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.
Garden Rakes Revisited: The Hall of Shame
Jason Sachs opens a Hall of Shame to catalog the everyday software "garden rakes" that steal time and focus. He walks through concrete examples from PowerPoint point editing and Office window behavior to Outlook undo bugs and TurboTax's opaque errors, showing how poor UI and hidden behaviors force you to work around the tool instead of with it. This is a short, cranky checklist for avoiding wasted effort.
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.
Bad Hash Functions and Other Stories: Trapped in a Cage of Irresponsibility and Garden Rakes
A tiny filename decision in MATLAB's publish() can silently swap rendered equations, and Jason Sachs shows why that matters. He reproduces the bug, walks through hash-function basics and collision math, and contrasts safe and unsafe caching strategies. The piece then broadens into practical lessons about software fringes, legacy constraints, and the usability traps that leave engineers repeatedly stumbling over avoidable design choices.
Efficiency Through the Looking-Glass
Efficiency numbers can be misleading, Jason Sachs argues, because they hide the real cost engineers pay in wasted watts. This post flips the focus from percent efficiency to absolute power loss, shows how losses often stay nearly constant across loads, and walks through a practical thermal method to measure those losses more reliably than subtracting input and output power. Read it to rethink how you budget heat and energy in designs.
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Integer overflow is stealthier than you think, and in embedded systems it can break control loops or corrupt data. Jason Sachs walks through the usual culprits, including addition, subtraction, multiplication, shifting and Q15 fixed-point traps, plus C-specific pitfalls such as undefined signed overflow and INT_MIN edge cases. He then lays out practical defenses: prefer fixed-width types, widen and saturate intermediates, enable wraparound where appropriate, and reason about modular congruence for compound arithmetic.
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.
Another 10 Circuit Components You Should Know
Jason Sachs walks through ten underrated circuit components every embedded engineer should know, from bus switches and thermocouple signal ICs to PCB stiffeners and opto-FET isolators. He mixes practical part examples, high-current hardware tips, and MCU features like CTMU and Peripheral Pin Select so you can pick the right trick when space, isolation, or precision matter.
Short Takes (EE Shanty): What shall we do with a zero-ohm resistor?
When you need flexibility on a PCB, zero-ohm resistors are the obvious shortcut, but Jason M. Sachs shows why the label zero is misleading. He compares common SMT jumper specs, high-current specialty parts, and a practical workaround using 1 milliohm resistors to avoid voltage drop. Read this for a quick checklist to pick jumpers that actually carry your board's current.
Fluxions for Fun and Profit: Euler, Trapezoidal, Verlet, or Runge-Kutta?
Which ODE solver should you pick for resource‑constrained embedded simulations? Jason Sachs walks through practical numerical methods — Euler, trapezoidal, midpoint, 4th‑order Runge‑Kutta, semi‑implicit Euler, Verlet and the Forest–Ruth symplectic scheme — using hands‑on examples (damped bead, Kepler orbit, pendulum). He highlights accuracy vs. function‑evaluation cost, timestep guidance, and why symplectic methods beat general solvers for long‑term energy conservation.
Linear Feedback Shift Registers for the Uninitiated, Part IX: Decimation, Trace Parity, and Cyclotomic Cosets
Taking every jth bit of a maximal-length LFSR uncovers a surprising algebraic structure. Jason Sachs walks through cyclotomic cosets, shows why decimation by powers of two preserves minimal polynomials, and connects LFSR output to trace parity and simple bitmask parity computations. The article uses hands-on Python with libgf2, Berlekamp-Massey, and state recovery so you can reproduce and automate these analyses.
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.
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.
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.
How to Succeed in Motor Control: Olaus Magnus, Donald Rumsfeld, and YouTube
Jason Sachs turned frustration with algorithm-heavy motor-control app notes into a practical MASTERs class, now available on YouTube. He walks through building a fifteen-minute field-oriented control refresher, the hazards teams commonly miss, and the months of prep required to make a polished technical lecture. Read for a candid behind-the-scenes look at teaching motor control to engineers and tips you can apply to your next drive project.
How to Build a Fixed-Point PI Controller That Just Works: Part II
Jason Sachs walks through practical, battle-tested rules for implementing PI controllers in fixed-point arithmetic. He explains Q-format choices, why the integrator needs extra fractional bits, and why scale-then-integrate simplifies design. The post also covers proportional gain scaling, saturation and anti-windup, and common C pitfalls that cause overflow or lost resolution on 16/32-bit microcontrollers.
Shibboleths: The Perils of Voiceless Sibilant Fricatives, Idiot Lights, and Other Binary-Outcome Tests
Binary tests look simple until you try to pick a threshold, because false positives, false negatives, and base rate all collide. Jason Sachs uses a deliberately absurd detective story, then walks through the math of expected value, medical screening tradeoffs, idiot lights, and even a triage-style three-way decision. The payoff is a practical way to think about when a pass/fail signal helps, and when raw data or a second test is worth the extra complexity.
Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders
Jason Sachs shows how linear feedback shift registers can be practical counters and compact absolute encoders, and why the choice of polynomial matters. He explains using primitive and reducible polynomials to get long but decode-friendly periods, demonstrates a 48-bit example, and lays out a De Bruijn chain-code encoder that turns an extra track into quick absolute resynchronization. Read to learn implementation tradeoffs and decoding strategies.
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.
How to Analyze a Three-Op-Amp Instrumentation Amplifier
The three-op-amp instrumentation amplifier gives you high input impedance, improved net bandwidth, and much lower sensitivity to resistor mismatch than a single-op-amp differential stage. Jason M. Sachs walks through the algebra, numeric examples, and historical notes to show how the preamp isolates common-mode, why splitting gain boosts bandwidth, how overall gain can be set with one resistor, and what practical limits to watch.
Modulation Alternatives for the Software Engineer
Jason starts with a hardware curiosity, the 7497 synchronous rate multiplier, and turns it into a practical lesson for firmware engineers. He contrasts conventional PWM with a simple accumulator-based method called "synthetic division," showing how it implements first-order delta-sigma behavior in software. The post explains when to pick PWM or delta-sigma and why the accumulator trick can give higher effective resolution at low update rates.
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.
Beware of Analog Switch Leakage Current
Leakage currents in analog switches can quietly wreck precision reference circuits at elevated temperature. Jason M. Sachs walks through three switch-topology implementations for a switchable 1.25 V reference and shows which topology gives the smallest worst-case output error using real part specs. He explains why op amp input bias is usually negligible and gives practical fixes: lower resistances, better switches, or limiting temperature range.
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.
Thoughts on Starting a New Career
Changing jobs can be a reset button for your engineering momentum. Jason Sachs reflects on leaving a 16-year role to join Microchip as an applications engineer in motor drives, and he distills practical advice on early-career choices, mentorship, networking, interview tactics, and keeping skills marketable. The post also highlights workplace factors and small perks that affect productivity, giving embedded engineers actionable steps to plan a career transition.
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.
Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders
Jason Sachs shows how linear feedback shift registers can be practical counters and compact absolute encoders, and why the choice of polynomial matters. He explains using primitive and reducible polynomials to get long but decode-friendly periods, demonstrates a 48-bit example, and lays out a De Bruijn chain-code encoder that turns an extra track into quick absolute resynchronization. Read to learn implementation tradeoffs and decoding strategies.
Implementation Complexity, Part I: The Tower of Babel, Gremlins, and The Mythical Man-Month
Jason Sachs argues that implementation complexity often outpaces manpower and good intentions, using the Tower of Babel and Fred Brooks's The Mythical Man-Month as lenses. He walks through communication costs, Kolmogorov complexity, and interface pitfalls with concrete examples like the NEMA 5-15 outlet, then offers pragmatic approaches such as modular design, gray-box awareness, and documenting assumptions to spot the gremlins before they derail a project.
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.
