Engineering Blog

arctan of a ratio cannot tell 3 + j4 from −3 − j4. That single-argument shortcut turns inductive loads capacitive and sends matching networks in the wrong direction. Here is why atan2 exists.

How many traces fit between two BGA balls is decided the moment you pick the pad diameter. Here is the arithmetic from pitch to channel width to trace count, and why NSMD and via-in-pad change the answer.

The ±20 ppm on the front page is only the initial tolerance. Temperature and aging are separate, and whether you sum them or root-sum-square them decides whether your product passes qualification or passes in the field.

A microstrip is half-buried in laminate and half in air, so the wave sees neither. Using the datasheet dielectric constant for a quarter-wave stub on FR-4 gets the length wrong by 13 percent — enough to move a filter edge hundreds of MHz.

A buried resistor is just sheet resistance times a count of squares. The design is trivial; the economics and the tolerance are not. Here is what determines whether burying resistors in the stack-up is worth it.

Coating your board can cut the required conductor spacing by more than four times. The IPC-2221B table has five conditions and picking the wrong row is the most common creepage mistake in PCB design.

A 100 µm microvia has a fifth the copper of a through-hole via and a fraction of its resistance. The IPC-2221 current formula gives two different answers depending on a constant nobody can definitively pick — and neither is what actually fails.

A spiral of copper costs nothing to add and gives you a few hundred nanohenries. The catch is self-resonance and series resistance — and the Q figure most calculators quote is only meaningful well below SRF.

Via capacitance sounds alarming until you subtract what a matched line would have had anyway. Only the excess is a discontinuity — and shrinking capacitance past the optimum makes reflection worse, not better.

A via is a thin-wall copper tube, not a solid plug, and its cross-section is smaller than most people assume. At 20 A through one via the drop is 26 mV and the dissipation is half a watt.

Real stack-ups rarely put a signal layer exactly halfway between two planes. What the offset does to impedance, which plane actually carries your return current, and why the common superposition formula reads high.

Stacking a differential pair on adjacent layers halves the routing width, which is why flex circuits use it everywhere. The impedance maths is clean. The failure mode is layer-to-layer registration.

CPW and grounded CPW put the return path right next to the signal. Here's when that beats microstrip, why the gap-to-height ratio decides whether you actually have CPW, and the copper-thickness effect most calculators miss.

Two routing layers between one plane pair saves copper and money. It also creates the tightest coupling geometry available on a PCB. Here's the number, and why routing direction is the only thing that saves you.

Onderdonk's equation was derived for round wire in 1928. Applying it to PCB traces requires knowing the actual cross-section — which isn't rectangular after etching. Here's the physics, the geometry correction, and why the answer is less conservative than you'd hope.

PCB design lives in two unit systems simultaneously. Copper weight is oz/ft squared, drill sizes are in mils, board dimensions are in millimetres, and IPC tables mix all three. Here's the conversion logic and the one constant worth memorising.

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. Mixing them up over-specifies your amplifier or under-models your channel.

Every trace is a transmission line at some frequency. The critical length threshold tells you whether your particular trace at your particular edge rate needs controlled impedance or not. The answer depends on two numbers and a judgment call.

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 heatsinking.

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 circuit reliability using strategic capacitor.

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. Walk through real examples with series/shunt elements, moving from load to source on the chart.

Smith Chart and VSWR both describe impedance mismatch — but they answer different questions. Learn when to use each, how they relate mathematically, and which view solves your problem faster.

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, worked examples with real MCUs, 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-budget automation: sweep frequency, rain availability, and elevation in pure Python using the ITU-Rpy reference implementation of P.618/P.676/P.840. Companion to the rftools Satellite Link Budget Analyzer.

Walkthrough of a free RF link budget calculator — enter Tx power, antenna gain, frequency, distance, and see EIRP, FSPL, received power, link margin, and max range. Three worked scenarios: LoRa, CubeSat, GEO broadcast.

Ansys STK sunset-ready: compute SGP4 pass predictions for your amateur-radio or cubesat ground station using Skyfield. Full Python walkthrough with TLE fetch, elevation masks, Doppler, and iCalendar export.

End-to-end link budget for an amateur-band 3U cubesat: EIRP, ground-station G/T, ITU-R propagation losses, and Monte Carlo availability. Uses the Amateur CubeSat preset.

Ansys is sunsetting STK Cloud in March 2026. Here are the free open-source replacements for the two things 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.

Learn how to design BLDC motor windings: calculate turns per coil from target Kv, select wire gauge for current density, understand slot/pole combinations, and choose between delta and 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). Compare BPSK, QPSK, and QAM modulation performance with Eb/N0 curves and worked examples.

Learn how to size a BLDC motor using Kv rating, torque constant Kt, and efficiency calculations. Includes worked examples for drone, robot, and vehicle motor selection.

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. Covers LC filter topology selection, cutoff frequency calculation, common-mode vs differential-mode filtering, and CISPR 32 limits.

Learn how to read and use a Smith Chart for impedance matching. Covers impedance circles, admittance overlays, matching network design, and worked examples with specific impedance values.

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 create precise current sources for analog.

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 techniques with PT100/PT1000 sensors, including calibration, resistance-to-temperature conversion, and critical engineering.

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. How Q, bandwidth, and gain interact in peaking, shelving, and notch filters, with worked examples.

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, 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, plane-pair cavity resonances, and using the genetic algorithm to select.

How to use the Radar Detection Simulator to compute Pd vs range for all five Swerling target models, add ITU-R P.838 rain attenuation, run Monte Carlo to.

A complete walkthrough of the RF Cascade Budget Analyzer: setting up a 5-stage LNA + mixer + IF chain, computing cascaded NF, gain, IIP3, and P1dB, then.

How to use the Satellite Link Budget Analyzer to compute a complete Ka-band downlink budget using ITU-R P.618 rain attenuation, P.676 gaseous absorption, and.

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: calculate required thermal resistance θ_SA from power dissipation and junction temperature, choose a heatsink rated below that value, then verify the full thermal path. Includes worked example and free calculator.

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 that.

A practical walkthrough of using the Radar Detection Monte Carlo simulator to evaluate a 10 GHz X-band weather radar — comparing Swerling models, quantifying.

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 practical walkthrough of using the Satellite Link Budget tool to design a Ku-band VSAT link — computing rain attenuation with ITU-R P.618, validating 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 Sizing.

How to choose decoupling capacitor values: self-resonant frequency (SRF) sets the effective bypass range — 100 nF works at ~5 MHz, 10 nF at ~50 MHz, 1 nF at ~500 MHz. ESR and ESL explained.

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.

A hardware startup's SBC fails FCC Part 15 Class B pre-compliance on the first scan. Follow the analysis in the EMI Radiated Emissions Estimator to identify.

A PCB designer routes a 10 Gbps SerDes lane across a 20 cm FR-4 trace with two connectors. Learn how to use S-parameter data and an eye diagram simulation to.

A step-by-step guide to running an FDTD simulation of a through-via transition in FR-4. Covers how to set up the simulation, interpret 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. Learn why L-networks fail on bandwidth, how Pi.

Designing a flyback transformer by hand means picking one core from hundreds and hoping your intuition about the efficiency-versus-size trade-off is close. The.

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

A 5th-order Chebyshev low-pass filter at 100 MHz looks perfect in simulation. But with 5% capacitors and inductors, Monte Carlo analysis reveals a yield.

A practical walkthrough of the S-parameter analysis pipeline: viewing raw VNA data, identifying connector response, applying time gating to isolate a PCB trace.

A step-by-step walkthrough of using the SMPS Control Loop Stability Analyzer to verify phase margin, gain margin, and crossover frequency for a 12V→5V buck.

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 work uses NEC2 simulation to verify gain, front-to-back ratio, and feedpoint.

A practical guide to designing audio amplifier stages: calculating power output, matching speaker impedance, managing noise floor, and choosing between 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. Covers RTDs, thermocouples, load cells, current shunts, and.

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 standards, explains temperature rise, and covers external vs internal.

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. Covers the Hammerstad-Jensen equations, material selection, manufacturing.