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...
Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough
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
April is Oscilloscope Month: In Which We Discover Agilent Offers Us a Happy Deal and a Sad Name
Last month I wrote that March is Oscilloscope Month, because Agilent had a deal on the MSOX2000 and MSOX3000 series scopes offering higher bandwidth at lower prices. I got an MSOX3034 oscilloscope and saved my company $3500! (Or rather, I didn't save them anything, but I got a 350MHz scope at a 200MHz price.)
The scope included a free 30-day trial for each of the application software modules. I used my 30-day trial for the serial decode + triggering module, to help debug some UART...
How to Analyze a Differential Amplifier
There are a handful of things that you just have to know if you do any decent amount of electronic circuit design work. One of them is a voltage divider. Another is the behavior of an RC filter. I'm not going to explain these two things or even link to a good reference on them — either you already know how they work, or you're smart enough to look it up yourself.
The handful of things also includes some others that are a little more interesting to discuss. One of them is this...
Garden Rakes Revisited: The Hall of Shame
A little while ago, I wrote about what I call the “garden rakes” syndrome in software, where there are little bugs or pitfalls lying around like sloppy garden rakes that no one has put away, and when you use these software programs, instead of zooming around getting things done, you’re either tripping over the garden rakes or carefully trying to avoid them. Either way, you lose focus on what you’re really trying to work on, and that causes a big hit in...
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...
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...
Efficiency Through the Looking-Glass
If you've ever designed or purchased a power supply, chances are you have had to work with efficiency calculations. I can remember in my beginning electronic circuits course in college, in the last lecture when the professor was talking about switching power converters, and saying how all of a sudden you could take a linear regulator that was 40% efficient and turn it into a switching regulator that was 80% efficient. I think that was the nail in the coffin for any plans I had to pursue a...
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow.
In the world of floating-point arithmetic, overflow is possible but not particularly common. You can get it when numbers become too large; IEEE double-precision floating-point numbers support a range of just under 21024, and if you go beyond that you have problems:
for k in [10, 100, 1000, 1020, 1023, 1023.9, 1023.9999, 1024]: try: ...How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part II (Tracking Loops and PLLs)
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...
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...
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...
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Last time we looked at spread-spectrum techniques using the output bit sequence of an LFSR as a pseudorandom bit sequence (PRBS). The main benefit we explored was increasing signal-to-noise ratio (SNR) relative to other disturbance signals in a communication system.
This time we’re going to use a PRBS from LFSR output to do something completely different: system identification. We’ll show two different methods of active system identification, one using sine waves and the other...
Fluxions for Fun and Profit: Euler, Trapezoidal, Verlet, or Runge-Kutta?
Today we're going to take another diversion from embedded systems, and into the world of differential equations, modeling, and computer simulation.
DON'T PANIC!First of all, just pretend I didn't bring up anything complicated. We're exposed to the effects of differential equations every day, whether we realize it or not. Your car speedometer and odometer are related by a differential equation, and whether you like math or not, you probably have some comprehension of what's going on: you...
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...
Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation
Last time we looked at the use of LFSRs in counters and position encoders.
This time we’re going to look at pseudorandom number generation, and why you may — or may not — want to use LFSRs for this purpose.
But first — an aside:
Science Fair 1983When I was in fourth grade, my father bought a Timex/Sinclair 1000. This was one of several personal computers introduced in 1982, along with the Commodore 64. The...
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...
Jaywalking Around the Compiler
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?
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...
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:
- the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
- the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream
The unusually-good correlation properties...
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...
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...
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...
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...
Short Takes (EE Shanty): What shall we do with a zero-ohm resistor?
In circuit board design you often need flexibility. It can cost hundreds or thousands of dollars to respin a circuit board, so I need flexibility for two main reasons:
- sometimes it's important to be able to use one circuit board design to serve more than one purpose
- risk reduction: I want to give myself the option to add in or leave out certain things when I'm not 100% sure I'll need them.
And so we have jumpers and DIP switches and zero-ohm resistors:
Jumpers and...
Wye Delta Tee Pi: Observations on Three-Terminal Networks
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
Isolated Sigma-Delta Modulators, Rah Rah Rah!
I recently faced a little "asterisk" problem, which looks like it can be solved with some interesting ICs.
I needed to plan out some test instrumentation to capture voltage and current information over a short period of time. Nothing too fancy, 10 or 20kHz sampling rate, about a half-dozen channels sampled simultaneously or near simultaneously, for maybe 5 or 10 seconds.
Here's the "asterisk": Oh, by the way, because the system in question was tied to the AC mains, I needed some...
How to Analyze a Differential Amplifier
There are a handful of things that you just have to know if you do any decent amount of electronic circuit design work. One of them is a voltage divider. Another is the behavior of an RC filter. I'm not going to explain these two things or even link to a good reference on them — either you already know how they work, or you're smart enough to look it up yourself.
The handful of things also includes some others that are a little more interesting to discuss. One of them is this...
Implementation Complexity, Part I: The Tower of Babel, Gremlins, and The Mythical Man-Month
I thought I'd post a follow-up, in a sense, to an older post about complexity in consumer electronics I wrote a year and a half ago. That was kind of a rant against overly complex user interfaces. I am a huge opponent of unnecessary complexity in almost any kind of interface, whether a user interface or a programming interface or an electrical interface. Interfaces should be clean and simple.
Now, instead of interface complexity, I'll be talking about implementation complexity, with a...
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Last time we looked at spread-spectrum techniques using the output bit sequence of an LFSR as a pseudorandom bit sequence (PRBS). The main benefit we explored was increasing signal-to-noise ratio (SNR) relative to other disturbance signals in a communication system.
This time we’re going to use a PRBS from LFSR output to do something completely different: system identification. We’ll show two different methods of active system identification, one using sine waves and the other...
