## 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

October 30, 20131 comment

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...

## 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...

## Lost Secrets of the H-Bridge, Part II: Ripple Current in the DC Link Capacitor

July 28, 2013

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...

## Lost Secrets of the H-Bridge, Part I: Ripple Current in Inductive Loads

July 8, 2013

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...

## Adventures in Signal Processing with Python

Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. While I don’t make it a secret of my dislike of many aspects of MATLAB — which I mention later in this article — I do hope they can improve their software and reduce the price. Please note this...

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

June 16, 2013

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 wall

OK, 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...

## 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...

## 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 XIV: Gold Codes

April 18, 2018

Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.

This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...

## Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC

July 7, 20181 comment

Last time, we continued a discussion about error detection and correction by covering Reed-Solomon encoding. I was going to move on to another topic, but then there was this post on Reddit asking how to determine unknown CRC parameters:

I am seeking to reverse engineer an 8-bit CRC. I don’t know the generator code that’s used, but can lay my hands on any number of output sequences given an input sequence.

This is something I call the “unknown oracle”...

## Tolerance Analysis

May 31, 2020

Today we’re going to talk about tolerance analysis. This is a topic that I have danced around in several previous articles, but never really touched upon in its own right. The closest I’ve come is Margin Call, where I discussed several different techniques of determining design margin, and ran through some calculations to justify that it was safe to allow a certain amount of current through an IRFP260N MOSFET.

Tolerance analysis...

## Modulation Alternatives for the Software Engineer

November 8, 20111 comment

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...

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

June 12, 2018

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 Ear

## Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation

December 20, 2017

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 1983

When 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 XII: Spread-Spectrum Fundamentals

December 29, 20171 comment

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 III: Multiplicative Inverse, and Blankinship's Algorithm

September 9, 2017

Last time we talked about basic arithmetic operations in the finite field $GF(2)[x]/p(x)$ — addition, multiplication, raising to a power, shift-left and shift-right — as well as how to determine whether a polynomial $p(x)$ is primitive. If a polynomial $p(x)$ is primitive, it can be used to define an LFSR with coefficients that correspond to the 1 terms in $p(x)$, that has maximal length of $2^N-1$, covering all bit patterns except the all-zero...