## 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

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

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

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...

## 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...

## 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...

## Oscilloscope review: Hameg HMO2024

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...

## How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part I

Here's a common problem: you have a quadrature encoder to measure the angular position of a motor, and you want to know both the position and the velocity. How do you do it? Some people do it poorly -- this article is how not to be one of them.

Well, first we need to get position. Quadrature encoders are incremental encoders, meaning they can only measure relative changes in position. They produce a pair of pulse trains, commonly called A and B, that look like...

## Chebyshev Approximation and How It Can Help You Save Money, Win Friends, and Influence People

Well... maybe that's a stretch. I don't think I can recommend anything to help you win friends. Not my forte.

But I am going to try to convince you why you should know about Chebyshev approximation, which is a technique for figuring out how you can come as close as possible to computing the result of a mathematical function, with a minimal amount of design effort and CPU power. Let's explore two use cases:

- Amy has a low-power 8-bit microcontroller and needs to compute \( \sqrt{x} \)...

## Scorchers, Part 1: Tools and Burn Rate

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...

## Have You Ever Seen an Ideal Op-Amp?

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...

## 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...

## Thoughts on Starting a New Career

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...

## 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...

## Lessons Learned from Embedded Code Reviews (Including Some Surprises)

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 “

## The CRC Wild Goose Chase: PPP Does What?!?!?!

I got a bad feeling yesterday when I had to include reference information about a 16-bit CRC in a serial protocol document I was writing. And I knew it wasn’t going to end well.

The last time I looked into CRC algorithms was about five years ago. And the time before that… sometime back in 2004 or 2005? It seems like it comes up periodically, like the seventeen-year locust or sunspots or El Niño,...

## 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...

## 10 Items of Test Equipment You Should Know

When life gets rough and a circuit board is letting you down, it’s time to turn to test equipment. The obvious ones are multimeters and oscilloscopes and power supplies. But you know about those already, right?

Here are some you may not have heard of:

Non-contact current sensors. Oscilloscope probes measure voltage. When you need to measure current, you need a different approach. Especially at high voltages, where maintaining galvanic isolation is important for safety. The usual...## Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford’s Method (And Friends)
- Part 4: Topological Sort

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. This algorithm uses quadratic interpolation, which has applications in the topic of...

## 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...

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

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...

## Trust, but Verify: Examining the Output of an Embedded Compiler

I work with motor control firmware on the Microchip dsPIC33 series of microcontrollers. The vast majority of that firmware is written in C, with only a few percent in assembly. And I got to thinking recently: I programmed in C and C++ on an Intel PC from roughly 1991 to 2009. But I don’t remember ever working with x86 assembly code. Not once. Not even reading it. Which seems odd. I do that all the time with embedded firmware. And I think you should too. Before I say why, here are...

## 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...

## Padé Delay is Okay Today

This article is going to be somewhat different in that I’m not really writing it for the typical embedded systems engineer. Rather it’s kind of a specialized topic, so don’t be surprised if you get bored and move on to something else. That’s fine by me.

Anyway, let’s just jump ahead to the punchline. Here’s a numerical simulation of a step response to a \( p=126, q=130 \) Padé approximation of a time delay:

Impressed? Maybe you should be. This...

## Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford’s Method (And Friends)
- Part 4: Topological Sort

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. This algorithm uses quadratic interpolation, which has applications in the topic of...

## 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...

## How to Include MathJax Equations in SVG With Less Than 100 Lines of JavaScript!

Today’s short and tangential note is an account of how I dug myself out of Documentation Despair. I’ve been working on some block diagrams. You know, this sort of thing, to describe feedback control systems:

And I had a problem. How do I draw diagrams like this?

I don’t have Visio and I don’t like Visio. I used to like Visio. But then it got Microsofted.

I can use MATLAB and Simulink, which are great for drawing block diagrams. Normally you use them to create a...

## Important Programming Concepts (Even on Embedded Systems) Part VI : Abstraction

Earlier articles:

- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines

We have come to the last part of the Important Programming Concepts series, on abstraction. I thought I might also talk about why there isn’t a Part VII, but decided it would distract from this article — so if you want to know the reason, along with what’s next,

## 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...