Second-Order Systems, Part I: Boing!!
I’ve already written about the unexciting (but useful) 1st-order system, and about slew-rate limiting. So now it’s time to cover second-order systems.
The most common second-order systems are RLC circuits and spring-mass-damper systems.
Spring-mass-damper systems are fairly common; you’ve seen these before, whether you realize it or not. One household example of these is the spring doorstop (BOING!!):
(For what it’s worth: the spring...
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,...
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...
You Will Make Mistakes
</scorpion>: FAILAnyone out there see the TV pilot of Scorpion? Genius hacker squad meets Homeland Security in a fast-paced thriller to save hundreds of airplanes from crashing after LAX air traffic control software upgrade fails and they didn’t save a backup of the old version (ZOMG!!!) so thousands of people are going to die because the planes… well, they just can’t land! They just can’t. Even if the weather is sunny and calm and there could quite possibly...
Important Programming Concepts (Even on Embedded Systems) Part II: Immutability
Other articles in this series:
- Part I: Idempotence
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines
- Part VI: Abstraction
This article will discuss immutability, and some of its variations in the topic of functional programming.
There are a whole series of benefits to using program variables that… well, that aren’t actually variable, but instead are immutable. The impact of...
Important Programming Concepts (Even on Embedded Systems) Part I: Idempotence
There are literally hundreds, if not thousands, of subtle concepts that contribute to high quality software design. Many of them are well-known, and can be found in books or the Internet. I’m going to highlight a few of the ones I think are important and often overlooked.
But first let’s start with a short diversion. I’m going to make a bold statement: unless you’re a novice, there’s at least one thing in computer programming about which you’ve picked up...
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...
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...Musings on Publication — and Zero Sequence Modulation
Perhaps you don’t think about it, but in order for you to read these articles, someone has to do something.
And I don’t just mean writing them. Stephane Boucher has set up this website so that it’s automatic, for the most part — at least from my end of things, as an author. When I get an idea for an article, I open up a new IPython Notebook, write my article, save it in a Mercurial repository, run a Python script to convert from IPython Notebook format to HTML, open...
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...
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...
How to Include MathJax Equations in SVG With Less Than 100 Lines of JavaScript!
Today’s short and tangential note is an account of how I dug myself out of Documentation Despair. I’ve been working on some block diagrams. You know, this sort of thing, to describe feedback control systems:
And I had a problem. How do I draw diagrams like this?
I don’t have Visio and I don’t like Visio. I used to like Visio. But then it got Microsofted.
I can use MATLAB and Simulink, which are great for drawing block diagrams. Normally you use them to create a...
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...
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...
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...
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 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...
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:
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...
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...
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...Lost Secrets of the H-Bridge, Part III: Practical Issues of Inductor and Capacitor Ripple Current
We've been analyzing the ripple current in an H-bridge, both in an inductive load and the DC link capacitor. Here's a really quick recap; if you want to get into more details, go back and read part I and part II until you've got equations coming out of your ears. I promise there will be a lot less grungy math in this post. So let's get most of it out of the way:
Switches QAH and QAL are being turned on and off with pulse-width modulation (PWM), to produce an average voltage DaVdc on...
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...
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
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...
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...
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...
You Will Make Mistakes
</scorpion>: FAILAnyone out there see the TV pilot of Scorpion? Genius hacker squad meets Homeland Security in a fast-paced thriller to save hundreds of airplanes from crashing after LAX air traffic control software upgrade fails and they didn’t save a backup of the old version (ZOMG!!!) so thousands of people are going to die because the planes… well, they just can’t land! They just can’t. Even if the weather is sunny and calm and there could quite possibly...
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...
