Electronics & Electrical Engineering

Minimum trace width for your current and temperature rise — IPC-2221 formula with copper weight, layer choice and a step-by-step worked example.

Z₀ of a surface microstrip from width, height and εr (IPC-2141A), plus effective dielectric constant and propagation delay.

Characteristic impedance of an embedded stripline trace from geometry and εr — the inner-layer companion to the microstrip tool.

How much current a plated via carries — annular copper cross-section through the IPC-2221 internal curve, plus via resistance.

DC resistance and voltage drop of a copper trace from length, width and copper weight — with temperature correction.

Edge-coupled microstrip and stripline Zdiff for USB, Ethernet and PCIe pairs — IPC-2141A coupled-line formulas with live coupling factor.

Temperature rise of a copper pour used as a heatsink — flat-plate convection model with the pour size needed for your power.

Current capacity of a thermal-relief pad from spoke count, width and copper weight — IPC-2221 with the equivalent trace width.

How much current an existing trace can carry at your allowed temperature rise — the inverse of the trace-width problem, per IPC-2221.

Self-inductance of a straight trace (Grover formula) with nH/mm and reactance at 100 MHz — why long decoupling traces ruin bypassing.

Worst-case annular ring from pad, hole and fab allowance — pass/fail against your minimum and the pad size needed to fix it.

Visual 4, 5 and 6-band resistor decoder with live colour preview, tolerance range and temperature coefficient — IEC 60062.

Decode 3-digit, 4-digit and EIA-96 SMD resistor markings to ohms — with the R-decimal style and tolerance handled.

Turn 3-digit ceramic capacitor codes like 104 into pF/nF/µF — with tolerance letters and voltage markings explained.

Output voltage, loading error and power of an R1/R2 divider — with E-series suggestions for your target ratio.

Total resistance of any list of resistors in series or parallel — understands 4.7k, 2k2 and 0R47 shorthand.

Series resistor for any LED — colour presets, LEDs in series, next-up E24 value, actual current and required wattage.

Nearest standard E12, E24 or E96 value to any target resistance, with neighbours and percentage error — IEC 60063.

Best series or parallel pair from your E12/E24 drawer to hit any target resistance — exhaustive search, exact arithmetic.

Decode EIA 3-digit, letter+digit (EIA-198) and R-decimal capacitor markings on chips and tantalums to real capacitance.

Wiper resistance vs rotation for linear, audio-log and reverse-log pots — plus the loaded-linear fake-log trick computed live.

Enter any two of voltage, current, resistance and power — get the other two with the substituted formula shown step by step.

Real, apparent and reactive power for DC, single-phase and three-phase systems with power factor — plus kWh per day.

Exact diameter, area, resistance and rule-of-thumb ampacity for any AWG gauge — from the ASTM B258 formula, not a lookup.

Round-trip voltage drop, percent loss and wasted watts for any cable run — copper or aluminium, AWG or metric.

Series/parallel cell counts for a target voltage and capacity — Li-ion, LiFePO₄, NiMH and lead-acid presets with voltage windows.

Runtime from capacity and load — constant or duty-cycled IoT profiles with sleep current, plus realistic derating.

PV wire size from Isc with the NEC 1.56× design factor AND a voltage-drop target — returns the AWG that satisfies both.

Watt-hours, voltage window and max current of any LiPo from S-count, mAh and C-rating — with airline 100/160 Wh limits checked.

Fuse rating from continuous load with headroom factor, snapped to standard sizes and checked against your wire's capacity.

Voltage, capacity, energy and internal resistance of any existing S×P battery arrangement — with sag at 1C computed.

Required stepper torque from axis force, screw lead and efficiency — sized with a safety factor and a NEMA class suggestion.

Pick the right NEMA frame (8–42) from your torque need — faceplate sizes, catalogue ranges and typical applications.

Ratio, output speed and output torque for one or two gear stages, with per-stage efficiency — teeth in, answers out.

Solve P = T·ω any direction with the 9550 rule — watts, newton-metres, RPM and horsepower, with the worked conversion.

Peak and RMS torque from your move profile — inertia, acceleration time and duty cycle, with the inertia-ratio check built in.

Driven RPM, ratio, belt speed and belt length from pulley diameters and centre distance — V-belt and timing-belt notes included.

Steps-per-mm, real resolution and top speed for any stepper + leadscrew combo — the firmware number plus why microstepping lies.

FLC from nameplate power for DC, single and three-phase motors — with efficiency, power factor and DOL starting current.

Reflected load inertia through a gear ratio, the motor:load ratio and the ideal gearing — rotary loads or leadscrew masses.

Shaft speed at any drive frequency from pole count and slip — with the constant-torque vs field-weakening region flagged.

Element lengths for half-wave dipoles, quarter-wave whips and 5/8-wave verticals at any frequency — with the 468/f cross-check.

Convert both ways with velocity factor for coax and PCB — plus λ/2, λ/4 and the λ/10 EMC rule of thumb computed live.

FSPL from distance and frequency, plus a full link budget — TX power, antenna gains, RX sensitivity and fade margin verdict.

Convert any reflection metric to all the others — SWR, return loss dB, |Γ|, reflected power percent and mismatch loss.

Attenuation of RG-58, RG-213, LMR-240/400/600 and more at any frequency and length — with the power actually reaching your antenna.

Series-L / shunt-C values to match any two resistances at your frequency — with network Q and bandwidth shown.

Starting dimensions for a 2–12 element Yagi — reflector, driven element, directors, spacing, boom length and gain estimate.

Power level conversions for RF work — dBm to watts to RMS/peak-to-peak volts at any system impedance.

First Fresnel-zone radius at the midpoint and at any obstacle along a link — with the 60 % clearance rule applied.

Rectangular patch W and L from frequency and substrate (Balanis transmission-line model) — FR-4 and Rogers presets included.

The heatsink thermal resistance you must buy — from power, Tj target, ambient and the junction-to-case chain.

Steady-state Tj through the θjc + θcs + θsa chain, case temperature, headroom and the max power your cooling allows.

Allowed power above the derating knee for resistors and semiconductors — with the 50 % conservative-design check.

θ of any thermal paste, pad or liquid-metal joint from thickness, conductivity and area — and what it costs you in °C.

Fan airflow needed for your heat load and allowed air rise — the 1.76·P/ΔT rule both directions, with back-pressure notes.

What actually heats up — linear regulators, diodes, MOSFETs and resistors, each with its own correct loss formula.

Thermal resistance of a via grid under a QFN/PowerPAD — per-via θ from geometry, divided across the array.

Self-consistent junction temperature with Rds(on) temperature feedback — converges to the real Tj or flags thermal runaway.

LED junction temperature from drive power and the star/heatsink chain — with lumen droop and lifetime band shown.

τ = Rθ·m·c and the full heating curve — how long your heatsink buys before things get hot, for intermittent loads.

Inverting and non-inverting gain from Rf and Rg, in ratio and dB — with noise gain and real-op-amp caveats.

Cutoff frequency from R and C plus the exact gain and phase at any frequency — first-order filters done right.

Solve f₀ = 1/2π√LC any direction, plus characteristic impedance, Q from loss resistance and bandwidth.

Component values for a 2nd-order Sallen-Key low-pass — Butterworth, Bessel or Chebyshev, from one chosen capacitor.

R1/R2/R3 for a multiple-feedback band-pass from f₀, Q and gain — the workhorse active band-pass, with the GBW check.

Rg for any gain (or gain from Rg) — INA128/AD620-style 49.4 kΩ equation and discrete 3-op-amp designs.

Required slew rate for a sine at any frequency and amplitude — or full-power bandwidth and max clean swing from your op-amp's SR.

RC time constant, unity-gain frequency, gain at any frequency and ramp rate — with the stability fixes every real circuit needs.

Closed-loop bandwidth from GBW and noise gain — and how splitting gain across stages multiplies usable bandwidth.

Schmitt-trigger thresholds and window from your reference and feedback resistors — kill comparator chatter by design.

Signed integers to binary/hex at 4–32 bits with the invert-and-add-one steps shown — plus range and sign-extension notes.

Click cells (0/1/X) on a Gray-coded K-map and get the exact minimal sum-of-products — Quine–McCluskey under the hood.

Type any expression in A–D and get the exact minimal SOP — supports ', !, ·, +, ^ and parentheses.

Full truth table for any boolean expression with minterm Σm and maxterm ΠM lists — ready for your K-map.

Register-style bitwise math with aligned binary view — accepts decimal, 0x hex and 0b input; logical vs arithmetic shifts.

Number ↔ float32 bit pattern with sign/exponent/mantissa split — see exactly why 0.1 + 0.2 ≠ 0.3.

Encode 4 data bits or decode-and-correct a 7-bit codeword — the syndrome literally points at the flipped bit.

Decimal to BCD groups and live 7-segment patterns — common-cathode/anode bytes for every digit, with the RTC 0x12 trap explained.

Clock a bit stream into a SIPO register and watch every state — with load time at your shift clock and daisy-chain notes.

f(max) and setup slack from tco, logic, routing and setup time — the timing-closure equation every FPGA report prints.

Minimum sampling rate for your bandwidth and where any tone aliases — with the anti-alias filter margin verdict.

Decibels to voltage or power ratios and back — with the 10-vs-20 log distinction made explicit and memorable anchors.

LSB size, code count, ideal SNR and the exact code for any input — 8 to 24 bits at your reference voltage.

UART real throughput with framing overhead, or M-ary modulation bit rates — why 115200 baud moves only 11.5 kB/s.

Signal-to-noise ratio from measured voltages or powers, the linear ratio, ENOB equivalent and a quality verdict.

Bin width, capture time and which bin any frequency lands in — with the leakage warning when you're off bin-centre.

The theoretical bit-rate ceiling from bandwidth and SNR, beside the Nyquist M-level limit — with spectral efficiency.

Bits per symbol and raw bit rate for BPSK through 1024-QAM at your symbol rate — with approximate Eb/N0 requirements.

q/√12 noise, SQNR and the effective bits gained by oversampling — with the dither caveat the formula hides.

How long a file takes over UART, I²C, SPI, BLE, WiFi or Ethernet — with realistic protocol efficiencies, not marketing rates.

Filterable ESP32 GPIO table with every trap flagged — strapping pins, ADC2-vs-WiFi, input-only pins and safe-pin list.

Filterable Uno pin table — PWM timers, SPI/I²C roles, interrupts and the current limits that silently kill projects.

AVR UBRR value, actual baud and error percent — including the infamous 16 MHz / 115200 case and the U2X fix.

PWM frequency, resolution bits and compare value from clock, prescaler and TOP — AVR, STM32 and ESP32 LEDC alike.

Best prescaler + compare value for any target period — searches the AVR set or powers of 2, with exact error shown.

Counts to volts and back at any resolution and reference — including input voltage dividers, both directions.

Per-pin and whole-chip drive limits for AVR, ESP32, STM32, RP2040 and ESP8266 — with a direct-drive LED check.

When any tick counter wraps and whether your interval survives it — with the unsigned-subtraction idiom explained.

How long your EEPROM, flash or FRAM lasts at your write rate — with wear-leveling factored and fixes ranked.

Integer divider for any target frequency from your clock tree — achieved frequency, error and the reachable neighbours.

Copper needed for 3 A / 5 A USB-C VBUS — IPC-2221 with PD-aware presets, routing tips and an FAQ for Type-C power design.

Why bed-power traces burn and how wide 15 A really needs — IPC-2221 presets plus the solder-bus-bar and 24 V fixes.

Size the ESP32 supply rail for WiFi TX bursts — trace width, decoupling and the brownout-reset checklist in one place.

Phase-trace copper for 5 A drivers sized for stall, not cruise — with Kelvin-sense and loop-area layout rules.

20 A PV paths on a PCB — IPC-2221 with the NEC 1.56× design current and hot-enclosure derating built into the presets.

How 30 A controllers really route current — bare-copper math plus the solder-channel and bus-wire reinforcement tricks.

25 A-per-ESC copper on a 40 mm board — burst-duty sizing, battery-pad reinforcement and the input-capacitor rule.

Trace sizing for PoE powered devices — per-class currents, 4-pair splitting and the isolation rules that matter more than width.

8 A of 12 V strip current through your controller — common-rail sizing, per-channel math and power-injection guidance.

Why internal traces need double the copper — IPC-2221 internal-k presets, 0.5 oz inner foil reality and via-stitch budgets.

Trace sizing at 85–105 °C ambient — 10 °C rise discipline, fuse hold-current reality and load-dump path notes.

The B−→FET→P− channel sized for pack current in still air — with balance-lead, Kelvin-shunt and FET-pour rules.

Wire gauge math for car, camper and van 12 V circuits — why 0.36 V is already your whole 3 % budget and which AWG keeps the fridge running.

PV-string wire sizing with the 1.56 × Isc design current and why every volt lost before the MPPT is energy you never get back.

Long runs, 7-way plugs and electric brakes — why trailer lights dim and brake controllers misbehave, with the gauge that fixes both.

ABYC-style wire sizing for bow-mounted trolling motors — 50 A draws, battery-to-bow runs and the 3 % rule that protects your runtime.

Why the far end of the strip goes orange — feed-wire sizing plus the power-injection math for 5 V, 12 V and 24 V strips.

100 A+ cable runs from battery to inverter — gauge, length limits and why the low-voltage alarm screams during the microwave's first second.

Battery-to-controller wire sizing for 36–72 V e-bikes — why connectors dominate short runs and sag costs you hill-climb watts.

Garden lighting runs, the multi-tap transformer trick and hub vs daisy-chain wiring — why the last fixture is always the dim one.

Series resistor for LEDs on 12 V — sized for the 14.4 V reality of a running engine, with the 3-in-series efficiency trick.

Why every Arduino tutorial says 220 Ω — pin current limits, the 40 mA myth and safe multi-LED fan-out from 5 V logic.

LED resistors for 3.3 V logic — the 12 mA GPIO reality, why blue LEDs barely light, and when to switch to a transistor.

The classic first circuit, done right — resistor value, honest battery-life math and the 3-in-series trick that triples runtime.

Infrared emitter resistors — low 1.4 V forward drop, pulsed-vs-continuous ratings and why your remote drives its LED at 10× 'maximum'.

Resistor ballast for 1 W and 3 W LEDs — honest wattage math, thermal-runaway warnings and where the constant-current driver wins.

Quarter-wave and dipole lengths for the 27 MHz CB band — why the classic whip is 102 inches, which channel to tune for, and how to read SWR like a tech.

The 17 cm wire that transforms cheap 433 MHz modules — exact quarter-wave and dipole lengths for ISM-band remotes, LoRa 433 and RC links.

Quarter-wave wire lengths for every LoRa region — 7.8 cm at 915 MHz, 8.2 cm at 868, 8.3 cm for India's 865 — and why a wrong-band antenna wrecks the link budget.

Why a 2.4 GHz quarter wave is just 29 mm — wire lengths for WiFi, BLE and ESP32 antenna mods, and where DIY stops making sense.

Cut a wire dipole for your favourite FM station — ~1.45 m total at 98 MHz, the classic 75 Ω T-dipole, and why height and orientation beat length tweaks.

How big a heatsink does a TO-220 need? The ~1.5 W bare-package ceiling, θ(sa) sizing math, insulator-pad tax and full-pack gotchas — solved live.

Linear-regulator heat math: P = (Vin−Vout)·I — find out whether your 7805 needs a heatsink, what size, and when a buck module should replace it.

NE555 astable oscillator solved live — f = 1.44/((R1+2R2)·C), high/low times, duty cycle, and why duty can't go below 50 % without a diode.

Design the classic blinking-LED circuit — R1/R2/C values for any flash rate from the 1 Hz preset, pin-3 drive limits and battery-life honesty included.

One-shot timer math — t = 1.1·R·C — pulse widths from microseconds to minutes, trigger rules, the retrigger gotcha and honest accuracy limits.