Book Review: "Turing's Cathedral"
The early days of electronic computing are explored through George Dyson's Turing's Cathedral, which traces the IAS machine, John von Neumann, and Princeton's Institute for Advanced Study from 1940 to 1958. Jason Sachs praises Dyson's archival access and narrative detail, especially on hardware like vacuum tubes and delay lines, but warns the book's software explanations feel vague and would have benefited from diagrams.
Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons
Singletons are convenient but often a modularity killer, especially in embedded firmware. Jason Sachs walks through the many faces of singletons, from static members and globals to hardware registers and user-visible application singletons, and shows practical ways to avoid tight coupling. Read this for concrete embedded examples and pragmatic fixes like passing state explicitly, using interfaces or factories, and isolating unavoidable globals in a HAL.
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.
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.
Important Programming Concepts (Even on Embedded Systems) Part III: Volatility
Jason Sachs takes volatility out of the basement and into practical embedded programming. He shows why data that can change outside your thread of control breaks assumptions, how the volatile qualifier in C/C++ and Java affects compiler and CPU behavior, and when to prefer shadow registers, locks, or proper concurrency libraries instead of ad hoc volatile usage.
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.
You Will Make Mistakes
Mistakes are inevitable in engineering, and they grow worse when teams are distributed and communication has long round-trip delays. Jason Sachs lays out practical, low-friction tactics to keep small errors from becoming project stoppers, from applying FMEA thinking to using issue trackers, event logging, clear interface specs, and better meeting habits. The post focuses on habits you can start using today to raise team reliability.
Important Programming Concepts (Even on Embedded Systems) Part II: Immutability
Immutable data can make embedded code easier to reason about, reduce concurrency bugs, and eliminate defensive copies. Jason Sachs walks through practical techniques that work in resource-constrained systems, from using const and pseudo-immutability to separating old and new state, to the limits of fully persistent data structures when you lack dynamic memory. The article also compares register-level state flow and advocates message passing as a concurrency alternative.
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.
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.
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.
Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery
Matrix methods for LFSRs look intimidating, but Jason Sachs walks through companion-matrix representations and shows why they matter for time shifts and state recovery. He derives lookahead masks from powers of the companion matrix, then translates those matrix insights into efficient bitwise and finite-field algorithms. The article includes two simple state-recovery methods and working Python/libgf2 examples you can run and adapt.
Have You Ever Seen an Ideal Op-Amp?
Forget the ideal op-amp fantasy, Jason Sachs walks through the practical nonidealities that make textbook gain formulas fail in real circuits. Using the uA741C and TLC081C as examples, he explains offset voltage, input bias and offset currents, common-mode and supply rejection, gain-bandwidth and slew-rate limits, plus capacitive loading, RF rectification and overload recovery. Read to learn which datasheet specs matter and why.
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.
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.
Book Review: "Turing's Cathedral"
The early days of electronic computing are explored through George Dyson's Turing's Cathedral, which traces the IAS machine, John von Neumann, and Princeton's Institute for Advanced Study from 1940 to 1958. Jason Sachs praises Dyson's archival access and narrative detail, especially on hardware like vacuum tubes and delay lines, but warns the book's software explanations feel vague and would have benefited from diagrams.
Racing to Sleep
Jason Sachs walks through a realistic field sensor case study, the BigBrotherBear 2000, to show how a careful power budget exposes surprising energy costs. He demonstrates that radios and data transmission often dwarf quiescent MCU current, explains the race-to-sleep principle for computation-bound tasks, and outlines practical wake-up and measurement trade-offs so engineers can extend battery lifetime in real deployments.
Important Programming Concepts (Even on Embedded Systems) Part II: Immutability
Immutable data can make embedded code easier to reason about, reduce concurrency bugs, and eliminate defensive copies. Jason Sachs walks through practical techniques that work in resource-constrained systems, from using const and pseudo-immutability to separating old and new state, to the limits of fully persistent data structures when you lack dynamic memory. The article also compares register-level state flow and advocates message passing as a concurrency alternative.
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.
Oscilloscope review: Hameg HMO2024
Jason Sachs tests the Hameg HMO2024, a 200MHz 4-channel mixed-signal oscilloscope that promises Agilent-like features at a lower price. He finds strong analog noise performance, useful hi-res and zoom modes, and inexpensive serial-decode options, but warns of clumsy digital-input handling, awkward data-transfer software, and missing per-channel thresholds and Ethernet waveform export. The review helps budget-conscious embedded engineers weigh the trade-offs.
Scorchers, Part 3: Bare-Metal Concurrency With Double-Buffering and the Revolving Fireplace
Jason Sachs presents a practical, low-overhead concurrency pattern for tiny bare-metal systems where an ISR (Speedy) must safely exchange data with a nonreal-time main loop (Poky). He describes the "revolving fireplace", a double-buffering variant that swaps ownership of two shared memory regions, and walks through C examples, atomic/volatile considerations, and testing strategies so you can implement it on RAM-constrained MCUs.
Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery
Matrix methods for LFSRs look intimidating, but Jason Sachs walks through companion-matrix representations and shows why they matter for time shifts and state recovery. He derives lookahead masks from powers of the companion matrix, then translates those matrix insights into efficient bitwise and finite-field algorithms. The article includes two simple state-recovery methods and working Python/libgf2 examples you can run and adapt.
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.
Important Programming Concepts (Even on Embedded Systems) Part VI : Abstraction
Abstraction is essential, but it is not free. Jason Sachs walks through the many faces of abstraction—pattern recognition, generalization, simplification, and indirection—and shows how each helps and hurts real projects. Using examples from math, API design, UI toolkits, schematics, and embedded C, he gives practical context so firmware engineers can apply abstractions without causing maintenance or debugging headaches.
Complexity in Consumer Electronics Considered Harmful
Jason Sachs watched his grandmother struggle with a Vizio TV remote, and it highlights a recurring usability failure in consumer electronics. He argues that small type, unclear icons, and modal controls make everyday tasks needlessly hard. The takeaway for embedded engineers is to prioritize common actions, separate advanced features, and design for low-vision and limited-memory users to avoid frustration and returns.
Wye Delta Tee Pi: Observations on Three-Terminal Networks
Three-terminal passive networks, wye, delta, tee, and pi, are more interchangeable than many engineers expect. Jason Sachs walks through Kennelly's wye-delta formulas, Z and Y matrix representations for tee and pi two-port networks, and worked examples ranging from balanced to highly skewed impedances. The post highlights practical payoffs, including using topology transforms to substitute hard-to-source capacitors with simpler, precision-friendly parts.
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...
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.
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.
March is Oscilloscope Month — and at Tim Scale!
Jason Sachs just upgraded his lab with an Agilent MSOX3034A after snagging a vendor promotion, and he walks through first-day wins from probe compensation to scripting. He shows why 10x probes need capacitive matching and how to use the scope's calibration square wave to compensate them. He also covers connecting the MSOX3000 to Python via pyvisa and SCPI, including decoding waveform data for export.
