## 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...

## First-Order Systems: The Happy Family

May 3, 20141 comment
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

April 19, 2014

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

April 13, 2014

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

April 12, 2014

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!

March 6, 2014

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

January 28, 20141 comment

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)

December 4, 2013

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: ...

## Trust, but Verify: Examining the Output of an Embedded Compiler

September 27, 2015

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

January 19, 2015

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 Me

My introductory circuits class in college included a section about diodes and transistors.

The ideal diode equation is...

## Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials

July 17, 2017

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...

## 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...

## Wye Delta Tee Pi: Observations on Three-Terminal Networks

December 23, 2018

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

## 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...

## Isolated Sigma-Delta Modulators, Rah Rah Rah!

April 25, 2013

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

April 13, 2014

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...

## Scorchers, Part 3: Bare-Metal Concurrency With Double-Buffering and the Revolving Fireplace

July 25, 2020

This is a short article about one technique for communicating between asynchronous processes on bare-metal embedded systems.

A: to To other side. get the

— Jason Whittington

There are many reasons why concurrency is

## Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm

October 18, 2017

The last two articles were on discrete logarithms in finite fields — in practical terms, how to take the state $S$ of an LFSR and its characteristic polynomial $p(x)$ and figure out how many shift steps are required to go from the state 000...001 to $S$. If we consider $S$ as a polynomial bit vector such that $S = x^k \bmod p(x)$, then this is equivalent to the task of figuring out $k$ from $S$ and $p(x)$.

This time we’re tackling something...