Linear Feedback Shift Registers for the Uninitiated
Jason Sachs assembled an eighteen-part deep dive into linear feedback shift registers, connecting the simple shift-register circuit to finite-field algebra and practical tools. The series walks through primitive polynomials, Berlekamp-Massey state recovery, libgf2-based analysis, discrete-log methods, and real-world uses from PRNGs and Gold codes to Reed-Solomon and CRC reverse-engineering. It’s a single reference for engineers who want both theory and working code.
Modeling Gate Drive Diodes
This is a short article about how to analyze the diode in some gate drive circuits when figuring out turn-off characteristics --- specifically, determining the relationship between gate drive current and gate voltage during turn-off of a power transistor.
Ten Little Algorithms, Part 7: Continued Fraction Approximation
In this article we explore the use of continued fractions to approximate any particular real number, with practical applications.
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.
Return of the Delta-Sigma Modulators, Part 1: Modulation
Jason Sachs returns to delta-sigma modulators with a hands-on, code-first treatment that focuses on the DAC side of things. Part 1 walks through first- and second-order kernels, linearized analysis, spectra, and practical coefficient choices while illustrating results with Python simulations. Expect clear rules of thumb for A, R, and B, a derivation of noise shaping behavior, and a useful error bound for RC filtering.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 4)
The chip shortage didn't end with 2021, it moved into older process nodes where cars and industrial gear live. In this installment Jason Sachs explains why mature-node and trailing-edge capacity remain tightly constrained, how NCNR commitments and price increases are reshaping supplier behavior, and what companies like NXP and Microchip are doing to cope. He warns the imbalance could take multiple semiconductor cycles to fix.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 3)
Jason Sachs pulls back the curtain on Moore's Law and the foundry business to explain why the semiconductor shortage exposed brittle economics. He traces how roadmaps, depreciation schedules, and node mix force foundries to juggle expensive new fabs and mature capacity, and shows why leading-edge nodes punch above their volume share in revenue. Engineers get practical insight into how capacity and timing decisions ripple through the supply chain.
In Memoriam: Frederick P. Brooks, Jr. and The Mythical Man-Month
Fred Brooks’ The Mythical Man-Month is still a surprisingly sharp guide to software projects, and Jason Sachs shows why it matters even more than its old mainframe setting suggests. He revisits Brooks’ ideas on surgical teams, conceptual integrity, throwaway prototypes, and schedule estimation, then maps them to modern embedded and software engineering realities. The result is a tribute, a book review, and a practical reminder that roles, architecture, and testing still make or break delivery.
Development of the MOS Technology 6502: A Historical Perspective
A tiny team at MOS Technology pulled off one of the most influential microprocessor wins of the 1970s, creating the 6502 by marrying clever circuit choices with pragmatic manufacturing techniques. This excerpt by Jason Sachs focuses on the NMOS depletion-load process, mask and layout workflows, and yield-improving tricks like Micralign projection lithography and spot-knocking, showing how engineering and process decisions made a low-cost CPU ubiquitous.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 2)
Jason Sachs zooms through semiconductor history, fab economics, and the microcomputer era to explain why the 2021 chip shortage unfolded the way it did. He blends technical explainers on photolithography, yields, and node migration with business lessons about risky multi-year fab investments and cyclic demand. Engineers get historical case studies and practical signals to watch when designing products for greater supply resilience.
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Jason Sachs demystifies Reed-Solomon codes with hands-on examples and pragmatic tips for embedded engineers. The article shows why RS encoding is just polynomial division in GF(2^m), why decoding is mathematically heavier, and how to implement encoders in Python and in C-friendly form using LFSRs and table-driven methods. Read this for working code, generator-polynomial examples, and an embedded-minded view of RS practicalities.
Important Programming Concepts (Even on Embedded Systems) Part I: Idempotence
Idempotence is a simple design principle that prevents duplicate effects when operations are retried or repeated. Jason Sachs shows why it matters in embedded systems, from HTTP submit buttons and capacitive touch inputs to garage-door remotes and SPI DAC writes. Read this post to learn three practical idempotent techniques and when redundant writes are a sensible reliability trade-off.
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Jason Sachs shows how a single-pole IIR low-pass filter, implementable in one line y += alpha * (x - y), tames noise in embedded signals without floating point. The post explains how to compute alpha from tau and delta-t, practical tradeoffs like phase lag and oversampling, and fixed-point pitfalls including how many extra state bits you need to avoid quantization. Short, practical, and code-ready.
How to Read a Power MOSFET Datasheet
Jason Sachs takes a soapbox to stop a recurring mistake: misreading power MOSFET datasheets. This practical guide separates marketing blurbs and typical graphs from the specifications you can actually rely on, and explains how to use RDS(on), VGS, gate charge, SOA and thermal data in real designs. Read this before you pick a MOSFET or size a gate driver.
Ten Little Algorithms, Part 3: Welford's Method (and Friends)
Jason Sachs takes a practical look at Welford's method, a numerically stable online algorithm for computing mean and sample variance without storing large batches. He demonstrates Python implementations, shows why the naive sum and sum-of-squares approach suffers catastrophic cancellation, and why Welford is a better fit for memory- and CPU-constrained embedded systems. Jason then turns Welford into simple filters for tracking time-varying noise and discusses heuristic fixes and tradeoffs.
Return of the Delta-Sigma Modulators, Part 1: Modulation
Jason Sachs returns to delta-sigma modulators with a hands-on, code-first treatment that focuses on the DAC side of things. Part 1 walks through first- and second-order kernels, linearized analysis, spectra, and practical coefficient choices while illustrating results with Python simulations. Expect clear rules of thumb for A, R, and B, a derivation of noise shaping behavior, and a useful error bound for RC filtering.
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.
Second-Order Systems, Part I: Boing!!
Jason Sachs takes the spring 'boing' of a doorstop into the math of second-order systems, using the series LRC circuit as a concrete example. He shows two standard transfer-function forms, explains why ωn only scales time while ζ sets the response shape, and derives pole locations plus an exact overshoot formula that helps tune embedded-system responses.
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.
Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough
Switching H-bridges can kick nasty voltage spikes onto the DC link, and a single electrolytic capacitor rarely fixes the problem. Jason Sachs uses simulations and practical PCB layout advice to show how a three-tier decoupling strategy — bulk electrolytic, mid-value ceramics or film, and many small HF bypass capacitors plus PCB plane capacitance — tames spikes, reduces EMI, and avoids harmful resonances when parts and vias are placed correctly.
Development of the MOS Technology 6502: A Historical Perspective
A tiny team at MOS Technology pulled off one of the most influential microprocessor wins of the 1970s, creating the 6502 by marrying clever circuit choices with pragmatic manufacturing techniques. This excerpt by Jason Sachs focuses on the NMOS depletion-load process, mask and layout workflows, and yield-improving tricks like Micralign projection lithography and spot-knocking, showing how engineering and process decisions made a low-cost CPU ubiquitous.
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 2)
Jason Sachs zooms through semiconductor history, fab economics, and the microcomputer era to explain why the 2021 chip shortage unfolded the way it did. He blends technical explainers on photolithography, yields, and node migration with business lessons about risky multi-year fab investments and cyclic demand. Engineers get historical case studies and practical signals to watch when designing products for greater supply resilience.
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.
Help, My Serial Data Has Been Framed: How To Handle Packets When All You Have Are Streams
Framing byte streams is easier to get wrong than you think, and a bad scheme can leave your embedded device acting on the wrong packet. Jason Sachs walks through common plaintext and binary framing approaches, explains why CRCs alone can still permit false resynchronization, and demonstrates COBS as a simple, low-overhead byte-stuffing method that prevents delimiter collisions and guarantees resynchronization.
10 Software Tools You Should Know
Embedded work gets a lot easier when you have the right software stack, and Jason Sachs lays out the tools he leans on every day. From revision control and file comparison to build systems, scripting, analysis, documentation, QA, and command-line utilities, he focuses on practical picks that save time and reduce mistakes. The list is opinionated, but it is full of the kind of workflow advice that helps engineers stay productive.
Byte and Switch (Part 1)
Driving a 24V electromagnet from a 3.3V microcontroller looks trivial, but Jason Sachs shows how that simple switch can fail spectacularly. He walks through the cause of MOSFET destruction when an inductive load is turned off, and explains the practical fixes you actually need: a flyback diode, a gate series resistor, and a gate pulldown to keep the transistor well behaved.
How to Build a Fixed-Point PI Controller That Just Works: Part I
Jason Sachs digs into the implementation choices that make a fixed-point PI controller reliable in real embedded systems. He focuses on practical fixes rather than tuning: prefer scale-then-integrate, fold the timestep into the integral gain, and apply anti-windup so saturations and sensor noise do not break the loop. Part I covers discrete-time pitfalls and sets up fixed-point scaling issues for Part II.
Important Programming Concepts (Even on Embedded Systems) Part V: State Machines
State machines are not glamorous, but they solve a lot of real embedded problems. Jason Sachs uses a motorized couch example to show how FSMs and Harel statecharts expose corner cases, simplify timing constraints, and make behavior easier to specify and review. The article walks through hand-rolled switches, tabular implementations, the state pattern, libraries like QP and Boost, and tool tradeoffs.
10 Circuit Components You Should Know
Jason Sachs pulls together ten underrated but highly practical circuit components that every embedded engineer should know. From multifunction logic gates that act like a Swiss Army knife for glue logic to TL431 shunt regulators and tiny charge-pump inverters, each item is presented with real-world use cases and caveats. Read this to expand your parts toolbox and simplify future designs.
Ten Little Algorithms, Part 3: Welford's Method (and Friends)
Jason Sachs takes a practical look at Welford's method, a numerically stable online algorithm for computing mean and sample variance without storing large batches. He demonstrates Python implementations, shows why the naive sum and sum-of-squares approach suffers catastrophic cancellation, and why Welford is a better fit for memory- and CPU-constrained embedded systems. Jason then turns Welford into simple filters for tracking time-varying noise and discusses heuristic fixes and tradeoffs.
