

This is where you will find the schedule for all the live broadcasts that?I will be doing from Embedded World next week.? Please note that the schedule will be evolving constantly, even during the show, so I suggest your refresh the page often.? For instance, I am still unsure if I will be able to do the 'opening of the doors' broadcast as...

## Two Capacitors Are Better Than One

I was looking for a good reference for some ADC-driving circuits, and ran across this diagram in Walt Jung’s Op-Amp Applications Handbook:

And I smiled to myself, because I immediately remembered a circuit I hadn’t used for years. Years! But it’s something you should file away in your bag of tricks.

Take a look at the RC-RC circuit formed by R1, R2, C1, and C2. It’s basically a stacked RC low-pass filter. The question is, why are there two capacitors?

I...

## Went 280km/h (174mph) in a Porsche Panamera in Germany!

Those of you who've?been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos. ?It all started with?Embedded World early this year, then continued at ESC Boston a couple of months ago and?the latest chapter just concluded as I returned from Germany after spending a?week at SEGGER's headquarters to produce a video to highlight their 25th anniversary. ?

## Optimizing Optoisolators, and Other Stories of Making Do With Less

It’s been a few months since I’ve rolled up my sleeves here and dug into some good old circuit design issues. I started out with circuit design articles, and I’ve missed it.

Today’s topic will be showing you some tricks for how to get more performance out of an optoisolator. These devices — and I’m tempted to be lazy and call them “optos”, but that sounds more like a cereal with Greek yogurt-covered raisins — are essentially just an LED...

## Stairway to Thévenin

This article was inspired by a recent post on reddit asking for help on Thévenin and Norton equivalent circuits.

(With apologies to Mr. Thévenin, the rest of the e's that follow will remain unaccented.)

I still remember my introductory circuits class on the subject, roughly as follows:

(NOTE: Do not get scared of what you see in the rest of this section. We're going to point out the traditional approach for teaching linear equivalent circuits first. If you have...

## 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:...

## How precise is my measurement?

Some might argue that measurement is a blend of skepticism and faith. While time constraints might make you lean toward faith, some healthy engineering skepticism should bring you back to statistics. This article reviews some practical statistics that can help you satisfy one common question posed by skeptical engineers: “How precise is my measurement?” As we’ll see, by understanding how to answer it, you gain a degree of control over your measurement time.

An accurate, precise...## Voltage Drops Are Falling on My Head: Operating Points, Linearization, Temperature Coefficients, and Thermal Runaway

Today’s topic was originally going to be called “Small Changes Caused by Various Things”, because I couldn’t think of a better title. Then I changed the title. This one’s not much better, though. Sorry.

What I had in mind was the Shockley diode equation and some other vaguely related subjects.

My Teachers Lied to MeMy introductory circuits class in college included a section about diodes and transistors.

The ideal diode equation is...

## The Other Kind of Bypass Capacitor

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...

## Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials

Last time, we looked at the basics of LFSRs and finite fields formed by the quotient ring \( GF(2)[x]/p(x) \).

LFSRs can be described by a list of binary coefficients, sometimes referred as the polynomial, since they correspond directly to the characteristic polynomial of the quotient ring.

Today we’re going to look at how to perform certain practical calculations in these finite fields. I maintain a Python library on bitbucket called...

## 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...

## Lost Secrets of the H-Bridge, 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...

## The Other Kind of Bypass Capacitor

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...

## Two jobs

For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.

edit - video of the event:

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...

## Went 280km/h (174mph) in a Porsche Panamera in Germany!

Those of you who've?been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos. ?It all started with?Embedded World early this year, then continued at ESC Boston a couple of months ago and?the latest chapter just concluded as I returned from Germany after spending a?week at SEGGER's headquarters to produce a video to highlight their 25th anniversary. ?

## Complexity in Consumer Electronics Considered Harmful

I recently returned from a visit to my grandmother, who lives in an assisted living community, and got to observe both her and my frustration first-hand with a new TV. This was a Vizio flatscreen TV that was fairly easy to set up, and the picture quality was good. But here's what the remote control looks like:

You will note:

- the small lettering (the number buttons are just under 1/4 inch in diameter)
- a typeface chosen for marketing purposes (matching Vizio's "futuristic" corporate...

## Digital PLL's -- Part 2

In?Part 1, we found the time response of a 2nd order PLL with a proportional + integral (lead-lag) loop filter.? Now let’s look at this PLL in the Z-domain [1, 2].? We will find that the response is characterized by a loop natural frequency ωn and damping coefficient ζ.?

Having a Z-domain model of the DPLL will allow us to do three things:

Compute the values of loop filter proportional gain KL and integrator gain KI that give the desired loop natural...## Finally got a drone!

As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process. ?When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce , the company bought a drone so we could?get an aerial shot of the party (at about the 1:35 mark in this video). ?Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...

## March is Oscilloscope Month — and at Tim Scale!

I got my oscilloscope today.

Maybe that was a bit of an understatement; I'll have to resort to gratuitous typography:

I GOT MY OSCILLOSCOPE TODAY!!!!Those of you who are reading this blog may remember I made a post about two years ago about searching for the right oscilloscope for me. Since then, I changed jobs and have been getting situated in the world of applications engineering, working on motor control projects. I've been gradually working to fill in gaps in the infrastructure...

## Embedded World 2018 - The Interviews

Once again this year, I had the chance to go to Embedded World in Nuremberg Germany.? And once again this year, I brought my video equipment to try and capture some of the most interesting things at the show.??

Something new this year, I asked Jacob Beningo if he would partner with me in doing interviews with a few vendors.? I would operate the camera while Jacob would ask the right?questions to the vendors to make them talk about the key products/features that...