Wye Delta Tee Pi: Observations on Three-Terminal Networks
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
The Least Interesting Circuit in the World
It does nothing, most of the time.
It cannot compute pi. It won’t oscillate. It doesn’t light up.
Often it makes other circuits stop working.
It is… the least interesting circuit in the world.
What is it?
About 25 years ago, I took a digital computer architecture course, and we were each given use of an ugly briefcase containing a bunch of solderless breadboards and a power supply and switches and LEDs — and a bunch of
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,...
R1C1R2C2: The Two-Pole Passive RC Filter
I keep running into this circuit every year or two, and need to do the same old calculations, which are kind of tiring. So I figured I’d just write up an article and then I can look it up the next time.
This is a two-pole passive RC filter. Doesn’t work as well as an LC filter or an active filter, but it is cheap. We’re going to find out a couple of things about its transfer function.
First let’s find out the transfer function of this circuit:
Not very...
Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
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”...
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...
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 Regression with Evenly-Spaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curve-fitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the best-fit linear curve, so \( \frac{x_i - \hat{x}_i}{\hat{\sigma}} = 0.3 \)) — Studentize me! would have been nice, but I couldn’t work it into the topic for today. Oh well.
I needed a little break from...
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
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 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...
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...
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
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...
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...
How to Build a Fixed-Point PI Controller That Just Works: Part I
This two-part article explains five tips to make a fixed-point PI controller work well. I am not going to talk about loop tuning -- there are hundreds of articles and books about that; any control-systems course will go over loop tuning enough to help you understand the fundamentals. There will always be some differences for each system you have to control, but the goals are the same: drive the average error to zero, keep the system stable, and maximize performance (keep overshoot and delay...
Help, My Serial Data Has Been Framed: How To Handle Packets When All You Have Are Streams
Today we're going to talk about data framing and something called COBS, which will make your life easier the next time you use serial communications on an embedded system -- but first, here's a quiz:
Quick Diversion, Part I: Which of the following is the toughest area of electrical engineering? analog circuit design digital circuit design power electronics communications radiofrequency (RF) circuit design electromagnetic...Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of the waveform they were sampled from.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 5)
In this article we’re going to take a look at cycle time, queues, and inventory. Cycle time is a manufacturing term — for anything, not just semiconductors — meaning how long it takes for an individual product to make its way through a manufacturing process, from start to finish. We’re going to try to understand how long it takes to manufacture semiconductors. In particular, we’re going to try to answer these questions:
- How long does it take...
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,...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.
One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...
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
How to Build a Fixed-Point PI Controller That Just Works: Part II
In Part I we talked about some of the issues around discrete-time proportional-integral (PI) controllers:
- various forms and whether to use the canonical form for z-transforms (don't do it!)
- order of operation in the integral term: whether to scale and then integrate (my recommendation), or integrate and then scale.
- saturation and anti-windup
In this part we'll talk about the issues surrounding fixed-point implementations of PI controllers. First let's recap the conceptual structure...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.
One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...
Which MOSFET topology?
A recent electronics.StackExchange question brings up a good topic for discussion. Let's say you have a power supply and a 2-wire load you want to be able to switch on and off from the power supply using a MOSFET. How do you choose which circuit topology to choose? You basically have four options, shown below:
From left to right, these are:
High-side switch, N-channel MOSFET High-side switch, P-channel MOSFET Low-side switch, N-channel...Development of the MOS Technology 6502: A Historical Perspective
One ubiquitous microprocessor of the late 1970s and 1980s was the MOS Technology MCS 6502. I included a section on the development of the 6502 in Part 2 of Supply Chain Games, and have posted it as an excerpt here, as I believe it is deserving in its own right.
(Note: MOS Technology is pronounced with the individual letters M-O-S “em oh ess”,[1] not “moss”, and should not be confused with another semiconductor company,
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 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...
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 2)
Welcome back! Today we’re going to zoom around again in some odd directions, and give a roundabout introduction to the semiconductor industry, touching on some of the following questions:
- How do semiconductors get designed and manufactured?
- What is the business of semiconductor manufacturing like?
- What are the different types of semiconductors, and how does that affect the business model of these manufacturers?
- How has the semiconductor industry evolved over...
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...
Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields
Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.
— Évariste Galois, May 29, 1832
I was going to call this short series of articles “LFSRs for Dummies”, but thought better of it. What is a linear feedback shift register? If you want the short answer, the Wikipedia article is a decent introduction. But these articles are aimed at those of you who want a little bit deeper mathematical understanding,...