## Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

I’m writing this article in a room with a bunch of other people talking, and while sometimes I wish they would just SHUT UP, it would be...

## Ten Little Algorithms, Part 1: Russian Peasant Multiplication

This blog needs some short posts to balance out the long ones, so I thought I’d cover some of the algorithms I’ve used over the years. Like the Euclidean algorithm and Extended Euclidean algorithm and Newton’s method — except those you should know already, and if not, you should be locked in a room until you do. Someday one of them may save your life. Well, you never know.

Other articles in this series:

- Part 1:

## 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...

## My Love-Hate Relationship with Stack Overflow: Arthur S., Arthur T., and the Soup Nazi

Warning: In the interest of maintaining a coherent stream of consciousness, I’m lowering the setting on my profanity filter for this post. Just wanted to let you know ahead of time.

I’ve been a user of Stack Overflow since December of 2008. And I say “user” both in the software sense, and in the drug-addict sense. I’m Jason S, user #44330, and I’m a programming addict. (Hi, Jason S.) The Gravatar, in case you were wondering, is a screen...

## 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...

## Important Programming Concepts (Even on Embedded Systems) Part V: State Machines

Other articles in this series:

- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part VI: Abstraction

Oh, hell, this article just had to be about state machines, didn’t it? State machines! Those damned little circles and arrows and q’s.

Yeah, I know you don’t like them. They bring back bad memories from University, those Mealy and Moore machines with their state transition tables, the ones you had to write up...

## 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...

## Book Review: "Turing's Cathedral"

My library had Turing’s Cathedral: The Origins of the Digital Universe by George Dyson on its new acquisitions shelf, so I read it. I’d recommend the book to anyone interested in the history of computing.

Turing’s Cathedral primarly covers the period in early computing from 1940-1958, and bridges a gap between a few other popular books: on the historic side, between Richard Rhodes’s

## 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

## 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...

## 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.

## 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...

## 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...

## 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,

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection

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 5: Quadratic Extremum Interpolation and Chandrupatla's Method

This article is mainly an excuse to scribble down some cryptic-looking mathematics — Don’t panic! Close your eyes and scroll down if you feel nauseous — and...

## 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...

## 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?

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...