Have You Ever Seen an Ideal Op-Amp?

Jason Sachs April 30, 2012

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...

Hot Fun in the Silicon: Thermal Testing with Power Semiconductors

Jason Sachs April 20, 2012

Here's a trick that is useful the next time you do thermal testing with your MOSFETs or IGBTs.

Thermal testing?!

Yes, that's right. It's important to make sure your power transistors don't overheat. In the datasheet, you will find some information that you can use to estimate how hot the junction inside the IC will get.

Let's look at an example. Here's a page from the IRF7739 DirectFET datasheet. I like this datasheet because it has almost all the thermal stuff on one page,...

How to Build a Fixed-Point PI Controller That Just Works: Part II

Jason Sachs March 24, 20122 comments

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...

How to Build a Fixed-Point PI Controller That Just Works: Part I

Jason Sachs February 26, 20127 comments

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...

10 More (Obscure) Circuit Components You Should Know

Jason Sachs February 5, 20121 comment

The interest in my previous article on obscure but useful electronics parts, "10 Circuit Components You Should Know" was encouraging enough that I thought I would write a followup. So here are another 10:

1. "Ideal Diode" controllers

Load-sharing circuits use diodes tied together at their cathode terminal to take the most positive voltage among the sources and connect it to a load. Works great: you have a DC/DC power supply, a battery, and a solar cell, and it will use whichever output is...

Oscilloscope Dreams

Jason Sachs January 14, 20125 comments

My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.

When I was in college in the early 1990's, our oscilloscopes looked like this:

Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:

Oscilloscopes are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...

Stairway to Thévenin

Jason Sachs December 31, 2011

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...

Organizational Reliability

Jason Sachs December 22, 20111 comment

I was cleaning out my email inbox at work today and ran across something I had forwarded on to a friend a few years ago, which I thought I would share, for those of you who are working in the engineering world.

Below is a handout I got about 10 years ago from Doug Field, an executive now at Apple. Doug is a superb and inspiring leader, whom I had the opportunity to work with briefly.

The following is a bit of a diversion from the topics I usually post, but is some good food for thought for...

Help, My Serial Data Has Been Framed: How To Handle Packets When All You Have Are Streams

Jason Sachs December 11, 201110 comments

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...

10 Circuit Components You Should Know

Jason Sachs November 27, 20112 comments

Chefs have their miscellaneous ingredients, like condensed milk, cream of tartar, and xanthan gum. As engineers, we too have quite our pick of circuits, and a good circuit designer should know what's out there. Not just the bread and butter ingredients like resistors, capacitors, op-amps, and comparators, but the miscellaneous "gadget" components as well.

Here are ten circuit components you may not have heard of, but which are occasionally quite useful.

1. Multifunction gate (

Scorchers, Part 1: Tools and Burn Rate

Jason Sachs April 12, 20165 comments

This is a short article about one aspect of purchasing, for engineers.

I had an engineering manager once — I’ll leave his real name out of it, but let’s call him Barney — who had a catchy response to the question “Can I buy XYZ?”, where XYZ was some piece of test equipment, like an oscilloscope or multimeter. Barney said, “Get what you need, need what you get.” We used purchase orders, which when I started in 1996 were these quaint forms on...

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

Jason Sachs 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

I have had a really really tough time writing this article. I like the...

Linear Regression with Evenly-Spaced Abscissae

Jason Sachs May 1, 20181 comment

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...

A Wish for Things That Work

Jason Sachs January 1, 20182 comments

As the end of the year approaches, I become introspective. This year I am frustrated by bad user interfaces in software.

Actually, every year, throughout the year, I am frustrated by bad user interfaces in software. And yet here it is, the end of 2017, and things aren’t getting much better! Argh!

I wrote about this sort of thing a bit back in 2011 (“Complexity in Consumer Electronics Considered Harmful”) but I think it’s time to revisit the topic. So I’m...

April is Oscilloscope Month: In Which We Discover Agilent Offers Us a Happy Deal and a Sad Name

Jason Sachs 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...

Python Code from My Articles Now Online in IPython Notebooks

Jason Sachs May 1, 2015

Ever since I started using IPython Notebooks to write these articles, I’ve been wanting to publish them in a form such that you can freely use my Python code. One of you (maredsous10) wanted this access as well.

Well, I finally bit the bullet and automated a script that will extract the Python code and create standalone notebooks, that are available publicly under the Apache license on my bitbucket account: https://bitbucket.org/jason_s/embedded-blog-public

This also means they...

How to Succeed in Motor Control: Olaus Magnus, Donald Rumsfeld, and YouTube

Jason Sachs December 11, 2016

Almost four years ago, I had this insight — we were doing it wrong! Most of the application notes on motor control were about the core algorithms: various six-step or field-oriented control methods, with Park and Clarke transforms, sensorless estimators, and whatnot. It was kind of like a driving school would be, if they taught you how the accelerator and brake pedal worked, and how the four-stroke Otto cycle works in internal combustion engines, and handed you a written...

Wye Delta Tee Pi: Observations on Three-Terminal Networks

Jason Sachs 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

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

Jason Sachs November 21, 2017

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 Dregs

Elwyn Berlekamp’s 1966 paper Non-Binary BCH Encoding covers some work on

Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders

Jason Sachs December 9, 2017

Last time we looked at LFSR output decimation and the computation of trace parity.

Today we are starting to look in detail at some applications of LFSRs, namely counters and encoders.


I mentioned counters briefly in the article on easy discrete logarithms. The idea here is that the propagation delay in an LFSR is smaller than in a counter, since the logic to compute the next LFSR state is simpler than in an ordinary counter. All you need to construct an LFSR is