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 “
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...
Oh Robot My Robot
Oh Robot! My Robot! You’ve broken off your nose! Your head is spinning round and round, your eye no longer glows, Each program after program tapped your golden memory, You used to have 12K, now there is none that I can see, Under smoldering antennae, Over long forgotten feet, My sister used your last part: The chip she tried to eat.
Oh Robot, My Robot, the remote controls—they call, The call—for...
Important Programming Concepts (Even on Embedded Systems) Part VI : Abstraction
Earlier articles:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines
We have come to the last part of the Important Programming Concepts series, on abstraction. I thought I might also talk about why there isn’t a Part VII, but decided it would distract from this article — so if you want to know the reason, along with what’s next,
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,...
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
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...
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...
10 Software Tools You Should Know
Unless you're designing small analog electronic circuits, it's pretty hard these days to get things done in embedded systems design without the help of computers. I thought I'd share a list of software tools that help me get my job done. Most of these are free or inexpensive. Most of them are also for working with software. If you never have to design, read, or edit any software, then you're one of a few people that won't benefit from reading this.
Disclaimer: the "best" software...
R1C1R2C2: The Two-Pole Passive RC Filter
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...
Important Programming Concepts (Even on Embedded Systems) Part III: Volatility
1vol·a·tile adjective \ˈvä-lə-təl, especially British -ˌtī(-ə)l\ : likely to change in a very sudden or extreme way : having or showing extreme or sudden changes of emotion : likely to become dangerous or out of control
— Merriam-Webster Online Dictionary
Other articles in this series:
Slew Rate Limiters: Nonlinear and Proud of It!
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...
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...
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.
Donald Knuth Is the Root of All Premature Optimization
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;DRThe 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...
Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons
Other articles in this series:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part V: State Machines
- Part VI: Abstraction
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
The CRC Wild Goose Chase: PPP Does What?!?!?!
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,...
10 More (Obscure) Circuit Components You Should Know
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...
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...
10 Items of Test Equipment You Should Know
When life gets rough and a circuit board is letting you down, it’s time to turn to test equipment. The obvious ones are multimeters and oscilloscopes and power supplies. But you know about those already, right?
Here are some you may not have heard of:
Non-contact current sensors. Oscilloscope probes measure voltage. When you need to measure current, you need a different approach. Especially at high voltages, where maintaining galvanic isolation is important for safety. The usual...Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World
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...
First-Order Systems: The Happy Family
Все счастли́вые се́мьи похо́жи друг на дру́га, ка́ждая несчастли́вая семья́ несчастли́ва по-сво́ему.— Лев Николаевич Толстой, Анна Каренина
Happy families are all alike; every unhappy family is unhappy in its own way.— Lev Nicholaevich Tolstoy, Anna Karenina
I was going to write an article about second-order systems, but then realized that it would be...
Important Programming Concepts (Even on Embedded Systems) Part III: Volatility
1vol·a·tile adjective \ˈvä-lə-təl, especially British -ˌtī(-ə)l\ : likely to change in a very sudden or extreme way : having or showing extreme or sudden changes of emotion : likely to become dangerous or out of control
— Merriam-Webster Online Dictionary
Other articles in this series:
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...
Bad Hash Functions and Other Stories: Trapped in a Cage of Irresponsibility and Garden Rakes
I was recently using the publish() function in MATLAB to develop some documentation, and I ran into a problem caused by a bad hash function.
In a resource-limited embedded system, you aren't likely to run into hash functions. They have three major applications: cryptography, data integrity, and data structures. In all these cases, hash functions are used to take some type of data, and deterministically boil it down to a fixed-size "fingerprint" or "hash" of the original data, such that...
