Slew Rate Limiters: Nonlinear and Proud of It!
Slew-rate limits are a small nonlinear detail that often decides whether a controller behaves nicely or wrecks hardware. Jason Sachs walks through why slew limits appear in electronics and actuators, then shows two practical digital ways to impose limits: constraining input increments and constraining input around the output. He compares performance on underdamped second-order systems, gives closed-form intuition for overshoot, and demonstrates simulations with scipy and ODE solvers.
First-Order Systems: The Happy Family
Jason Sachs takes the modest topic of first-order systems and makes it useful, showing how RC filters behave in both time and frequency domains and why they all share the same shape. He steps through step, ramp, and sinusoidal responses, explains poles, zeros, and Bode behavior, and uses Python plots to make tracking error and the role of tau easy to visualize.
How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part II (Tracking Loops and PLLs)
Jason Sachs explains why simple differentiation of encoder counts often fails and how tracking loops and PLLs give more robust velocity estimates. Using a pendulum thought experiment and Python examples, he shows how a PI-based tracking loop reduces noise and eliminates steady-state ramp error, and why vector PLLs with quadrature mixing avoid cycle slips and atan2 unwrap pitfalls in noisy or analog sensing.
Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World
Jason Sachs previews a hands-on Python contest to find the best velocity estimator for a noisy, low-cost quadrature encoder. The post explains the Estimator API, submission constraints, and a 5 second, 10 kHz evaluation harness that uses a simulated "Lucky Wheel" encoder with realistic manufacturing timing errors. Jason also includes a simple baseline estimator and discusses the practical tradeoff between noise reduction and phase lag in velocity estimation.
Lost Secrets of the H-Bridge, Part III: Practical Issues of Inductor and Capacitor Ripple Current
Jason Sachs cuts through the math to show what ripple current actually does to H-bridge hardware. He explains why peak current is the limiting factor for inductors, why capacitor ESR usually dominates DC-link voltage ripple, and how center-aligned PWM and duty selection reduce harmonics and ripple. Read this if you want practical rules of thumb and calculation templates for real power-electronics designs.
Lost Secrets of the H-Bridge, Part II: Ripple Current in the DC Link Capacitor
DC link capacitor ripple often determines capacitor life, yet the H-bridge waveform has a lot more structure than you might expect. Jason Sachs separates capacitor current into ramp and pulse components, derives closed-form peak and RMS expressions for edge and center PWM, and shows harmonic amplitudes. The post includes Python simulation so you can visualize the waveforms and apply the formulas to capacitor selection and EMI analysis.
Lost Secrets of the H-Bridge, Part I: Ripple Current in Inductive Loads
Jason Sachs digs into what PWM switching actually does to current in an H-bridge with an inductive load, and why that ripple matters for motors and power converters. He derives closed-form ripple formulas, shows how to compute a reference current I_R0 = VDC·T/L, and uses Python and sympy to plot and verify results. Read it for practical rules to halve ripple and raise its frequency.
Adventures in Signal Processing with Python
Jason Sachs shows how PyLab (numpy, scipy, matplotlib) can handle many signal-processing and visualization tasks engineers usually reach for MATLAB to do. He walks through practical examples including PWM ripple, two pole RC filters, and symbolic math with SymPy, and shares real-world installation tips and trade-offs. The post closes with pointers to IPython and pandas to speed interactive analysis and data handling.
How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part I
Encoder velocity estimation is easy to get wrong, and Jason Sachs walks through the traps engineers fall into. He demolishes the common advice to time between encoder edges, shows how encoder quantization and state-width errors break that approach, and argues for fixed-rate sampling with sensible filtering for most control uses. Part II will cover more advanced estimators for higher performance needs.
First-Order Systems: The Happy Family
Jason Sachs takes the modest topic of first-order systems and makes it useful, showing how RC filters behave in both time and frequency domains and why they all share the same shape. He steps through step, ramp, and sinusoidal responses, explains poles, zeros, and Bode behavior, and uses Python plots to make tracking error and the role of tau easy to visualize.
Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World
Jason Sachs previews a hands-on Python contest to find the best velocity estimator for a noisy, low-cost quadrature encoder. The post explains the Estimator API, submission constraints, and a 5 second, 10 kHz evaluation harness that uses a simulated "Lucky Wheel" encoder with realistic manufacturing timing errors. Jason also includes a simple baseline estimator and discusses the practical tradeoff between noise reduction and phase lag in velocity estimation.
Two Capacitors Are Better Than One
Jason Sachs revisits a simple stacked RC trick that dramatically reduces DC error from capacitor insulation leakage in long time-constant filters. Splitting one RC into two stages forces most of the DC drop onto the lower capacitor, squaring the remaining error while changing the effective pole locations. The post walks through the math, practical component tradeoffs, and when to prefer a digital approach.
Here Comes The Noise!
Noise. That awful thing which nobody wants that most sadly never learn about. It's time to change that with this blog post.
Linear Regression with Evenly-Spaced Abscissae
Jason Sachs cuts through the matrix algebra to show a tiny trick for linear regression when x values are evenly spaced. You can compute the intercept as the mean and the slope as a simple weighted sum with arithmetic weights, using q = 12/(m^3 - m). The post includes Python examples and a compact routine to get least-squares coefficients without matrix solvers.
A Second Look at Slew Rate Limiters
Picking the right slew rate can cut overshoot dramatically while keeping delay reasonable, Jason shows. He numerically analyzes a feedforward slew-rate-limited step into a normalized second-order system and proposes a simple empirical rule R = Δx/(2π α τ) with α ≈ 1. The post includes Python/Scipy code and a 3→5 V example that demonstrates about a 3× overshoot reduction and a ≈5τ peak delay.
Getting Started With CUDA C on an Nvidia Jetson: A Meaningful Algorithm
In this blog post, I demonstrate a use case and corresponding GPU implementation where meaningful performance gains are realized and observed. Specifically, I implement a "blurring" algorithm on a large 1000x1000 pixel image. I show that the GPU-based implementation is 1000x faster than the CPU-based implementation.
Debugging DSP code.
Strange sinusoidal confidence scores from an HTM neural model revealed a familiar class of DSP bugs. Drawing from forum troubleshooting, the post maps common root causes: signed versus absolute value errors, wrong intermediate references, scaling mistakes, and sampling/stride problems in integer math. Embedded engineers will recognize the diagnostic clues and practical suspects to check first when DSP outputs vary with the input.
Unraveling the Enigma: Object Detection in the World of Pixels
Exploring the realm of embedded systems co-design for object recognition, this blog navigates the convergence of hardware and software in revolutionizing industries. Delving into real-time image analysis and environmental sensing, the discussion highlights advanced object detection and image segmentation techniques. With insights into Convolutional Neural Networks (CNNs) decoding pixel data and autonomously extracting features, the blog emphasizes their pivotal role in modern computer vision. Practical examples, including digit classification using TensorFlow and Keras on the MNIST dataset, underscore the power of CNNs. Through industry insights and visualization aids, the blog unveils a tapestry of innovation, charting a course towards seamless interaction between intelligent embedded systems and the world.
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Jason Sachs shows why LFSR-generated pseudonoise is a natural fit for direct-sequence spread spectrum, then walks through Fourier basics, spectral plots, and runnable Python examples. The article demonstrates how DSSS multiplies a UART bitstream with a chipping sequence to spread energy, how despreading concentrates the desired signal while scrambling narrowband interference, and how multiple transmitters can share bandwidth when using uncorrelated sequences.
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Jason Sachs shows how the output of a linear feedback shift register can be used for active system identification, not just spread-spectrum testing. The article compares traditional sine-wave probing with LFSR-based PRBS methods, demonstrates a worked Ra-Rb-C example, and unpacks practical issues such as reflected pseudonoise, ADC quantization, sample counts, and noise-shaping tricks to improve estimates.
Linear Regression with Evenly-Spaced Abscissae
Jason Sachs cuts through the matrix algebra to show a tiny trick for linear regression when x values are evenly spaced. You can compute the intercept as the mean and the slope as a simple weighted sum with arithmetic weights, using q = 12/(m^3 - m). The post includes Python examples and a compact routine to get least-squares coefficients without matrix solvers.
A Second Look at Slew Rate Limiters
Picking the right slew rate can cut overshoot dramatically while keeping delay reasonable, Jason shows. He numerically analyzes a feedforward slew-rate-limited step into a normalized second-order system and proposes a simple empirical rule R = Δx/(2π α τ) with α ≈ 1. The post includes Python/Scipy code and a 3→5 V example that demonstrates about a 3× overshoot reduction and a ≈5τ peak delay.
Breaking AES with an Oscilloscope
AES is a powerful encryption algorithm that protects some our most important secrets. But did you know that many devices are inadvertently leaking the value of their private key through their power pins?! Join me in this special preview of my upcoming workshop at the Embedded Systems Summit (14-16 October 2025 in San Jose, CA) as we explore the world of hardware security and discover just how easy it could be to break AES encryption with only an oscilloscope and some math.
Here Comes The Noise!
Noise. That awful thing which nobody wants that most sadly never learn about. It's time to change that with this blog post.
Getting Started With CUDA C on an Nvidia Jetson: A Meaningful Algorithm
In this blog post, I demonstrate a use case and corresponding GPU implementation where meaningful performance gains are realized and observed. Specifically, I implement a "blurring" algorithm on a large 1000x1000 pixel image. I show that the GPU-based implementation is 1000x faster than the CPU-based implementation.
Debugging DSP code.
Strange sinusoidal confidence scores from an HTM neural model revealed a familiar class of DSP bugs. Drawing from forum troubleshooting, the post maps common root causes: signed versus absolute value errors, wrong intermediate references, scaling mistakes, and sampling/stride problems in integer math. Embedded engineers will recognize the diagnostic clues and practical suspects to check first when DSP outputs vary with the input.
Unraveling the Enigma: Object Detection in the World of Pixels
Exploring the realm of embedded systems co-design for object recognition, this blog navigates the convergence of hardware and software in revolutionizing industries. Delving into real-time image analysis and environmental sensing, the discussion highlights advanced object detection and image segmentation techniques. With insights into Convolutional Neural Networks (CNNs) decoding pixel data and autonomously extracting features, the blog emphasizes their pivotal role in modern computer vision. Practical examples, including digit classification using TensorFlow and Keras on the MNIST dataset, underscore the power of CNNs. Through industry insights and visualization aids, the blog unveils a tapestry of innovation, charting a course towards seamless interaction between intelligent embedded systems and the world.
