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
Introduction
There 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...
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 frequency and...Digital PLL's -- Part 1
1. IntroductionFigure 1.1 is a block diagram of a digital PLL (DPLL). The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal. The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance. The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.
One application of the DPLL is to recover the timing in a digital...
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,...
Lost Secrets of the H-Bridge, Part I: Ripple Current in Inductive Loads
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...
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...
PID Without a PhD
I both consult and teach in the area of digital control. Through both of these efforts, I have found that while there certainly are control problems that require all the expertise I can bring to bear, there are a great number of control problems that can be solved with the most basic knowledge of simple controllers, without resort to any formal control theory at all.
This article will tell you how to implement a simple controller in software and how to tune it without getting into heavy...
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...
Real-time clocks: Does anybody really know what time it is?
We recently started writing software to make use of a real-time clock IC, and found to our chagrin that the chip was missing a rather useful function, namely elapsed time in seconds since the standard epoch (January 1, 1970, midnight UTC).Let me back up a second.A real-time clock/calendar (RTC) is a micropower chip that has an oscillator on it that keeps counting time, independent of main system power. Usually this is done with a lithium battery that can power the RTC for years, so that even...
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...
Feedback Controllers - Making Hardware with Firmware. Part 7. Turbo-charged DSP Oscillators
This article will look at some DSP Sine-wave oscillators and will show how an FPGA with limited floating-point performance due to latency, can be persuaded to produce much higher sample-rate sine-waves of high quality.
Comparisons will be made between implementations on Intel Cyclone V and Cyclone 10 GX FPGAs. An...
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 frequency and...Linear Feedback Shift Registers for the Uninitiated, Part III: Multiplicative Inverse, and Blankinship's Algorithm
Last time we talked about basic arithmetic operations in the finite field \( GF(2)[x]/p(x) \) — addition, multiplication, raising to a power, shift-left and shift-right — as well as how to determine whether a polynomial \( p(x) \) is primitive. If a polynomial \( p(x) \) is primitive, it can be used to define an LFSR with coefficients that correspond to the 1 terms in \( p(x) \), that has maximal length of \( 2^N-1 \), covering all bit patterns except the all-zero...
Recruiting New Bloggers!
Previous calls for bloggers have been very successful in recruiting some great communicators - Rick Lyons, Jason Sachs, Victor Yurkovsky, Mike Silva, Markus Nentwig, Gene Breniman, Stephen Friederichs,
Real-time clocks: Does anybody really know what time it is?
We recently started writing software to make use of a real-time clock IC, and found to our chagrin that the chip was missing a rather useful function, namely elapsed time in seconds since the standard epoch (January 1, 1970, midnight UTC).Let me back up a second.A real-time clock/calendar (RTC) is a micropower chip that has an oscillator on it that keeps counting time, independent of main system power. Usually this is done with a lithium battery that can power the RTC for years, so that even...
Digital PLL's -- Part 1
1. IntroductionFigure 1.1 is a block diagram of a digital PLL (DPLL). The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal. The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance. The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.
One application of the DPLL is to recover the timing in a digital...
Have You Ever Seen an Ideal Op-Amp?
Somewhere, along with unicorns and the Loch Ness Monster, lies a small colony of ideal op-amps. Op-amp is short for operational amplifier, and we start our education on them by learning about these mythical beasts, which have the following properties:
- Infinite gain
- Infinite input impedance
- Zero output impedance
And on top of it all, they will do whatever it takes to change their output in order to make their two inputs equal.
But they don't exist. Real op-amps have...
Oscilloscope review: Hameg HMO2024
Last year I wrote about some of the key characteristics of oscilloscopes that are important to me for working with embedded microcontrollers. In that blog entry I rated the Agilent MSOX3024A 4-channel 16-digital-input oscilloscope highly.
Since then I have moved to a different career, and I am again on the lookout for an oscilloscope. I still consider the Agilent MSOX3024A the best choice for a...
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...
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...
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...
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...
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.
I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other as a parent of three kids. My job...
