Lazy Properties in Python Using Descriptors
Python descriptors let you outsource attribute lookup, and Jason Sachs walks through a practical use: lazy, cached properties. He presents a LazyProperty descriptor that defaults to a WeakKeyDictionary cache so computed results are stored on first access and automatically purged when objects are garbage collected. The post shows how to share caches by value using attrkey or swap cache classes for different use cases.
Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm
Jason Sachs breaks down the Berlekamp-Massey algorithm and shows how to recover an LFSR's minimal connection polynomial from a stream of output bits. The article mixes intuition, worked examples, and Python code to demonstrate the update rule, visual debugging tables, and when the solution is unique. Expect practical implementation notes, a complexity discussion, and a libgf2 example you can run in an IPython notebook.
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Most discrete-log problems are hopeless by brute force, but clever algorithms cut that cost to feasible levels. This installment walks through baby-step giant-step, Pollard’s rho and kangaroo methods, and how Silver-Pohlig-Hellman and index calculus leverage group structure to speed attacks on GF(2^n) fields. Jason Sachs includes Python examples, heuristics, and complexity nuggets so you can see when each method is practical.
Linear Feedback Shift Registers for the Uninitiated, Part IV: Easy Discrete Logarithms and the Silver-Pohlig-Hellman Algorithm
Discrete logarithms can be either trivial or infeasible depending on how group elements are represented, and Jason Sachs shows a practical route when they are intentionally easy. This article walks through using LFSRs as fast counters, why a smooth group order matters, and how the Silver-Pohlig-Hellman algorithm plus the Chinese Remainder Theorem recovers exponents in GF(2) with small prime factors.
Linear Feedback Shift Registers for the Uninitiated, Part III: Multiplicative Inverse, and Blankinship's Algorithm
Jason Sachs walks through Blankinship's constant-space variant of the Extended Euclidean Algorithm and shows how to compute multiplicative inverses both modulo an integer and in GF(2)[x]. The article uses clear numeric and polynomial examples, Python snippets, and an LFSR finite-field example to show how the algorithm yields Bézout coefficients and inverses useful for discrete-log tricks and cryptographic contexts. Readers get a practical recipe for inverse computation.
Linear Feedback Shift Registers for the Uninitiated, Part II: libgf2 and Primitive Polynomials
Jason Sachs digs into practical finite-field arithmetic for LFSRs, using his libgf2 Python library as the hands-on guide. He shows how to test whether a polynomial is primitive, why that matters for maximal-length sequences, and how the library implements addition, multiplication, exponentiation, and shifts over GF(2). The post is both a math refresher and a code walkthrough for engineers who want to compute with LFSRs instead of just talk about them.
Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields
Jason Sachs demystifies linear feedback shift registers with a practical, bitwise view and the algebra that explains why they work. Readable examples compare Fibonacci and Galois implementations, show a simple software implementation, and reveal the correspondence between N-bit Galois LFSRs and GF(2^N) so you can pick taps and reason about maximal-length pseudorandom sequences.
Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection
Jason shows how Green's Theorem becomes a practical, low-cost method to detect real-time rotation from two orthogonal sensors by accumulating swept area. The post derives a compact discrete integrator S[n] = S[n-1] + (x[n]*(y[n]-y[n-1]) - y[n]*(x[n]-x[n-1]))/2, compares integer and floating implementations, and analyzes noise scaling and sampling rate tradeoffs. Includes Python demos and threshold guidance.
Donald Knuth Is the Root of All Premature Optimization
Knuth's famous line "premature optimization is the root of all evil" has turned into a blunt rule on forums, Jason Sachs argues, and that overuse masks important nuance. He walks through concrete embedded examples, from dsPIC33E floating-point timings to an ROI analysis in the Kittens Game and a continuous optimization toy problem, to show when to measure, when to speculate, and why profilers can mislead.
Zebras Hate You For No Reason: Why Amdahl's Law is Misleading in a World of Cats (And Maybe in Ours Too)
Amdahl’s Law is a useful warning, but Jason Sachs argues it can be misleading if you stop at the equation. Using the Kittens Game as a playful model, he shows how Gustafson’s perspective, positive feedback loops, and system-level synergy can turn modest component speedups into big real-world wins. The article closes with concrete embedded-systems examples like ISR timing and developer productivity.
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Most discrete-log problems are hopeless by brute force, but clever algorithms cut that cost to feasible levels. This installment walks through baby-step giant-step, Pollard’s rho and kangaroo methods, and how Silver-Pohlig-Hellman and index calculus leverage group structure to speed attacks on GF(2^n) fields. Jason Sachs includes Python examples, heuristics, and complexity nuggets so you can see when each method is practical.
Linear Feedback Shift Registers for the Uninitiated, Part XVIII: Primitive Polynomial Generation
Jason Sachs walks through how to find primitive polynomials for GF(2) LFSRs, moving from naive exhaustive checks to smarter synthetic constructions. The article compares sieve and constructive methods, shows practical optimizations like parity checks and companion-matrix updates, and demonstrates decimation plus Berlekamp-Massey to generate all primitives from one seed; it also teases a novel Falling Coyote Algorithm for additional speedups.
Analog-to-Digital Confusion: Pitfalls of Driving an ADC
Wayne's thermistor board showed one ADC channel changing when another was heated, a classic case of ADC input cross-coupling. The post walks through how multiplexed ADCs, the small sample-and-hold capacitor, source impedance, sampling time, repeated sampling rates, and added charge reservoirs interact to create errors. Learn practical fixes including increasing sample time, sizing external caps, adding op-amp buffers, and using an RC dampener with PCB layout tips.
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.
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.
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.
How to Analyze a Differential Amplifier
Jason Sachs walks through the algebra and intuition behind the classic four-resistor differential amplifier. He derives the exact output equation, isolates error terms from resistor mismatch and op-amp imperfections, and explains why common-mode gain depends on mismatch not on the differential gain. Read this for clear formulas, modal insight into common-mode versus differential-mode, and practical steps to reduce offsets in real designs.
Stuck with Jira — and Stuckons
Jason Sachs vents about Jira’s quirks and why it still feels stuck despite years of fixes. He walks through concrete pain points: nonstandard markup, relentless notification noise, poor meta-task support, and limited analytics that make day-to-day engineering work harder. To explain why schedules blow up, he introduces a simple kepton model of planons, workons, and stuckons that highlights unexpected work.
Margin Call: Fermi Problems, Highway Horrors, Black Swans, and Why You Should Worry About When You Should Worry
Jason Sachs walks through practical strategies for choosing engineering margin, from split-second Fermi estimates to industry-grade safety factors. He blends highway and boiler anecdotes with a MOSFET thermal example to show why probabilistic thinking, experiments, and documentation matter when you must decide fast or later justify your choices. Read this to learn how to balance conservatism, cost, and risk in real projects.
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.
Lessons Learned from Embedded Code Reviews (Including Some Surprises)
Jason Sachs recounts a round of motor-controller code reviews and the practical lessons his team learned about quality and tooling. He explains how a simple "ready for review" checklist and automated style checks kept meetings focused on substantive issues, and why choosing the right review tool matters after discovering lost comments in Stash. Read for concrete tips on process, subgit mirroring, vera++, and Upsource.
Someday We’ll Find It, The Kelvin Connection
Low-ohm measurements will fool your multimeter unless you use Kelvin connections. Jason Sachs walks through four-wire sensing using a current-limited supply and two DMMs, explains thermoelectric and connector-related errors, and shows why schematics and PCB layout must reflect Kelvin sense pads to avoid subtle measurement and circuit problems.
The CRC Wild Goose Chase: PPP Does What?!?!?!
Jason Sachs walks through a CRC rabbit hole and explains why ambiguous CRC names and incomplete specs lead to subtle protocol bugs. He demonstrates how XMODEM and KERMIT variants with a zero initial value can miss dropped leading-zero bytes, praises the X.25 standard for providing test vectors and a clear CRC16 definition, and warns that RFCs that ship only sample code are a poor substitute for a proper specification.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 5)
Most of the time a wafer spends in a fab is spent waiting in queues, not being processed. Jason Sachs peels back why cycle times stretch weeks to months, covering WIP accounting, die and wafer banks, the days per mask layer metric, and how variability and utilization tradeoffs turned fab behavior into a major factor in the 2021 chip shortage.
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.
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.
Donald Knuth Is the Root of All Premature Optimization
Knuth's famous line "premature optimization is the root of all evil" has turned into a blunt rule on forums, Jason Sachs argues, and that overuse masks important nuance. He walks through concrete embedded examples, from dsPIC33E floating-point timings to an ROI analysis in the Kittens Game and a continuous optimization toy problem, to show when to measure, when to speculate, and why profilers can mislead.
Real-time clocks: Does anybody really know what time it is?
Most RTC chips still expose calendar fields rather than seconds-since-epoch, forcing embedded engineers to write ugly conversion code. Jason Sachs makes the case for offset encoding, subseconds, and an explicit snapshot feature to simplify interval math, raise precision, and avoid rare timing bugs. Read this practical take on RTC trade-offs and a short wishlist for chip makers.
Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection
Jason shows how Green's Theorem becomes a practical, low-cost method to detect real-time rotation from two orthogonal sensors by accumulating swept area. The post derives a compact discrete integrator S[n] = S[n-1] + (x[n]*(y[n]-y[n-1]) - y[n]*(x[n]-x[n-1]))/2, compares integer and floating implementations, and analyzes noise scaling and sampling rate tradeoffs. Includes Python demos and threshold guidance.
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.
