## 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...

## Another 10 Circuit Components You Should Know

It's that time again to review all the oddball goodies available in electronic components. These are things you should have in your bag of tricks when you need to design a circuit board. If you read my previous posts and were looking forward to more, this article's for you!

1. Bus switches

I can't believe I haven't mentioned bus switches before. What is a bus switch?

There are lots of different options for switches:

- mechanical switch / relay: All purpose, two...

## 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...

## 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...

## 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...

## Implementation Complexity, Part II: Catastrophe, Dear Liza, and the M Word

In my last post, I talked about the Tower of Babel as a warning against implementation complexity, and I mentioned a number of issues that can occur at the time of design or construction of a project.

The Tower of Babel, Pieter Bruegel the Elder, c. 1563 (from Wikipedia)

Success and throwing it over the wallOK, so let's say that the right people get together into a well-functioning team, and build our Tower of Babel, whether it's the Empire State Building, or the electrical grid, or...

## 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...

## Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery

Last time we looked at a dsPIC implementation of LFSR updates. Now we’re going to go back to basics and look at some matrix methods, which is the third approach to represent LFSRs that I mentioned in Part I. And we’re going to explore the problem of converting from LFSR output to LFSR state.

Matrices: Beloved Historical DregsElwyn Berlekamp’s 1966 paper Non-Binary BCH Encoding covers some work on

## 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 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...

## 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...

## 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 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...

## Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction

Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.

This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.

Ernie, You Have a Banana in Your EarI have had a really really tough time writing this article. I like the...

## 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.

## 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...

## 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...

## 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 XVIII: Primitive Polynomial Generation

Last time we figured out how to reverse-engineer parameters of an unknown CRC computation by providing sample inputs and analyzing the corresponding outputs. One of the things we discovered was that the polynomial \( x^{16} + x^{12} + x^5 + 1 \) used in the 16-bit X.25 CRC is not primitive — which just means that all the nonzero elements in the corresponding quotient ring can’t be generated by powers of \( x \), and therefore the corresponding 16-bit LFSR with taps in bits 0, 5,...

## 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...

## 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...

## Modulation Alternatives for the Software Engineer

Before I get to talking about modulation, here's a brief diversion.

A long time ago -- 1993, to be precise -- I took my first course on digital electronics and processors. In that class, we had to buy a copy of the TTL Data Book* from Texas Instruments.

If you have any experience in digital logic design you probably know that TTL stands for Transistor-transistor logic (thereby making the phrase "TTL Logic" an example of RAS...

## 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...