Engineering Blog

Johnson-Nyquist thermal noise explained for RF and electronics engineers. Formula, real-world values, design impact, and common mistakes.

NTC thermistor basics: Steinhart-Hart equation, real-world examples, common mistakes, and when to use them in your designs.

Learn free space path loss from first principles. Formula, worked examples, common mistakes, and when it matters in RF design.

Learn 3-wire RTD calculations and lead resistance compensation. Includes formulas, worked examples, and common mistakes engineers make.

Design planar spiral inductors for RF and analog circuits. Learn Mohan vs Wheeler models, SRF limits, Q factor, and common PCB layout mistakes.

Learn how to calculate required heatsink thermal resistance. Real-world example: 50W power dissipation, max junction temp 150°C. Step-by-step thermal path.

Master edge-coupled embedded microstrip. Calculate differential impedance, propagation delay, and effective dielectric constant for PCB differential pairs.

Calculate impedance for dual stripline PCBs with two signal layers between ground planes. Includes coupling effects, propagation delay, and design examples.

Design sealed or ported subwoofer boxes using Vas, Qts, and Fs. Real examples, common mistakes, and when each enclosure type wins.

Master coplanar waveguide design with the CPW & GCPW calculator. Learn impedance control, substrate selection, and practical layout techniques for RF circuits.

A drill has to reach corner to corner; a cutter has to fit inside the short side.

Centred, offset, or under soldermask: where an edge-coupled pair lives, why only one case has an exact solution, and why the surface case accumulates skew.

Conductor and dielectric loss through a 1.6 mm via is under a sixth of a decibel at 20 GHz. The same via can cost 2.27 dB.

Routing one conductor between two pads costs its own width plus an extra clearance — and on a fine-pitch part the clearance is the bigger half.

A 0.3 mm drill does not give you a 0.3 mm hole, and the pad around it has to absorb drill wander, registration error, and plating build-up.

arctan of a ratio cannot tell 3 + j4 from −3 − j4.

How many traces fit between two BGA balls is decided the moment you pick the pad diameter.

The ±20 ppm on the front page is only the initial tolerance.

A microstrip is half-buried in laminate and half in air, so the wave sees neither.

A buried resistor is just sheet resistance times a count of squares. The design is trivial; the economics and the tolerance are not.

Coating your board can cut the required conductor spacing by more than four times.

A 100 µm microvia has a fifth the copper of a through-hole via and a fraction of its resistance.

A spiral of copper costs nothing to add and gives you a few hundred nanohenries.

Via capacitance sounds alarming until you subtract what a matched line would have had anyway.

A via is a thin-wall copper tube, not a solid plug, and its cross-section is smaller than most people assume.

Real stack-ups rarely put a signal layer exactly halfway between two planes.

Stacking a differential pair on adjacent layers halves its routing width, so flex circuits use it everywhere. The failure mode is layer-to-layer registration.

CPW and grounded CPW put the return path right next to the signal.

Two routing layers between one plane pair saves copper and money. It also creates the tightest coupling geometry available on a PCB.

Onderdonk's equation was derived for round wire in 1928. Applying it to a PCB trace needs the real cross-section, which isn't rectangular after etching.

PCB design lives in two unit systems simultaneously.

The 0.35 in the rise-time-bandwidth rule isn't a fudge factor — it's ln(9)/2π exactly. The 0.5 knee frequency answers a completely different question.

Every trace is a transmission line at some frequency.

Convert angles between degrees, radians, gradians, arcminutes, and arcseconds. Essential for antenna pointing, phase calculations, and servo control.

Calculate antenna beamwidth and gain from aperture dimensions. Covers 3dB beamwidth, first null, and real examples for dish and horn antennas.

Calculate real ADC dynamic range from bit depth and oversampling. Covers SNR theory, sigma-delta gains, and why datasheet specs mislead.

Calculate balun turns ratios, impedance matching, and insertion loss for RF transformers. Covers real-world antenna matching with worked examples.

Calculate how cable capacitance kills your high frequencies. Understand the RC filter formed by source impedance and cable length.

Calculate capacitor stored energy, charge, and charging current. Includes worked examples, real numbers, and common mistakes engineers make.

Convert between joules, electron-volts, kWh, calories, and BTU for real engineering work. Practical guide with ESD, battery, and semiconductor examples.

Calculate gear ratios, output torque, and speed for motor systems. Includes efficiency losses, worked examples, and common design mistakes.

Calculate ground plane impedance vs frequency. Understand skin effect, AC resistance, and inductance in PCB ground planes for EMC compliance.

Learn to convert between lux, foot-candles, phot, and other illuminance units. Practical examples for sensor calibration and optical design.

Calculate junction temperature from power dissipation and thermal resistances. Includes worked examples, thermal margin analysis, and common heatsink mistakes.

Calculate load cell amplifier gain for ADC input. Covers sensitivity, excitation voltage, full-scale output, and matching gain to your ADC range.

Learn to design rectangular microstrip patch antennas with real calculations for WiFi, 5G mmWave, and more. Includes worked examples and common pitfalls.

Calculate PCB trace temperature rise from current, width, and copper weight. Includes worked examples, IPC-2152 context, and common thermal design mistakes.

Learn to design stable PLL loop filters with proper phase margin. Covers component calculation, bandwidth selection, and common mistakes engineers make.

Calculate PWM duty cycle, average voltage, and RMS voltage from on-time and period. Includes worked examples and common mistakes engineers make.

Calculate ADC quantization noise, SQNR, and ENOB. Learn why your 12-bit ADC might only give you 10 effective bits in practice.

Learn to calculate radar detection range with real worked examples. Covers SNR, RCS, noise figure, and the gotchas that trip up engineers.

Estimate E-field emissions from PCB current loops and check CISPR 22 Class B margins before your product hits the chamber.

Calculate servo motor torque, back-EMF, and efficiency from real operating conditions. Includes worked examples and common sizing mistakes.

Learn how via stub resonance impacts signal integrity and how to calculate critical frequencies for precise PCB design and signal performance.

Learn how to calculate power amplifier gain with precision, understand key metrics, and avoid common engineering pitfalls in audio electronics.

Master RF power conversion: Learn how to accurately translate dBm measurements to watts with practical engineering insights and real-world examples.

Master decoupling capacitor selection with precise EMC techniques. Learn how to minimize noise and improve reliability with strategic capacitor placement.

Learn how to precisely convert phase noise measurements to jitter metrics for high-performance RF and digital communication systems.

Master magnetic flux density conversions with real-world examples. Learn how to translate between millitesla, microtesla, nanotesla, and gauss units.

Learn how to design L-network matching circuits using the Smith Chart.

Smith Chart and VSWR both describe impedance mismatch — but they answer different questions.

Learn how thermal via arrays solve critical heat management challenges in electronic designs with practical engineering insights.

Learn how to calculate motor starting torque, stall current, and critical performance parameters for electric motor design and selection.

A practical guide to UART baud rates: why 9600 and 115200 exist, how clock error causes framing failures, and the 2% rule every embedded engineer needs to know.

Learn how to accurately calculate thermocouple voltages, handle cold junction compensation, and avoid common measurement pitfalls.

Master BLDC motor winding design with our comprehensive calculator. Learn wire selection, turns calculation, and performance optimization techniques.

Uncover the secrets of Class D amplifier efficiency, from MOSFET selection to power loss calculation with practical engineering insights.

STK-free link budgets: sweep frequency, rain availability, and elevation in pure Python with ITU-Rpy, the reference implementation of P.618/P.676/P.840.

A walkthrough of a free RF link budget calculator: EIRP, FSPL, received power, link margin and max range, with LoRa, CubeSat and GEO broadcast scenarios.

Ansys STK sunset-ready: compute SGP4 pass predictions for your amateur-radio or cubesat ground station using Skyfield.

End-to-end link budget for an amateur-band 3U cubesat: EIRP, slant range, ground-station G/T, propagation losses and Monte Carlo margin.

Ansys is sunsetting STK Cloud in March 2026. Here are free open-source replacements for what it did best: ITU-R link budgets and orbital pass prediction.

Master RF power density calculations with real-world examples and critical engineering insights for wireless and electromagnetic safety analysis.

Learn how to calculate precise transmission line impedance across complex PCB stackups with expert techniques and real-world insights.

Master photodiode signal conditioning with our transimpedance amplifier calculator: optimize bandwidth, noise, and gain for precision sensor designs.

Master accelerometer sensitivity calculations and avoid common signal conditioning pitfalls in embedded sensor design

Discover how battery internal resistance impacts power delivery, efficiency, and device performance in real-world electronics design.

Master BLDC motor efficiency calculation with our comprehensive analyzer — learn how to optimize power, minimize losses, and improve motor design.

Master BLDC motor performance prediction with our comprehensive calculator and detailed engineering breakdown of motor electrical parameters.

Learn how to accurately calculate RF transmission line losses with our comprehensive coaxial cable loss calculator and expert insights.

Master Delta-Wye circuit conversions with our comprehensive calculator and technical breakdown of star-delta transformations in electrical networks.

Master inductance unit conversions with real-world examples. Learn how to seamlessly translate between nH, μH, mH, and H for RF and analog circuits.

Learn how to precisely calculate LIN bus timing parameters, understand frame structures, and avoid common design pitfalls in automotive communication systems.

Master microstrip transmission line impedance calculation with our comprehensive engineering guide and practical RF tool

Learn how temperature impacts motor winding resistance and why accurate thermal modeling matters for electrical design and performance.

Learn how to accurately calculate noise figure across multiple RF stages and understand the critical factors that impact system performance.

Learn how to calculate and mitigate PCB crosstalk with our comprehensive guide and interactive calculator for electronics engineers.

Master power supply ripple filtering techniques with our comprehensive calculator and expert insights for clean, stable electronics design

Learn how coupler directivity, source match, and measurement techniques impact return loss accuracy in RF systems

Learn how room modes impact audio performance and how to calculate critical acoustic parameters for optimal sound engineering

Master passive speaker crossover design with precise calculations, component selection, and real-world engineering insights for audio electronics projects.

Dive deep into switching regulator output ripple calculation with real-world techniques, critical design insights, and practical error analysis.

Master precise temperature unit conversions with practical insights for electronics design and thermal management

Master torque unit conversions with precision. Learn how to seamlessly translate between N·m, lb·ft, oz·in, and more for accurate engineering calculations.

Master PCB trace width design with IPC-2221 and IPC-2152 standards. Learn how to calculate trace width for safe current handling.

How to design BLDC motor windings: turns per coil from target Kv, wire gauge for current density, slot/pole combinations, and delta versus wye configurations.

Learn how to calculate Bit Error Rate (BER) using Signal-to-Noise Ratio and different modulation schemes for robust digital communications

Understand the relationship between Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR).

Learn how to size a BLDC motor using Kv rating, torque constant Kt, and efficiency calculations.

Learn how to convert power levels across different impedances and units with precision using our comprehensive dBm Power Converter tool.

Design EMI filters for conducted emissions compliance.

Learn how to read and use a Smith Chart for impedance matching.

Master BJT transistor biasing with our comprehensive calculator and learn how to set the perfect DC operating point for your analog circuits.

Learn how to calculate and design 4-20 mA sensor transmitters with precision, covering voltage, resistance, and critical design considerations.

Master op-amp gain and bandwidth calculations with practical insights, real-world examples, and common design pitfalls to watch out for.

Master data rate unit conversions with our comprehensive guide. Learn how to translate between bps, bytes, and network speeds effortlessly.

Master BJT transistor switch design with a powerful calculator. Learn critical design parameters, avoid common mistakes, and calculate key performance metrics.

Learn how to accurately calculate PT100/PT1000 sensor resistance, understand temperature sensitivity, and avoid common measurement pitfalls.

Master LDO linear regulator thermal design with our dropout voltage calculator — prevent power supply failures before they happen.

Explore Ohm's Law calculations with precision. Learn how to calculate voltage, current, resistance, and power with our comprehensive engineering tool.

Master LC circuit analysis with our comprehensive resonance calculator. Learn frequency, Q factor, and impedance calculations for RF and electronics design.

Master ESD diode selection with expert insights: learn how to calculate peak current, power dissipation, and protect your sensitive electronics

Master passive filter design with precision: Learn how to calculate RC and LC filter components for optimal signal processing performance.

Master current mirror design with our comprehensive calculator. Learn techniques, avoid common pitfalls, and build precise current sources for analog circuits.

Master motor thermal design with our comprehensive heat dissipation calculator and expert insights into preventing catastrophic motor failures

Master op-amp closed-loop bandwidth calculations with practical insights and real-world performance analysis techniques for electronics design

Master RTD temperature measurement with PT100/PT1000 sensors, including calibration, resistance-to-temperature conversion, and key design considerations.

Learn how to calculate precise CAN bus timing parameters for reliable embedded communication across different microcontroller clock speeds and baud rates.

Learn how to calculate transformer turns ratio, secondary current, and real power delivery with worked examples. Free online calculator included.

Learn Ziegler-Nichols PID tuning using process gain, dead time & time constant. Worked example with real motor control values. Free online calculator.

Learn how to convert torque units between N·m, lb-ft, oz-in, kg-cm & more. Worked examples for servo, stepper, and automotive motor applications.

Learn how to decode 3-digit capacitor codes into pF, nF, and µF values. Worked examples, the math behind the system, and a free online calculator.

Learn how capacitive proximity sensors work, calculate capacitance & sensitivity from plate area, gap, and permittivity using our free calculator.

Learn to calculate conduction and switching losses in MOSFET H-bridge motor drivers. Worked example with real numbers using our power dissipation calculator.

Q factor = f₀ / BW — higher Q means a narrower, more surgical EQ cut or boost.

Calculate Ethernet cable attenuation, max length, and pass/fail status for Cat5e–Cat8 runs. Includes worked examples and real engineering numbers.

Learn how to convert frequency to wavelength in free space and PCB substrates. Worked examples for WiFi, radar, and antenna design using our calculator.

Learn how to design small loop antennas with real examples. Calculate radiation resistance, gain, loss resistance, and bandwidth for HF loops.

Learn how to calculate NTC thermistor cold resistance, energy absorption, and time constant to limit inrush current in capacitive power supplies.

Learn how to calculate AM modulation index, sideband frequencies, bandwidth, and power efficiency with real worked examples for RF engineers.

Learn how to design PCB layer stacks for controlled impedance. Covers microstrip, stripline, differential pairs, and CPWG with Hammerstad-Jensen formulas.

The rftools Python package gives you programmatic access to 203 RF and electronics calculators from rftools.io, with a typed API, a CLI, batch mode, and async.

Learn how audio transformer turns ratio links impedance, voltage, and current. Worked examples and formulas for matching audio sources to loads.

Calculate the correct LED current limiting resistor for any supply voltage and LED color. Includes worked examples, E24 selection, and power dissipation.

Estimate battery runtime under motor load. Covers LiPo, NiMH, lead-acid packs with drive efficiency, depth of discharge, and real worked examples.

A practical walkthrough of the PDN Impedance Analyzer: modeling VRM impedance and plane-pair resonances, and choosing capacitors with a genetic algorithm.

Pd versus range for all five Swerling models, ITU-R P.838-3 rain loss at S-band and X-band, and the ROC curve, worked through the Radar Detection Simulator.

A 5-stage 2.4 GHz receive chain through the RF Cascade Budget Analyzer: cascaded NF, gain, IIP3 and P1dB, Monte Carlo yield, and which stage to change.

A Ka-band direct-to-home downlink in London through the Satellite Link Budget Analyzer: ITU-R climate at the site, P.618 rain, gas and cloud, and availability.

Learn how VSWR relates to return loss, reflection coefficient & mismatch loss. Includes worked examples and an online calculator for RF engineers.

Calculate cable shield effectiveness and transfer impedance from DC resistance, length, and frequency. Includes worked examples for EMC engineers.

Calculate chassis resonant frequencies from enclosure dimensions. Avoid EMC failures by predicting TE₁₀₁ and TE₁₁₀ cavity modes in metal housings.

Calculate series & parallel resistor, capacitor & inductor totals plus voltage divider ratios. Worked examples and formulas for everyday circuit design.

Size a heatsink in 3 steps: find the required θ_SA from power dissipation and junction temperature, pick a heatsink rated below it, then check the thermal path.

A 1.0 V / 30 A FPGA power rail needs flat impedance from 100 kHz to 1 GHz. Cavity resonances between the power and ground planes create impedance spikes.

A practical walkthrough of the Radar Detection Monte Carlo simulator on a 10 GHz X-band weather radar, comparing Swerling target models.

A step-by-step walkthrough of designing a 6-stage Ku-band receiver using the RF Cascade Budget Analyzer — optimizing the LNA/filter sequence for system NF.

A Ku-band VSAT uplink from Munich in the Satellite Link Budget tool: clear-sky budget first, then ITU-R rain at the site, availability and Monte Carlo margin.

rftools.io now ships an MCP server that lets AI assistants like Claude Desktop, Cursor, and Claude Code run any of our 197 RF & electronics calculators.

Learn how to size solar panels, batteries, and charge controllers for off-grid systems. Worked example with real numbers using our solar panel calculator.

How to choose decoupling capacitor values: self-resonant frequency sets the bypass range — 100 nF at ~5 MHz, 10 nF at ~50 MHz, 1 nF at ~500 MHz.

Learn how to calculate EIRP and ERP for regulatory compliance. Worked examples for FCC Part 15, ETSI 2.4 GHz, and ISM 433 MHz with margin analysis.

An SBC fails FCC Part 15 Class B pre-compliance. The EMI Radiated Emissions Estimator separates the power loop from the USB cable and shows which fix matters.

How much insertion loss a 10 Gbps SerDes lane can take: a Touchstone S21 through the Eye Diagram tool, with eye height, width and jitter against data rate.

A step-by-step guide to running an FDTD simulation of a through-via transition in FR-4: setting up the simulation and interpreting the S11/S21 results.

A practical walkthrough of matching a 50 Ω source to a 200 Ω LNA input across the 800–1200 MHz cellular band, and why L-networks fail on bandwidth.

A 48 V to 12 V, 36 W flyback through the Magnetics Optimizer: the loss-versus-size Pareto front, core loss from datasheets, and what interleaving is worth.

Learn how to calculate pressure sensor bridge output voltage from excitation, sensitivity, and applied pressure. Includes worked examples and formulas.

A 5th-order Chebyshev anti-alias filter at 100 MHz meets its spec on paper.

What the S-Parameter Analysis Pipeline shows about fixture effects in VNA data — passivity, TDR, time gating, cascading — and what de-embedding needs beyond it.

A 12 V to 5 V buck through the SMPS Control Loop Stability Analyzer: phase margin, Monte Carlo yield, and why a ceramic output capacitor breaks a stable loop.

Learn to calculate junction temperature using thermal resistance networks. Worked examples with θJC, θCS, θSA for heatsink design and thermal margin analysis.

A radio amateur designing a 5-element Yagi for 144 MHz EME and tropo scatter uses NEC2 simulation to verify gain, front-to-back ratio, and feedpoint impedance.

A practical guide to designing audio amplifier stages: power output, speaker impedance matching, noise floor, and choosing an amplifier class.

Complete guide to controlling DC motors with PWM: selecting the right H-bridge driver, sizing the MOSFET, and closing the loop with an encoder.

Master decibels for RF and audio engineering. Understand the difference between dB (ratio), dBm (power relative to 1 mW), dBV (voltage), dBi (antenna gain).

A practical guide to EMC pre-compliance testing, PCB layout for low emissions, and common failure modes that cause first-attempt failures at the test house.

How to design the amplifier, filter, and ADC interface between a sensor and a microcontroller, for RTDs, thermocouples, load cells, and current shunts.

How to choose and design active filters. Compares Butterworth, Chebyshev, and Bessel responses with practical examples for signal processing and RF.

How to design a synchronous buck converter from scratch. Calculates duty cycle, inductor value, output capacitor, and estimates efficiency with worked examples.

How to calculate PCB trace width for a given current. Compares IPC-2221 and IPC-2152, explains temperature rise, and covers external vs internal layers.

Learn how to perform an RF link budget analysis from scratch. Covers free-space path loss, antenna gain, cable losses, receiver sensitivity, and link margin.

A practical guide to designing controlled-impedance microstrip traces on PCBs: the Hammerstad-Jensen equations, material selection, and manufacturing.