How to Analyze a Differential Amplifier

Jason Sachs April 14, 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

Jason Sachs 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!

Jason Sachs 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

Jason Sachs 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

Jason Sachs December 8, 20134 comments

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)

Jason Sachs 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: ...

How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part II (Tracking Loops and PLLs)

Jason Sachs November 18, 20138 comments

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

Jason Sachs 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?

Jason Sachs October 19, 20132 comments

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?

Jason Sachs September 30, 20132 comments

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...


Oscilloscope review: Hameg HMO2024

Jason Sachs March 28, 20133 comments

Last year I wrote about some of the key characteristics of oscilloscopes that are important to me for working with embedded microcontrollers. In that blog entry I rated the Agilent MSOX3024A 4-channel 16-digital-input oscilloscope highly.

Since then I have moved to a different career, and I am again on the lookout for an oscilloscope. I still consider the Agilent MSOX3024A the best choice for a...


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...


Important Programming Concepts (Even on Embedded Systems) Part III: Volatility

Jason Sachs October 10, 2014

1vol·a·tile adjective \ˈvä-lə-təl, especially British -ˌtī(-ə)l\ : likely to change in a very sudden or extreme way : having or showing extreme or sudden changes of emotion : likely to become dangerous or out of control

Merriam-Webster Online Dictionary

Other articles in this series:


March is Oscilloscope Month — and at Tim Scale!

Jason Sachs 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...


Real-time clocks: Does anybody really know what time it is?

Jason Sachs May 30, 20118 comments

We recently started writing software to make use of a real-time clock IC, and found to our chagrin that the chip was missing a rather useful function, namely elapsed time in seconds since the standard epoch (January 1, 1970, midnight UTC).Let me back up a second.A real-time clock/calendar (RTC) is a micropower chip that has an oscillator on it that keeps counting time, independent of main system power. Usually this is done with a lithium battery that can power the RTC for years, so that even...


Thoughts on Starting a New Career

Jason Sachs July 23, 20127 comments

I recently completed a 16-year stint at an engineering company. I started there fresh out of college in June 1996. This June I just started a new career as an applications engineer in the area of motor drives at Microchip Technology in Chandler, Arizona. The experience I had in switching jobs was a very enlightening one for me, and has given me an opportunity to reflect on my career. I want to share some of that reflection with you.

Disclaimer: the opinions expressed in this and other blogs...


Lessons Learned from Embedded Code Reviews (Including Some Surprises)

Jason Sachs August 16, 20151 comment

My software team recently finished a round of code reviews for some of our motor controller code. I learned a lot from the experience, most notably why you would want to have code reviews in the first place.

My background is originally from the medical device industry. In the United States, software in medical devices gets a lot of scrutiny from the Food and Drug Administration, and for good reason; it’s a place for complexity to hide latent bugs. (Can you say “


Second-Order Systems, Part I: Boing!!

Jason Sachs October 29, 2014

I’ve already written about the unexciting (but useful) 1st-order system, and about slew-rate limiting. So now it’s time to cover second-order systems.

The most common second-order systems are RLC circuits and spring-mass-damper systems.

Spring-mass-damper systems are fairly common; you’ve seen these before, whether you realize it or not. One household example of these is the spring doorstop (BOING!!):

(For what it’s worth: the spring...


Slew Rate Limiters: Nonlinear and Proud of It!

Jason Sachs October 6, 2014

I first learned about slew rate limits when I was in college. Usually the subject comes up when talking about the nonideal behavior of op-amps. In order for the op-amp output to swing up and down quickly, it has to charge up an internal capacitor with a transistor circuit that’s limited in its current capability. So the slew rate limit \( \frac{dV}{dt} = \frac{I_{\rm max}}{C} \). And as long as the amplitude and frequency aren’t too high, you won’t notice it. But try to...


Someday We’ll Find It, The Kelvin Connection

Jason Sachs July 28, 20142 comments

You’d think it wouldn’t be too hard to measure electrical resistance accurately. And it’s really not, at least according to wikiHow.com: you just follow these easy steps:

  • Choose the item whose resistance you wish to measure.
  • Plug the probes into the correct test sockets.
  • Turn on the multimeter.
  • Select the best testing range.
  • Touch the multimeter probes to the item you wish to measure.
  • Set the multimeter to a high voltage range after finishing the...